Daily Papers

Reward models have been increasingly critical for improving the reasoning capability of LLMs. Existing research has shown that a well-trained reward model can substantially improve model performances at inference time via search. However, the potential of reward models during RL training time still remains largely under-explored. It is currently unclear whether these reward models can provide additional training signals to enhance the reasoning capabilities of LLMs in RL training that uses sparse success rewards, which verify the correctness of solutions. In this work, we evaluate popular reward models for RL training, including the Outcome-supervised Reward Model (ORM) and the Process-supervised Reward Model (PRM), and train a collection of LLMs for math problems using RL by combining these learned rewards with success rewards. Surprisingly, even though these learned reward models have strong inference-time performances, they may NOT help or even hurt RL training, producing worse performances than LLMs trained with the success reward only. Our analysis reveals that an LLM can receive high rewards from some of these reward models by repeating correct but unnecessary reasoning steps, leading to a severe reward hacking issue. Therefore, we introduce two novel reward refinement techniques, including Clipping and Delta. The key idea is to ensure the accumulative reward of any reasoning trajectory is upper-bounded to keep a learned reward model effective without being exploited. We evaluate our techniques with multiple reward models over a set of 1.5B and 7B LLMs on MATH and GSM8K benchmarks and demonstrate that with a carefully designed reward function, RL training without any additional supervised tuning can improve all the evaluated LLMs, including the state-of-the-art 7B LLM Qwen2.5-Math-7B-Instruct on MATH and GSM8K benchmarks.

Solving complex mathematical problems via system-2 reasoning is a natural human skill, yet it remains a significant challenge for current large language models (LLMs). We identify the scarcity of deliberate multi-step reasoning data as a primary limiting factor. To this end, we introduce Enriched Instruction Tuning (EIT), a method that enriches existing human-annotated mathematical datasets by synergizing human and AI feedback to create fine-grained reasoning trajectories. These datasets are then used to fine-tune open-source LLMs, enhancing their mathematical reasoning abilities without reliance on any symbolic verification program. Concretely, EIT is composed of two critical steps: Enriching with Reasoning Plan (ERP) and Enriching with Reasoning Step (ERS). The former generates a high-level plan that breaks down complex instructions into a sequence of simpler objectives, while ERS fills in reasoning contexts often overlooked by human annotators, creating a smoother reasoning trajectory for LLM fine-tuning. Unlike existing CoT prompting methods that generate reasoning chains only depending on LLM's internal knowledge, our method leverages human-annotated initial answers as ``meta-knowledge'' to help LLMs generate more detailed and precise reasoning processes, leading to a more trustworthy LLM expert for complex mathematical problems. In experiments, EIT achieves an accuracy of 84.1% on GSM8K and 32.5% on MATH, surpassing state-of-the-art fine-tuning and prompting methods, and even matching the performance of tool-augmented methods.

The breakthrough of OpenAI o1 highlights the potential of enhancing reasoning to improve LLM. Yet, most research in reasoning has focused on mathematical tasks, leaving domains like medicine underexplored. The medical domain, though distinct from mathematics, also demands robust reasoning to provide reliable answers, given the high standards of healthcare. However, verifying medical reasoning is challenging, unlike those in mathematics. To address this, we propose verifiable medical problems with a medical verifier to check the correctness of model outputs. This verifiable nature enables advancements in medical reasoning through a two-stage approach: (1) using the verifier to guide the search for a complex reasoning trajectory for fine-tuning LLMs, (2) applying reinforcement learning (RL) with verifier-based rewards to enhance complex reasoning further. Finally, we introduce HuatuoGPT-o1, a medical LLM capable of complex reasoning, which outperforms general and medical-specific baselines using only 40K verifiable problems. Experiments show complex reasoning improves medical problem-solving and benefits more from RL. We hope our approach inspires advancements in reasoning across medical and other specialized domains.

Enhancing the capability of large language models (LLMs) in reasoning has gained significant attention in recent years. Previous studies have demonstrated the effectiveness of various prompting strategies in aiding LLMs in reasoning (called "reasoning actions"), such as step-by-step thinking, reflecting before answering, solving with programs, and their combinations. However, these approaches often applied static, predefined reasoning actions uniformly to all questions, without considering the specific characteristics of each question or the capability of the task-solving LLM. In this paper, we propose DOTS, an approach enabling LLMs to reason dynamically via optimal reasoning trajectory search, tailored to the specific characteristics of each question and the inherent capability of the task-solving LLM. Our approach involves three key steps: i) defining atomic reasoning action modules that can be composed into various reasoning action trajectories; ii) searching for the optimal action trajectory for each training question through iterative exploration and evaluation for the specific task-solving LLM; and iii) using the collected optimal trajectories to train an LLM to plan for the reasoning trajectories of unseen questions. In particular, we propose two learning paradigms, i.e., fine-tuning an external LLM as a planner to guide the task-solving LLM, or directly fine-tuning the task-solving LLM with an internalized capability for reasoning actions planning. Our experiments across eight reasoning tasks show that our method consistently outperforms static reasoning techniques and the vanilla instruction tuning approach. Further analysis reveals that our method enables LLMs to adjust their computation based on problem complexity, allocating deeper thinking and reasoning to harder problems.

The LLM-as-a-Judge paradigm shows promise for evaluating generative content but lacks reliability in reasoning-intensive scenarios, such as programming. Inspired by recent advances in reasoning models and shifts in scaling laws, we pioneer bringing test-time computation into LLM-as-a-Judge, proposing MCTS-Judge, a resource-efficient, System-2 thinking framework for code correctness evaluation. MCTS-Judge leverages Monte Carlo Tree Search (MCTS) to decompose problems into simpler, multi-perspective evaluations. Through a node-selection strategy that combines self-assessment based on historical actions in the current trajectory and the Upper Confidence Bound for Trees based on prior rollouts, MCTS-Judge balances global optimization and refinement of the current trajectory. We further designed a high-precision, unit-test-level reward mechanism to encourage the Large Language Model (LLM) to perform line-by-line analysis. Extensive experiments on three benchmarks and five LLMs demonstrate the effectiveness of MCTS-Judge, which improves the base model's accuracy from 41% to 80%, surpassing the o1-series models with 3x fewer tokens. Further evaluations validate the superiority of its reasoning trajectory in logic, analytics, thoroughness, and overall quality, while revealing the test-time scaling law of the LLM-as-a-Judge paradigm.

Different from its counterpart outcome reward models (ORMs), which evaluate the entire responses, a process reward model (PRM) scores a reasoning trajectory step by step, providing denser and more fine grained rewards. However, training a PRM requires labels annotated at every intermediate step, presenting significant challenges for both manual and automatic data collection. This paper aims to address this challenge. Both theoretically and empirically, we show that an implicit PRM can be obtained at no additional cost, by simply training an ORM on the cheaper response-level labels. The only assumption is to parameterize the outcome reward as the log-likelihood ratios of the policy and reference models, which can be optimized regardless of the specific choice of loss objectives. In experiments, we instantiate our implicit PRMs with various objectives and evaluate their performance on MATH. We show that our implicit PRM outperforms a strong MCTS-based baseline \'a la Math-Shepherd using less than 1/38 of the training data. Its performance can be further improved with majority voting. We further find that scaling up instructions and responses benefits our implicit PRM, and the latter brings a larger gain. Particularly, we find that our implicit PRM, when instantiated with the cross-entropy (CE) loss, is more data-efficient and can keep improving generation models even when trained with only one response per instruction, the setup that suffers from extreme data scarcity and imbalance. Further, instructions should be relevant to downstream tasks while the diversity of responses does not bring gains. Surprisingly, training on extra Math-Shepherd step labels brings no further improvements to our implicit PRM trained on only outcome data. We hope that our work will encourage a rethinking of PRM training approaches and contribute to making training PRMs more accessible.

Enabling effective collaboration among LLMs is a crucial step toward developing autonomous systems capable of solving complex problems. While LLMs are typically used as single-model generators, where humans critique and refine their outputs, the potential for jointly-trained collaborative models remains largely unexplored. Despite promising results in multi-agent communication and debate settings, little progress has been made in training models to work together on tasks. In this paper, we present a first step toward "Multi-agent LLM training" (MALT) on reasoning problems. Our approach employs a sequential multi-agent setup with heterogeneous LLMs assigned specialized roles: a generator, verifier, and refinement model iteratively solving problems. We propose a trajectory-expansion-based synthetic data generation process and a credit assignment strategy driven by joint outcome based rewards. This enables our post-training setup to utilize both positive and negative trajectories to autonomously improve each model's specialized capabilities as part of a joint sequential system. We evaluate our approach across MATH, GSM8k, and CQA, where MALT on Llama 3.1 8B models achieves relative improvements of 14.14%, 7.12%, and 9.40% respectively over the same baseline model. This demonstrates an early advance in multi-agent cooperative capabilities for performance on mathematical and common sense reasoning questions. More generally, our work provides a concrete direction for research around multi-agent LLM training approaches.

We present that hierarchical LLM reasoning via scaling thought templates can effectively optimize the reasoning search space and outperform the mathematical reasoning capabilities of powerful LLMs like OpenAI o1-preview and DeepSeek V3. We train our ReasonFlux-32B model with only 8 GPUs and introduces three innovations: (i) a structured and generic thought template library, containing around 500 high-level thought templates capable of generalizing to similar or relevant reasoning problems; (ii) performing hierarchical reinforcement learning on a sequence of thought templates instead of long CoTs, optimizing a base LLM to plan out an optimal template trajectory for gradually handling complex problems; (iii) a brand new inference scaling system that enables hierarchical LLM reasoning by adaptively scaling thought templates at inference time. With a template trajectory containing sequential thought templates, our ReasonFlux-32B significantly advances math reasoning capabilities to state-of-the-art levels. Notably, on the MATH benchmark, it achieves an accuracy of 91.2% and surpasses o1-preview by 6.7%. On the USA Math Olympiad (AIME) benchmark, ReasonFlux-32B solves an average of 56.7% of problems, surpassing o1-preview and DeepSeek-V3 by 27% and 45%, respectively. Code: https://github.com/Gen-Verse/ReasonFlux

Learning visual features from unlabeled images has proven successful for semantic categorization, often by mapping different views of the same object to the same feature to achieve recognition invariance. However, visual recognition involves not only identifying what an object is but also understanding how it is presented. For example, seeing a car from the side versus head-on is crucial for deciding whether to stay put or jump out of the way. While unsupervised feature learning for downstream viewpoint reasoning is important, it remains under-explored, partly due to the lack of a standardized evaluation method and benchmarks. We introduce a new dataset of adjacent image triplets obtained from a viewpoint trajectory, without any semantic or pose labels. We benchmark both semantic classification and pose estimation accuracies on the same visual feature. Additionally, we propose a viewpoint trajectory regularization loss for learning features from unlabeled image triplets. Our experiments demonstrate that this approach helps develop a visual representation that encodes object identity and organizes objects by their poses, retaining semantic classification accuracy while achieving emergent global pose awareness and better generalization to novel objects. Our dataset and code are available at http://pwang.pw/trajSSL/.

Post-training Large Language Models (LLMs) with explicit reasoning trajectories can enhance their reasoning abilities. However, acquiring such high-quality trajectory data typically demands meticulous supervision from humans or superior models, which can be either expensive or license-constrained. In this paper, we explore how far an LLM can improve its reasoning by self-synthesizing reasoning paths as training data without any additional supervision. Existing self-synthesizing methods, such as STaR, suffer from poor generalization to out-of-domain (OOD) reasoning tasks. We hypothesize it is due to that their self-synthesized reasoning paths are too task-specific, lacking general task-agnostic reasoning guidance. To address this, we propose Reasoning Generalist via Self-Improvement (ReGenesis), a method to self-synthesize reasoning paths as post-training data by progressing from abstract to concrete. More specifically, ReGenesis self-synthesizes reasoning paths by converting general reasoning guidelines into task-specific ones, generating reasoning structures, and subsequently transforming these structures into reasoning paths, without the need for human-designed task-specific examples used in existing methods. We show that ReGenesis achieves superior performance on all in-domain and OOD settings tested compared to existing methods. For six OOD tasks specifically, while previous methods exhibited an average performance decrease of approximately 4.6% after post training, ReGenesis delivers around 6.1% performance improvement. We also conduct in-depth analysis of our framework and show ReGenesis is effective across various LLMs and design choices.

Offline reinforcement learning (RL) holds promise as a means to learn high-reward policies from a static dataset, without the need for further environment interactions. However, a key challenge in offline RL lies in effectively stitching portions of suboptimal trajectories from the static dataset while avoiding extrapolation errors arising due to a lack of support in the dataset. Existing approaches use conservative methods that are tricky to tune and struggle with multi-modal data (as we show) or rely on noisy Monte Carlo return-to-go samples for reward conditioning. In this work, we propose a novel approach that leverages the expressiveness of latent diffusion to model in-support trajectory sequences as compressed latent skills. This facilitates learning a Q-function while avoiding extrapolation error via batch-constraining. The latent space is also expressive and gracefully copes with multi-modal data. We show that the learned temporally-abstract latent space encodes richer task-specific information for offline RL tasks as compared to raw state-actions. This improves credit assignment and facilitates faster reward propagation during Q-learning. Our method demonstrates state-of-the-art performance on the D4RL benchmarks, particularly excelling in long-horizon, sparse-reward tasks.

This paper introduces rStar, a self-play mutual reasoning approach that significantly improves reasoning capabilities of small language models (SLMs) without fine-tuning or superior models. rStar decouples reasoning into a self-play mutual generation-discrimination process. First, a target SLM augments the Monte Carlo Tree Search (MCTS) with a rich set of human-like reasoning actions to construct higher quality reasoning trajectories. Next, another SLM, with capabilities similar to the target SLM, acts as a discriminator to verify each trajectory generated by the target SLM. The mutually agreed reasoning trajectories are considered mutual consistent, thus are more likely to be correct. Extensive experiments across five SLMs demonstrate rStar can effectively solve diverse reasoning problems, including GSM8K, GSM-Hard, MATH, SVAMP, and StrategyQA. Remarkably, rStar boosts GSM8K accuracy from 12.51% to 63.91% for LLaMA2-7B, from 36.46% to 81.88% for Mistral-7B, from 74.53% to 91.13% for LLaMA3-8B-Instruct. Code will be available at https://github.com/zhentingqi/rStar.

Recent work on neural algorithmic reasoning has investigated the reasoning capabilities of neural networks, effectively demonstrating they can learn to execute classical algorithms on unseen data coming from the train distribution. However, the performance of existing neural reasoners significantly degrades on out-of-distribution (OOD) test data, where inputs have larger sizes. In this work, we make an important observation: there are many different inputs for which an algorithm will perform certain intermediate computations identically. This insight allows us to develop data augmentation procedures that, given an algorithm's intermediate trajectory, produce inputs for which the target algorithm would have exactly the same next trajectory step. Then, we employ a causal framework to design a corresponding self-supervised objective, and we prove that it improves the OOD generalisation capabilities of the reasoner. We evaluate our method on the CLRS algorithmic reasoning benchmark, where we show up to 3times improvements on the OOD test data.

Traditional agentic workflows rely on external prompts to manage interactions with tools and the environment, which limits the autonomy of reasoning models. We position Large Agent Models (LAMs) that internalize the generation of Chain-of-Action (CoA), enabling the model to autonomously decide when and how to use external tools. Our proposed AutoCoA framework combines supervised fine-tuning (SFT) and reinforcement learning (RL), allowing the model to seamlessly switch between reasoning and action while efficiently managing environment interactions. Main components include step-level action triggering, trajectory-level CoA optimization, and an internal world model to reduce real-environment interaction costs. Evaluations on open-domain QA tasks demonstrate that AutoCoA-trained agent models significantly outperform ReAct-based workflows in task completion, especially in tasks that require long-term reasoning and multi-step actions. Code and dataset are available at https://github.com/ADaM-BJTU/AutoCoA

In this work, we introduce a novel evaluation paradigm for Large Language Models, one that challenges them to engage in meta-reasoning. This approach addresses critical shortcomings in existing math problem-solving benchmarks, traditionally used to evaluate the cognitive capabilities of agents. Our paradigm shifts the focus from result-oriented assessments, which often overlook the reasoning process, to a more holistic evaluation that effectively differentiates the cognitive capabilities among models. For example, in our benchmark, GPT-4 demonstrates a performance ten times more accurate than GPT3-5. The significance of this new paradigm lies in its ability to reveal potential cognitive deficiencies in LLMs that current benchmarks, such as GSM8K, fail to uncover due to their saturation and lack of effective differentiation among varying reasoning abilities. Our comprehensive analysis includes several state-of-the-art math models from both open-source and closed-source communities, uncovering fundamental deficiencies in their training and evaluation approaches. This paper not only advocates for a paradigm shift in the assessment of LLMs but also contributes to the ongoing discourse on the trajectory towards Artificial General Intelligence (AGI). By promoting the adoption of meta-reasoning evaluation methods similar to ours, we aim to facilitate a more accurate assessment of the true cognitive abilities of LLMs.

Trained with an unprecedented scale of data, large language models (LLMs) like ChatGPT and GPT-4 exhibit the emergence of significant reasoning abilities from model scaling. Such a trend underscored the potential of training LLMs with unlimited language data, advancing the development of a universal embodied agent. In this work, we introduce the NavGPT, a purely LLM-based instruction-following navigation agent, to reveal the reasoning capability of GPT models in complex embodied scenes by performing zero-shot sequential action prediction for vision-and-language navigation (VLN). At each step, NavGPT takes the textual descriptions of visual observations, navigation history, and future explorable directions as inputs to reason the agent's current status, and makes the decision to approach the target. Through comprehensive experiments, we demonstrate NavGPT can explicitly perform high-level planning for navigation, including decomposing instruction into sub-goal, integrating commonsense knowledge relevant to navigation task resolution, identifying landmarks from observed scenes, tracking navigation progress, and adapting to exceptions with plan adjustment. Furthermore, we show that LLMs is capable of generating high-quality navigational instructions from observations and actions along a path, as well as drawing accurate top-down metric trajectory given the agent's navigation history. Despite the performance of using NavGPT to zero-shot R2R tasks still falling short of trained models, we suggest adapting multi-modality inputs for LLMs to use as visual navigation agents and applying the explicit reasoning of LLMs to benefit learning-based models.

Large language models (LLMs) have demonstrated strong reasoning capabilities. Nevertheless, they still suffer from factual errors when tackling knowledge-intensive tasks. Retrieval-augmented reasoning represents a promising approach. However, significant challenges still persist, including inaccurate and insufficient retrieval for complex questions, as well as difficulty in integrating multi-source knowledge. To address this, we propose Beam Aggregation Reasoning, BeamAggR, a reasoning framework for knowledge-intensive multi-hop QA. BeamAggR explores and prioritizes promising answers at each hop of question. Concretely, we parse the complex questions into trees, which include atom and composite questions, followed by bottom-up reasoning. For atomic questions, the LLM conducts reasoning on multi-source knowledge to get answer candidates. For composite questions, the LLM combines beam candidates, explores multiple reasoning paths through probabilistic aggregation, and prioritizes the most promising trajectory. Extensive experiments on four open-domain multi-hop reasoning datasets show that our method significantly outperforms SOTA methods by 8.5%. Furthermore, our analysis reveals that BeamAggR elicits better knowledge collaboration and answer aggregation.

Chain-of-thought (CoT) reasoning has been widely applied in the mathematical reasoning of Large Language Models (LLMs). Recently, the introduction of derivative process supervision on CoT trajectories has sparked discussions on enhancing scaling capabilities during test time, thereby boosting the potential of these models. However, in multimodal mathematical reasoning, the scarcity of high-quality CoT training data has hindered existing models from achieving high-precision CoT reasoning and has limited the realization of reasoning potential during test time. In this work, we propose a three-module synthesis strategy that integrates CoT distillation, trajectory-format rewriting, and format unification. It results in a high-quality CoT reasoning instruction fine-tuning dataset in multimodal mathematics, MMathCoT-1M. We comprehensively validate the state-of-the-art (SOTA) performance of the trained URSA-7B model on multiple multimodal mathematical benchmarks. For test-time scaling, we introduce a data synthesis strategy that automatically generates process annotation datasets, known as DualMath-1.1M, focusing on both interpretation and logic. By further training URSA-7B on DualMath-1.1M, we transition from CoT reasoning capabilities to robust supervision abilities. The trained URSA-RM-7B acts as a verifier, effectively enhancing the performance of URSA-7B at test time. URSA-RM-7B also demonstrates excellent out-of-distribution (OOD) verifying capabilities, showcasing its generalization. Model weights, training data and code will be open-sourced.

Traditional reinforcement learning-based robotic control methods are often task-specific and fail to generalize across diverse environments or unseen objects and instructions. Visual Language Models (VLMs) demonstrate strong scene understanding and planning capabilities but lack the ability to generate actionable policies tailored to specific robotic embodiments. To address this, Visual-Language-Action (VLA) models have emerged, yet they face challenges in long-horizon spatial reasoning and grounded task planning. In this work, we propose the Embodied Multimodal Action Model with Grounded Chain of Thought and Look-ahead Spatial Reasoning, Emma-X. Emma-X leverages our constructed hierarchical embodiment dataset based on BridgeV2, containing 60,000 robot manipulation trajectories auto-annotated with grounded task reasoning and spatial guidance. Additionally, we introduce a trajectory segmentation strategy based on gripper states and motion trajectories, which can help mitigate hallucination in grounding subtask reasoning generation. Experimental results demonstrate that Emma-X achieves superior performance over competitive baselines, particularly in real-world robotic tasks requiring spatial reasoning.

The Retrieval-Augmented Language Model (RALM) has shown remarkable performance on knowledge-intensive tasks by incorporating external knowledge during inference, which mitigates the factual hallucinations inherited in large language models (LLMs). Despite these advancements, challenges persist in the implementation of RALMs, particularly concerning their reliability and traceability. To be specific, the irrelevant document retrieval may result in unhelpful response generation or even deteriorate the performance of LLMs, while the lack of proper citations in generated outputs complicates efforts to verify the trustworthiness of the models. To this end, we propose a novel self-reasoning framework aimed at improving the reliability and traceability of RALMs, whose core idea is to leverage reasoning trajectories generated by the LLM itself. The framework involves constructing self-reason trajectories with three processes: a relevance-aware process, an evidence-aware selective process, and a trajectory analysis process. We have evaluated our framework across four public datasets (two short-form QA datasets, one long-form QA dataset, and one fact verification dataset) to demonstrate the superiority of our method, which can outperform existing state-of-art models and can achieve comparable performance with GPT-4, while only using 2,000 training samples.

Building a conversational embodied agent to execute real-life tasks has been a long-standing yet quite challenging research goal, as it requires effective human-agent communication, multi-modal understanding, long-range sequential decision making, etc. Traditional symbolic methods have scaling and generalization issues, while end-to-end deep learning models suffer from data scarcity and high task complexity, and are often hard to explain. To benefit from both worlds, we propose JARVIS, a neuro-symbolic commonsense reasoning framework for modular, generalizable, and interpretable conversational embodied agents. First, it acquires symbolic representations by prompting large language models (LLMs) for language understanding and sub-goal planning, and by constructing semantic maps from visual observations. Then the symbolic module reasons for sub-goal planning and action generation based on task- and action-level common sense. Extensive experiments on the TEACh dataset validate the efficacy and efficiency of our JARVIS framework, which achieves state-of-the-art (SOTA) results on all three dialog-based embodied tasks, including Execution from Dialog History (EDH), Trajectory from Dialog (TfD), and Two-Agent Task Completion (TATC) (e.g., our method boosts the unseen Success Rate on EDH from 6.1\% to 15.8\%). Moreover, we systematically analyze the essential factors that affect the task performance and also demonstrate the superiority of our method in few-shot settings. Our JARVIS model ranks first in the Alexa Prize SimBot Public Benchmark Challenge.

Learning to predict agent motions with relationship reasoning is important for many applications. In motion prediction tasks, maintaining motion equivariance under Euclidean geometric transformations and invariance of agent interaction is a critical and fundamental principle. However, such equivariance and invariance properties are overlooked by most existing methods. To fill this gap, we propose EqMotion, an efficient equivariant motion prediction model with invariant interaction reasoning. To achieve motion equivariance, we propose an equivariant geometric feature learning module to learn a Euclidean transformable feature through dedicated designs of equivariant operations. To reason agent's interactions, we propose an invariant interaction reasoning module to achieve a more stable interaction modeling. To further promote more comprehensive motion features, we propose an invariant pattern feature learning module to learn an invariant pattern feature, which cooperates with the equivariant geometric feature to enhance network expressiveness. We conduct experiments for the proposed model on four distinct scenarios: particle dynamics, molecule dynamics, human skeleton motion prediction and pedestrian trajectory prediction. Experimental results show that our method is not only generally applicable, but also achieves state-of-the-art prediction performances on all the four tasks, improving by 24.0/30.1/8.6/9.2%. Code is available at https://github.com/MediaBrain-SJTU/EqMotion.

Robotic manipulation is often challenging due to the long-horizon tasks and the complex object relationships. A common solution is to develop a task and motion planning framework that integrates planning for high-level task and low-level motion. Recently, inspired by the powerful reasoning ability of Large Language Models (LLMs), LLM-based planning approaches have achieved remarkable progress. However, these methods still heavily rely on expert-specific knowledge, often generating invalid plans for unseen and unfamiliar tasks. To address this issue, we propose an innovative language-guided symbolic task planning (LM-SymOpt) framework with optimization. It is the first expert-free planning framework since we combine the world knowledge from LLMs with formal reasoning, resulting in improved generalization capability to new tasks. Specifically, differ to most existing work, our LM-SymOpt employs LLMs to translate natural language instructions into symbolic representations, thereby representing actions as high-level symbols and reducing the search space for planning. Next, after evaluating the action probability of completing the task using LLMs, a weighted random sampling method is introduced to generate candidate plans. Their feasibility is assessed through symbolic reasoning and their cost efficiency is then evaluated using trajectory optimization for selecting the optimal planning. Our experimental results show that LM-SymOpt outperforms existing LLM-based planning approaches.

Large Language Models (LLMs) have shown superior capability to solve reasoning problems with programs. While being a promising direction, most of such frameworks are trained and evaluated in settings with a prior knowledge of task requirements. However, as LLMs become more capable, it is necessary to assess their reasoning abilities in more realistic scenarios where many real-world problems are open-ended with ambiguous scope, and often require multiple formalisms to solve. To investigate this, we introduce the task of reasoning in the wild, where an LLM is tasked to solve a reasoning problem of unknown type by identifying the subproblems and their corresponding formalisms, and writing a program to solve each subproblem, guided by a tactic. We create a large tactic-guided trajectory dataset containing detailed solutions to a diverse set of reasoning problems, ranging from well-defined single-form reasoning (e.g., math, logic), to ambiguous and hybrid ones (e.g., commonsense, combined math and logic). This allows us to test various aspects of LLMs reasoning at the fine-grained level such as the selection and execution of tactics, and the tendency to take undesired shortcuts. In experiments, we highlight that existing LLMs fail significantly on problems with ambiguous and mixed scope, revealing critical limitations and overfitting issues (e.g. accuracy on GSM8K drops by at least 50\%). We further show the potential of finetuning a local LLM on the tactic-guided trajectories in achieving better performance. Project repo is available at github.com/gblackout/Reason-in-the-Wild

Large language models (LLMs) demonstrate impressive reasoning abilities, but translating reasoning into actions in the real world remains challenging. In particular, it remains unclear how to complete a given task provably within a minimum number of interactions with the external environment, e.g., through an internal mechanism of reasoning. To this end, we propose a principled framework with provable regret guarantees to orchestrate reasoning and acting, which we call "reason for future, act for now" (RAFA). Specifically, we design a prompt template for reasoning that learns from the memory buffer and plans a future trajectory over a long horizon ("reason for future"). At each step, the LLM agent takes the initial action of the planned trajectory ("act for now"), stores the collected feedback in the memory buffer, and reinvokes the reasoning routine to replan the future trajectory from the new state. The key idea is to cast reasoning in LLMs as learning and planning in Bayesian adaptive Markov decision processes (MDPs). Correspondingly, we prompt LLMs to form an updated posterior of the unknown environment from the memory buffer (learning) and generate an optimal trajectory for multiple future steps that maximizes a value function (planning). The learning and planning subroutines are performed in an "in-context" manner to emulate the actor-critic update for MDPs. Our theoretical analysis proves that the novel combination of long-term reasoning and short-term acting achieves a T regret. In particular, the regret bound highlights an intriguing interplay between the prior knowledge obtained through pretraining and the uncertainty reduction achieved by reasoning and acting. Our empirical validation shows that it outperforms various existing frameworks and achieves nearly perfect scores on a few benchmarks.

In the domain of complex reasoning tasks, such as mathematical reasoning, recent advancements have proposed the use of Direct Preference Optimization (DPO) to suppress output of dispreferred responses, thereby enhancing the long-chain reasoning capabilities of large language models (LLMs). To this end, these studies employed LLMs to generate preference trees via Tree-of-thoughts (ToT) and sample the paired preference responses required by the DPO algorithm. However, the DPO algorithm based on binary preference optimization is unable to learn multiple responses with varying degrees of preference/dispreference that provided by the preference trees, resulting in incomplete preference learning. In this work, we introduce Tree Preference Optimization (TPO), that does not sample paired preference responses from the preference tree; instead, it directly learns from the entire preference tree during the fine-tuning. Specifically, TPO formulates the language model alignment as a Preference List Ranking problem, where the policy can potentially learn more effectively from a ranked preference list of responses given the prompt. In addition, to further assist LLMs in identifying discriminative steps within long-chain reasoning and increase the relative reward margin in the preference list, TPO utilizes Adaptive Step Reward to adjust the reward values of each step in trajectory for performing fine-grained preference optimization. We carry out extensive experiments on mathematical reasoning tasks to evaluate TPO. The experimental results indicate that TPO consistently outperforms DPO across three public large language models on four datasets.

Test-time inference has emerged as a powerful paradigm for enabling language models to ``think'' longer and more carefully about complex challenges, much like skilled human experts. While reinforcement learning (RL) can drive self-improvement in language models on verifiable tasks, some models exhibit substantial gains while others quickly plateau. For instance, we find that Qwen-2.5-3B far exceeds Llama-3.2-3B under identical RL training for the game of Countdown. This discrepancy raises a critical question: what intrinsic properties enable effective self-improvement? We introduce a framework to investigate this question by analyzing four key cognitive behaviors -- verification, backtracking, subgoal setting, and backward chaining -- that both expert human problem solvers and successful language models employ. Our study reveals that Qwen naturally exhibits these reasoning behaviors, whereas Llama initially lacks them. In systematic experimentation with controlled behavioral datasets, we find that priming Llama with examples containing these reasoning behaviors enables substantial improvements during RL, matching or exceeding Qwen's performance. Importantly, the presence of reasoning behaviors, rather than correctness of answers, proves to be the critical factor -- models primed with incorrect solutions containing proper reasoning patterns achieve comparable performance to those trained on correct solutions. Finally, leveraging continued pretraining with OpenWebMath data, filtered to amplify reasoning behaviors, enables the Llama model to match Qwen's self-improvement trajectory. Our findings establish a fundamental relationship between initial reasoning behaviors and the capacity for improvement, explaining why some language models effectively utilize additional computation while others plateau.

Recent agent frameworks and inference-time algorithms often struggle with complex planning problems due to limitations in verifying generated plans or reasoning and varying complexity of instances within a single task. Many existing methods for these tasks either perform task-level verification without considering constraints or apply inference-time algorithms without adapting to instance-level complexity. To address these limitations, we propose PlanGEN, a model-agnostic and easily scalable agent framework with three key components: constraint, verification, and selection agents. Specifically, our approach proposes constraint-guided iterative verification to enhance performance of inference-time algorithms--Best of N, Tree-of-Thought, and REBASE. In PlanGEN framework, the selection agent optimizes algorithm choice based on instance complexity, ensuring better adaptability to complex planning problems. Experimental results demonstrate significant improvements over the strongest baseline across multiple benchmarks, achieving state-of-the-art results on NATURAL PLAN (sim8%uparrow), OlympiadBench (sim4%uparrow), DocFinQA (sim7%uparrow), and GPQA (sim1%uparrow). Our key finding highlights that constraint-guided iterative verification improves inference-time algorithms, and adaptive selection further boosts performance on complex planning and reasoning problems.

Large Language Models (LLMs) have exhibited remarkable performance on reasoning tasks. They utilize autoregressive token generation to construct reasoning trajectories, enabling the development of a coherent chain of thought. In this work, we explore the impact of individual tokens on the final outcomes of reasoning tasks. We identify the existence of ``critical tokens'' that lead to incorrect reasoning trajectories in LLMs. Specifically, we find that LLMs tend to produce positive outcomes when forced to decode other tokens instead of critical tokens. Motivated by this observation, we propose a novel approach - cDPO - designed to automatically recognize and conduct token-level rewards for the critical tokens during the alignment process. Specifically, we develop a contrastive estimation approach to automatically identify critical tokens. It is achieved by comparing the generation likelihood of positive and negative models. To achieve this, we separately fine-tune the positive and negative models on various reasoning trajectories, consequently, they are capable of identifying identify critical tokens within incorrect trajectories that contribute to erroneous outcomes. Moreover, to further align the model with the critical token information during the alignment process, we extend the conventional DPO algorithms to token-level DPO and utilize the differential likelihood from the aforementioned positive and negative model as important weight for token-level DPO learning.Experimental results on GSM8K and MATH500 benchmarks with two-widely used models Llama-3 (8B and 70B) and deepseek-math (7B) demonstrate the effectiveness of the propsoed approach cDPO.

Language has long been conceived as an essential tool for human reasoning. The breakthrough of Large Language Models (LLMs) has sparked significant research interest in leveraging these models to tackle complex reasoning tasks. Researchers have moved beyond simple autoregressive token generation by introducing the concept of "thought" -- a sequence of tokens representing intermediate steps in the reasoning process. This innovative paradigm enables LLMs' to mimic complex human reasoning processes, such as tree search and reflective thinking. Recently, an emerging trend of learning to reason has applied reinforcement learning (RL) to train LLMs to master reasoning processes. This approach enables the automatic generation of high-quality reasoning trajectories through trial-and-error search algorithms, significantly expanding LLMs' reasoning capacity by providing substantially more training data. Furthermore, recent studies demonstrate that encouraging LLMs to "think" with more tokens during test-time inference can further significantly boost reasoning accuracy. Therefore, the train-time and test-time scaling combined to show a new research frontier -- a path toward Large Reasoning Model. The introduction of OpenAI's o1 series marks a significant milestone in this research direction. In this survey, we present a comprehensive review of recent progress in LLM reasoning. We begin by introducing the foundational background of LLMs and then explore the key technical components driving the development of large reasoning models, with a focus on automated data construction, learning-to-reason techniques, and test-time scaling. We also analyze popular open-source projects at building large reasoning models, and conclude with open challenges and future research directions.

Large language models (LLMs) have shown exceptional performance as general-purpose assistants, excelling across a variety of reasoning tasks. This achievement represents a significant step toward achieving artificial general intelligence (AGI). Despite these advancements, the effectiveness of LLMs often hinges on the specific prompting strategies employed, and there remains a lack of a robust framework to facilitate learning and generalization across diverse reasoning tasks. To address these challenges, we introduce a novel learning framework, THOUGHT-LIKE-PRO In this framework, we utilize imitation learning to imitate the Chain-of-Thought (CoT) process which is verified and translated from reasoning trajectories generated by a symbolic Prolog logic engine. This framework proceeds in a self-driven manner, that enables LLMs to formulate rules and statements from given instructions and leverage the symbolic Prolog engine to derive results. Subsequently, LLMs convert Prolog-derived successive reasoning trajectories into natural language CoT for imitation learning. Our empirical findings indicate that our proposed approach substantially enhances the reasoning abilities of LLMs and demonstrates robust generalization across out-of-distribution reasoning tasks.

Recently DeepSeek R1 demonstrated how reinforcement learning with simple rule-based incentives can enable autonomous development of complex reasoning in large language models, characterized by the "aha moment", in which the model manifest self-reflection and increased response length during training. However, attempts to extend this success to multimodal reasoning often failed to reproduce these key characteristics. In this report, we present the first successful replication of these emergent characteristics for multimodal reasoning on only a non-SFT 2B model. Starting with Qwen2-VL-2B and applying reinforcement learning directly on the SAT dataset, our model achieves 59.47% accuracy on CVBench, outperforming the base model by approximately ~30% and exceeding both SFT setting by ~2%. In addition, we share our failed attempts and insights in attempting to achieve R1-like reasoning using RL with instruct models. aiming to shed light on the challenges involved. Our key observations include: (1) applying RL on instruct model often results in trivial reasoning trajectories, and (2) naive length reward are ineffective in eliciting reasoning capabilities. The project code is available at https://github.com/turningpoint-ai/VisualThinker-R1-Zero

Hallucinations (i.e., generating plausible but inaccurate content) and laziness (i.e. excessive refusals or defaulting to "I don't know") persist as major challenges in LLM reasoning. Current efforts to reduce hallucinations primarily focus on factual errors in knowledge-grounded tasks, often neglecting hallucinations related to faulty reasoning. Meanwhile, some approaches render LLMs overly conservative, limiting their problem-solving capabilities. To mitigate hallucination and laziness in reasoning tasks, we propose Automatic Curriculum Expert Iteration (Auto-CEI) to enhance LLM reasoning and align responses to the model's capabilities--assertively answering within its limits and declining when tasks exceed them. In our method, Expert Iteration explores the reasoning trajectories near the LLM policy, guiding incorrect paths back on track to reduce compounding errors and improve robustness; it also promotes appropriate "I don't know" responses after sufficient reasoning attempts. The curriculum automatically adjusts rewards, incentivizing extended reasoning before acknowledging incapability, thereby pushing the limits of LLM reasoning and aligning its behaviour with these limits. We compare Auto-CEI with various SOTA baselines across logical reasoning, mathematics, and planning tasks, where Auto-CEI achieves superior alignment by effectively balancing assertiveness and conservativeness.

Answering Questions over Knowledge Graphs (KGQA) is key to well-functioning autonomous language agents in various real-life applications. To improve the neural-symbolic reasoning capabilities of language agents powered by Large Language Models (LLMs) in KGQA, we propose the DecompositionAlignment-Reasoning Agent (DARA) framework. DARA effectively parses questions into formal queries through a dual mechanism: high-level iterative task decomposition and low-level task grounding. Importantly, DARA can be efficiently trained with a small number of high-quality reasoning trajectories. Our experimental results demonstrate that DARA fine-tuned on LLMs (e.g. Llama-2-7B, Mistral) outperforms both in-context learning-based agents with GPT-4 and alternative fine-tuned agents, across different benchmarks in zero-shot evaluation, making such models more accessible for real-life applications. We also show that DARA attains performance comparable to state-of-the-art enumerating-and-ranking-based methods for KGQA.

Large language models (LLMs) have recently demonstrated remarkable success in mathematical reasoning. Despite progress in methods like chain-of-thought prompting and self-consistency sampling, these advances often focus on final correctness without ensuring that the underlying reasoning process is coherent and reliable. This paper introduces Step-KTO, a training framework that combines process-level and outcome-level binary feedback to guide LLMs toward more trustworthy reasoning trajectories. By providing binary evaluations for both the intermediate reasoning steps and the final answer, Step-KTO encourages the model to adhere to logical progressions rather than relying on superficial shortcuts. Our experiments on challenging mathematical benchmarks show that Step-KTO significantly improves both final answer accuracy and the quality of intermediate reasoning steps. For example, on the MATH-500 dataset, Step-KTO achieves a notable improvement in Pass@1 accuracy over strong baselines. These results highlight the promise of integrating stepwise process feedback into LLM training, paving the way toward more interpretable and dependable reasoning capabilities.

We present rStar-Math to demonstrate that small language models (SLMs) can rival or even surpass the math reasoning capability of OpenAI o1, without distillation from superior models. rStar-Math achieves this by exercising "deep thinking" through Monte Carlo Tree Search (MCTS), where a math policy SLM performs test-time search guided by an SLM-based process reward model. rStar-Math introduces three innovations to tackle the challenges in training the two SLMs: (1) a novel code-augmented CoT data sythesis method, which performs extensive MCTS rollouts to generate step-by-step verified reasoning trajectories used to train the policy SLM; (2) a novel process reward model training method that avoids na\"ive step-level score annotation, yielding a more effective process preference model (PPM); (3) a self-evolution recipe in which the policy SLM and PPM are built from scratch and iteratively evolved to improve reasoning capabilities. Through 4 rounds of self-evolution with millions of synthesized solutions for 747k math problems, rStar-Math boosts SLMs' math reasoning to state-of-the-art levels. On the MATH benchmark, it improves Qwen2.5-Math-7B from 58.8% to 90.0% and Phi3-mini-3.8B from 41.4% to 86.4%, surpassing o1-preview by +4.5% and +0.9%. On the USA Math Olympiad (AIME), rStar-Math solves an average of 53.3% (8/15) of problems, ranking among the top 20% the brightest high school math students. Code and data will be available at https://github.com/microsoft/rStar.

Multi-agent AI systems powered by large language models (LLMs) are increasingly applied to solve complex tasks. However, these systems often rely on fragile, manually designed prompts and heuristics, making optimization difficult. A key challenge in optimizing multi-agent systems is acquiring suitable training data for specialized agents. We introduce SiriuS, a self-improving, reasoning-driven optimization framework for multi-agent systems. Central to our approach is the construction of an experience library: a repository of high-quality reasoning trajectories. The library is built by retaining reasoning steps that lead to successful outcomes, providing a robust training set for optimizing multi-agent system. Additionally, we introduce a library augmentation procedure that refines unsuccessful trajectories, further enriching the library. SiriuS boosts performance by 2.86\% to 21.88\% on reasoning and biomedical QA and enhances agent negotiation in competitive settings. Our results show that SiriuS enhances multi-agent performance while generating reusable data for self-correction and self-play enhancement in the future.

Knowledge Graphs (KGs) can serve as reliable knowledge sources for question answering (QA) due to their structured representation of knowledge. Existing research on the utilization of KG for large language models (LLMs) prevalently relies on subgraph retriever or iterative prompting, overlooking the potential synergy of LLMs' step-wise reasoning capabilities and KGs' structural nature. In this paper, we present DoG (Decoding on Graphs), a novel framework that facilitates a deep synergy between LLMs and KGs. We first define a concept, well-formed chain, which consists of a sequence of interrelated fact triplets on the KGs, starting from question entities and leading to answers. We argue that this concept can serve as a principle for making faithful and sound reasoning for KGQA. To enable LLMs to generate well-formed chains, we propose graph-aware constrained decoding, in which a constraint derived from the topology of the KG regulates the decoding process of the LLMs. This constrained decoding method ensures the generation of well-formed chains while making full use of the step-wise reasoning capabilities of LLMs. Based on the above, DoG, a training-free approach, is able to provide faithful and sound reasoning trajectories grounded on the KGs. Experiments across various KGQA tasks with different background KGs demonstrate that DoG achieves superior and robust performance. DoG also shows general applicability with various open-source LLMs.

Reasoning abilities, especially those for solving complex math problems, are crucial components of general intelligence. Recent advances by proprietary companies, such as o-series models of OpenAI, have made remarkable progress on reasoning tasks. However, the complete technical details remain unrevealed, and the techniques that are believed certainly to be adopted are only reinforcement learning (RL) and the long chain of thoughts. This paper proposes a new RL framework, termed OREAL, to pursue the performance limit that can be achieved through Outcome REwArd-based reinforcement Learning for mathematical reasoning tasks, where only binary outcome rewards are easily accessible. We theoretically prove that behavior cloning on positive trajectories from best-of-N (BoN) sampling is sufficient to learn the KL-regularized optimal policy in binary feedback environments. This formulation further implies that the rewards of negative samples should be reshaped to ensure the gradient consistency between positive and negative samples. To alleviate the long-existing difficulties brought by sparse rewards in RL, which are even exacerbated by the partial correctness of the long chain of thought for reasoning tasks, we further apply a token-level reward model to sample important tokens in reasoning trajectories for learning. With OREAL, for the first time, a 7B model can obtain 94.0 pass@1 accuracy on MATH-500 through RL, being on par with 32B models. OREAL-32B also surpasses previous 32B models trained by distillation with 95.0 pass@1 accuracy on MATH-500. Our investigation also indicates the importance of initial policy models and training queries for RL. Code, models, and data will be released to benefit future researchhttps://github.com/InternLM/OREAL.

Large language models (LLMs) have significantly improved their reasoning capabilities; however, they still struggle with complex multi-step mathematical problem-solving due to error propagation, lack of self-correction, and limited adaptability to diverse reasoning styles. Existing methods rely on static fine-tuning or prompt engineering, which fail to generalize across problem complexities, while the scarcity of high-quality preference data further hinders reliable reasoning. We introduce SPHERE, a self-evolving data generation pipeline that enhances reasoning in small language models (SLMs) by iteratively generating, correcting, and diversifying reasoning chains. SPHERE operates in three stages: (i) Self-Generation, where the model autonomously constructs problem-solving steps; (ii) Self-Correction, enabling it to identify and rectify errors; and (iii) Diversity Induction, improving robustness through multiple valid reasoning trajectories. This self-evolution mechanism strengthens mathematical reasoning and enhances model reliability. Evaluations on MATH 500, GSM8K, AIME, AMC, and Olympiad show that SPHERE-trained models achieve significant gains over their base versions and match/surpass GPT-4o on certain benchmarks. Our findings demonstrate that self-evolving models can close the reasoning gap between SLMs and state-of-the-art LLMs, making mathematical AI more reliable, scalable, and efficient.

Recent advancements have highlighted that Large Language Models (LLMs) are prone to hallucinations when solving complex reasoning problems, leading to erroneous results. To tackle this issue, researchers incorporate Knowledge Graphs (KGs) to improve the reasoning ability of LLMs. However, existing methods face two limitations: 1) they typically assume that all answers to the questions are contained in KGs, neglecting the incompleteness issue of KGs, and 2) they treat the KG as a static repository and overlook the implicit logical reasoning structures inherent in KGs. In this paper, we introduce SymAgent, an innovative neural-symbolic agent framework that achieves collaborative augmentation between KGs and LLMs. We conceptualize KGs as dynamic environments and transform complex reasoning tasks into a multi-step interactive process, enabling KGs to participate deeply in the reasoning process. SymAgent consists of two modules: Agent-Planner and Agent-Executor. The Agent-Planner leverages LLM's inductive reasoning capability to extract symbolic rules from KGs, guiding efficient question decomposition. The Agent-Executor autonomously invokes predefined action tools to integrate information from KGs and external documents, addressing the issues of KG incompleteness. Furthermore, we design a self-learning framework comprising online exploration and offline iterative policy updating phases, enabling the agent to automatically synthesize reasoning trajectories and improve performance. Experimental results demonstrate that SymAgent with weak LLM backbones (i.e., 7B series) yields better or comparable performance compared to various strong baselines. Further analysis reveals that our agent can identify missing triples, facilitating automatic KG updates.

Reasoning is central to a wide range of intellectual activities, and while the capabilities of large language models (LLMs) continue to advance, their performance in reasoning tasks remains limited. The processes and mechanisms underlying reasoning are not yet fully understood, but key elements include path exploration, selection of relevant knowledge, and multi-step inference. Problems are solved through the synthesis of these components. In this paper, we propose a benchmark that focuses on a specific aspect of reasoning ability: the direct evaluation of multi-step inference. To this end, we design a special reasoning task where multi-step inference is specifically focused by largely eliminating path exploration and implicit knowledge utilization. Our dataset comprises pairs of explicit instructions and corresponding questions, where the procedures necessary for solving the questions are entirely detailed within the instructions. This setup allows models to solve problems solely by following the provided directives. By constructing problems that require varying numbers of steps to solve and evaluating responses at each step, we enable a thorough assessment of state-of-the-art LLMs' ability to follow instructions. To ensure the robustness of our evaluation, we include multiple distinct tasks. Furthermore, by comparing accuracy across tasks, utilizing step-aware metrics, and applying separately defined measures of complexity, we conduct experiments that offer insights into the capabilities and limitations of LLMs in reasoning tasks. Our findings have significant implications for the development of LLMs and highlight areas for future research in advancing their reasoning abilities. Our dataset is available at https://huggingface.co/datasets/ifujisawa/procbench and code at https://github.com/ifujisawa/proc-bench.

Reasoning is a fundamental aspect of human intelligence that plays a crucial role in activities such as problem solving, decision making, and critical thinking. In recent years, large language models (LLMs) have made significant progress in natural language processing, and there is observation that these models may exhibit reasoning abilities when they are sufficiently large. However, it is not yet clear to what extent LLMs are capable of reasoning. This paper provides a comprehensive overview of the current state of knowledge on reasoning in LLMs, including techniques for improving and eliciting reasoning in these models, methods and benchmarks for evaluating reasoning abilities, findings and implications of previous research in this field, and suggestions on future directions. Our aim is to provide a detailed and up-to-date review of this topic and stimulate meaningful discussion and future work.

Recently, slow-thinking reasoning systems, such as o1, have demonstrated remarkable capabilities in solving complex reasoning tasks. These systems typically engage in an extended thinking process before responding to a query, allowing them to generate more thorough, accurate, and well-reasoned solutions. These systems are primarily developed and maintained by industry, with their core techniques not publicly disclosed. In response, an increasing number of studies from the research community aim to explore the technical foundations underlying these powerful reasoning systems. Building on these prior efforts, this paper presents a reproduction report on implementing o1-like reasoning systems. We introduce an "imitate, explore, and self-improve" framework as our primary technical approach to train the reasoning model. In the initial phase, we use distilled long-form thought data to fine-tune the reasoning model, enabling it to invoke a slow-thinking mode. The model is then encouraged to explore challenging problems by generating multiple rollouts, which can result in increasingly more high-quality trajectories that lead to correct answers. Furthermore, the model undergoes self-improvement by iteratively refining its training dataset. To verify the effectiveness of this approach, we conduct extensive experiments on three challenging benchmarks. The experimental results demonstrate that our approach achieves competitive performance compared to industry-level reasoning systems on these benchmarks.

Achieving human-level intelligence requires refining the transition from the fast, intuitive System 1 to the slower, more deliberate System 2 reasoning. While System 1 excels in quick, heuristic decisions, System 2 relies on logical reasoning for more accurate judgments and reduced biases. Foundational Large Language Models (LLMs) excel at fast decision-making but lack the depth for complex reasoning, as they have not yet fully embraced the step-by-step analysis characteristic of true System 2 thinking. Recently, reasoning LLMs like OpenAI's o1/o3 and DeepSeek's R1 have demonstrated expert-level performance in fields such as mathematics and coding, closely mimicking the deliberate reasoning of System 2 and showcasing human-like cognitive abilities. This survey begins with a brief overview of the progress in foundational LLMs and the early development of System 2 technologies, exploring how their combination has paved the way for reasoning LLMs. Next, we discuss how to construct reasoning LLMs, analyzing their features, the core methods enabling advanced reasoning, and the evolution of various reasoning LLMs. Additionally, we provide an overview of reasoning benchmarks, offering an in-depth comparison of the performance of representative reasoning LLMs. Finally, we explore promising directions for advancing reasoning LLMs and maintain a real-time https://github.com/zzli2022/Awesome-Slow-Reason-System{GitHub Repository} to track the latest developments. We hope this survey will serve as a valuable resource to inspire innovation and drive progress in this rapidly evolving field.

Advanced models such as OpenAI o1 exhibit impressive problem-solving capabilities through step-by-step reasoning. However, they may still falter on more complex problems, making errors that disrupt their reasoning paths. We attribute this to the expansive solution space, where each step has the risk of diverging into mistakes. To enhance language model reasoning, we introduce a specialized training framework called Reasoning Paths Optimization (RPO), which enables learning to reason and explore from diverse paths. Our approach encourages favorable branches at each reasoning step while penalizing unfavorable ones, enhancing the model's overall problem-solving performance. Reasoning Paths Optimization does not rely on large-scale human-annotated rationales or outputs from closed-source models, making it scalable and data-efficient. We focus on multi-step reasoning tasks, such as math word problems and science-based exam questions. The experiments demonstrate that our framework significantly enhances the reasoning performance of large language models, with up to 3.1% and 4.3% improvement on GSM8K and MMLU (STEM) respectively. Our data and code can be found at https://reasoning-paths.github.io.

Large language models (LLMs) have shown promise in performing complex multi-step reasoning, yet they continue to struggle with mathematical reasoning, often making systematic errors. A promising solution is reinforcement learning (RL) guided by reward models, particularly those focusing on process rewards, which score each intermediate step rather than solely evaluating the final outcome. This approach is more effective at guiding policy models towards correct reasoning trajectories. In this work, we propose an entropy-regularized process reward model (ER-PRM) that integrates KL-regularized Markov Decision Processes (MDP) to balance policy optimization with the need to prevent the policy from shifting too far from its initial distribution. We derive a novel reward construction method based on the theoretical results. Our theoretical analysis shows that we could derive the optimal reward model from the initial policy sampling. Our empirical experiments on the MATH and GSM8K benchmarks demonstrate that ER-PRM consistently outperforms existing process reward models, achieving 1% improvement on GSM8K and 2-3% improvement on MATH under best-of-N evaluation, and more than 1% improvement under RLHF. These results highlight the efficacy of entropy-regularization in enhancing LLMs' reasoning capabilities.

Large reasoning models (LRMs) like OpenAI-o1 and DeepSeek-R1 have demonstrated remarkable capabilities in complex reasoning tasks through the utilization of long Chain-of-thought (CoT). However, these models often suffer from hallucinations and inefficiencies due to their reliance solely on internal reasoning processes. In this paper, we introduce START (Self-Taught Reasoner with Tools), a novel tool-integrated long CoT reasoning LLM that significantly enhances reasoning capabilities by leveraging external tools. Through code execution, START is capable of performing complex computations, self-checking, exploring diverse methods, and self-debugging, thereby addressing the limitations of LRMs. The core innovation of START lies in its self-learning framework, which comprises two key techniques: 1) Hint-infer: We demonstrate that inserting artificially designed hints (e.g., ``Wait, maybe using Python here is a good idea.'') during the inference process of a LRM effectively stimulates its ability to utilize external tools without the need for any demonstration data. Hint-infer can also serve as a simple and effective sequential test-time scaling method; 2) Hint Rejection Sampling Fine-Tuning (Hint-RFT): Hint-RFT combines Hint-infer and RFT by scoring, filtering, and modifying the reasoning trajectories with tool invocation generated by a LRM via Hint-infer, followed by fine-tuning the LRM. Through this framework, we have fine-tuned the QwQ-32B model to achieve START. On PhD-level science QA (GPQA), competition-level math benchmarks (AMC23, AIME24, AIME25), and the competition-level code benchmark (LiveCodeBench), START achieves accuracy rates of 63.6%, 95.0%, 66.7%, 47.1%, and 47.3%, respectively. It significantly outperforms the base QwQ-32B and achieves performance comparable to the state-of-the-art open-weight model R1-Distill-Qwen-32B and the proprietary model o1-Preview.

While there have been extensive studies in code generation by large language models (LLM), where benchmarks like HumanEval have been surpassed with an impressive 96.3% success rate, these benchmarks predominantly judge a model's performance on basic function-level code generation and lack the critical thinking and concept of scope required of real-world scenarios such as solving GitHub issues. This research introduces the application of the Tree of Thoughts (ToT) language model reasoning framework for enhancing the decision-making and problem-solving abilities of LLMs for this complex task. Compared to traditional input-output (IO) prompting and Retrieval Augmented Generation (RAG) techniques, ToT is designed to improve performance by facilitating a structured exploration of multiple reasoning trajectories and enabling self-assessment of potential solutions. We experimentally deploy ToT in tackling a Github issue contained within an instance of the SWE-bench. However, our results reveal that the ToT framework alone is not enough to give LLMs the critical reasoning capabilities to outperform existing methods. In this paper we analyze the potential causes of these shortcomings and identify key areas for improvement such as deepening the thought process and introducing agentic capabilities. The insights of this research are aimed at informing future directions for refining the application of ToT and better harnessing the potential of LLMs in real-world problem-solving scenarios.

Scaling up language models to billions of parameters has opened up possibilities for in-context learning, allowing instruction tuning and few-shot learning on tasks that the model was not specifically trained for. This has achieved breakthrough performance on language tasks such as translation, summarization, and question-answering. Furthermore, in addition to these associative "System 1" tasks, recent advances in Chain-of-thought prompt learning have demonstrated strong "System 2" reasoning abilities, answering a question in the field of artificial general intelligence whether LLMs can reason. The field started with the question whether LLMs can solve grade school math word problems. This paper reviews the rapidly expanding field of prompt-based reasoning with LLMs. Our taxonomy identifies different ways to generate, evaluate, and control multi-step reasoning. We provide an in-depth coverage of core approaches and open problems, and we propose a research agenda for the near future. Finally, we highlight the relation between reasoning and prompt-based learning, and we discuss the relation between reasoning, sequential decision processes, and reinforcement learning. We find that self-improvement, self-reflection, and some metacognitive abilities of the reasoning processes are possible through the judicious use of prompts. True self-improvement and self-reasoning, to go from reasoning with LLMs to reasoning by LLMs, remains future work.

Large Language Models (LLMs) have demonstrated significant potential in handling complex reasoning tasks through step-by-step rationale generation. However, recent studies have raised concerns regarding the hallucination and flaws in their reasoning process. Substantial efforts are being made to improve the reliability and faithfulness of the generated rationales. Some approaches model reasoning as planning, while others focus on annotating for process supervision. Nevertheless, the planning-based search process often results in high latency due to the frequent assessment of intermediate reasoning states and the extensive exploration space. Additionally, supervising the reasoning process with human annotation is costly and challenging to scale for LLM training. To address these issues, in this paper, we propose a framework to learn planning-based reasoning through direct preference optimization (DPO) on collected trajectories, which are ranked according to synthesized process rewards. Our results on challenging logical reasoning benchmarks demonstrate the effectiveness of our learning framework, showing that our 7B model can surpass the strong counterparts like GPT-3.5-Turbo.

Recent research developing neural network architectures with external memory have often used the benchmark bAbI question and answering dataset which provides a challenging number of tasks requiring reasoning. Here we employed a classic associative inference task from the memory-based reasoning neuroscience literature in order to more carefully probe the reasoning capacity of existing memory-augmented architectures. This task is thought to capture the essence of reasoning -- the appreciation of distant relationships among elements distributed across multiple facts or memories. Surprisingly, we found that current architectures struggle to reason over long distance associations. Similar results were obtained on a more complex task involving finding the shortest path between nodes in a path. We therefore developed MEMO, an architecture endowed with the capacity to reason over longer distances. This was accomplished with the addition of two novel components. First, it introduces a separation between memories (facts) stored in external memory and the items that comprise these facts in external memory. Second, it makes use of an adaptive retrieval mechanism, allowing a variable number of "memory hops" before the answer is produced. MEMO is capable of solving our novel reasoning tasks, as well as match state of the art results in bAbI.

Reasoning, as an essential ability for complex problem-solving, can provide back-end support for various real-world applications, such as medical diagnosis, negotiation, etc. This paper provides a comprehensive survey of cutting-edge research on reasoning with language model prompting. We introduce research works with comparisons and summaries and provide systematic resources to help beginners. We also discuss the potential reasons for emerging such reasoning abilities and highlight future research directions. Resources are available at https://github.com/zjunlp/Prompt4ReasoningPapers (updated periodically).

Reasoning is a cognitive process of using evidence to reach a sound conclusion. The reasoning capability is essential for large language models (LLMs) to serve as the brain of the artificial general intelligence agent. Recent studies reveal that fine-tuning LLMs on data with the chain of thought (COT) reasoning process can significantly enhance their reasoning capabilities. However, we find that the fine-tuned LLMs suffer from an Assessment Misalignment problem, i.e., they frequently assign higher scores to subpar COTs, leading to potential limitations in their reasoning abilities. To address this problem, we introduce an Alignment Fine-Tuning (AFT) paradigm, which involves three steps: 1) fine-tuning LLMs with COT training data; 2) generating multiple COT responses for each question, and categorizing them into positive and negative ones based on whether they achieve the correct answer; 3) calibrating the scores of positive and negative responses given by LLMs with a novel constraint alignment loss. Specifically, the constraint alignment loss has two objectives: a) Alignment, which guarantees that positive scores surpass negative scores to encourage answers with high-quality COTs; b) Constraint, which keeps the negative scores confined to a reasonable range to prevent the model degradation. Beyond just the binary positive and negative feedback, the constraint alignment loss can be seamlessly adapted to the ranking situations when ranking feedback is accessible. Furthermore, we also delve deeply into recent ranking-based alignment methods, such as DPO, RRHF, and PRO, and discover that the constraint, which has been overlooked by these approaches, is also crucial for their performance. Extensive experiments on four reasoning benchmarks with both binary and ranking feedback demonstrate the effectiveness of AFT.

Although Large Language Models (LLMs) achieve remarkable performance across various tasks, they often struggle with complex reasoning tasks, such as answering mathematical questions. Recent efforts to address this issue have primarily focused on leveraging mathematical datasets through supervised fine-tuning or self-improvement techniques. However, these methods often depend on high-quality datasets that are difficult to prepare, or they require substantial computational resources for fine-tuning. Inspired by findings that LLMs know how to produce the right answer but struggle to select the correct reasoning path, we propose a purely inference-based searching method -- MindStar (M*). This method formulates reasoning tasks as searching problems and proposes two search ideas to identify the optimal reasoning paths. We evaluate the M* framework on both the GSM8K and MATH datasets, comparing its performance with existing open and closed-source LLMs. Our results demonstrate that M* significantly enhances the reasoning abilities of open-source models, such as Llama-2-13B and Mistral-7B, and achieves comparable performance to GPT-3.5 and Grok-1, but with substantially reduced model size and computational costs.

With the emergence of advanced reasoning models like OpenAI o3 and DeepSeek-R1, large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, their ability to perform rigorous logical reasoning remains an open question. This survey synthesizes recent advancements in logical reasoning within LLMs, a critical area of AI research. It outlines the scope of logical reasoning in LLMs, its theoretical foundations, and the benchmarks used to evaluate reasoning proficiency. We analyze existing capabilities across different reasoning paradigms - deductive, inductive, abductive, and analogical - and assess strategies to enhance reasoning performance, including data-centric tuning, reinforcement learning, decoding strategies, and neuro-symbolic approaches. The review concludes with future directions, emphasizing the need for further exploration to strengthen logical reasoning in AI systems.

Logical reading comprehension is a challenging task that entails grasping the underlying semantics of text and applying reasoning to deduce the correct answer. Prior researches have primarily focused on enhancing logical reasoning capabilities through Chain-of-Thought (CoT) or data augmentation. However, previous work constructing chain-of-thought rationales concentrates solely on analyzing correct options, neglecting the incorrect alternatives. Addtionally, earlier efforts on data augmentation by altering contexts rely on rule-based methods, which result in generated contexts that lack diversity and coherence. To address these issues, we propose a Premise-Oriented Data Augmentation (PODA) framework. This framework can generate CoT rationales including analyses for both correct and incorrect options, while constructing diverse and high-quality counterfactual contexts from incorrect candidate options. We integrate summarizing premises and identifying premises for each option into rationales. Subsequently, we employ multi-step prompts with identified premises to construct counterfactual context. To facilitate the model's capabilities to better differentiate the reasoning process associated with each option, we introduce a novel thought-path contrastive learning method that compares reasoning paths between the original and counterfactual samples. Experimental results on three representative LLMs demonstrate that our method can improve the baselines substantially across two challenging logical reasoning benchmarks (ReClor and LogiQA 2.0). The data and code are released at https://github.com/lalalamdbf/TPReasoner.

Reasoning is an essential component of human intelligence as it plays a fundamental role in our ability to think critically, support responsible decisions, and solve challenging problems. Traditionally, AI has addressed reasoning in the context of logic-based representations of knowledge. However, the recent leap forward in natural language processing, with the emergence of language models based on transformers, is hinting at the possibility that these models exhibit reasoning abilities, particularly as they grow in size and are trained on more data. Despite ongoing discussions about what reasoning is in language models, it is still not easy to pin down to what extent these models are actually capable of reasoning. The goal of this workshop is to create a platform for researchers from different disciplines and/or AI perspectives, to explore approaches and techniques with the aim to reconcile reasoning between language models using transformers and using logic-based representations. The specific objectives include analyzing the reasoning abilities of language models measured alongside KR methods, injecting KR-style reasoning abilities into language models (including by neuro-symbolic means), and formalizing the kind of reasoning language models carry out. This exploration aims to uncover how language models can effectively integrate and leverage knowledge and reasoning with it, thus improving their application and utility in areas where precision and reliability are a key requirement.

Logical reasoning task has attracted great interest since it was proposed. Faced with such a task, current competitive models, even large language models (e.g., ChatGPT and PaLM 2), still perform badly. Previous promising LMs struggle in logical consistency modeling and logical structure perception. To this end, we model the logical reasoning task by transforming each logical sample into reasoning paths and propose an architecture PathReasoner. It addresses the task from the views of both data and model. To expand the diversity of the logical samples, we propose an atom extension strategy supported by equivalent logical formulas, to form new reasoning paths. From the model perspective, we design a stack of transformer-style blocks. In particular, we propose a path-attention module to joint model in-atom and cross-atom relations with the high-order diffusion strategy. Experiments show that PathReasoner achieves competitive performances on two logical reasoning benchmarks and great generalization abilities.

Analytical reasoning is an essential and challenging task that requires a system to analyze a scenario involving a set of particular circumstances and perform reasoning over it to make conclusions. In this paper, we study the challenge of analytical reasoning of text and introduce a new dataset consisting of questions from the Law School Admission Test from 1991 to 2016. We analyze what knowledge understanding and reasoning abilities are required to do well on this task. Furthermore, to address this reasoning challenge, we design two different baselines: (1) a Transformer-based method which leverages the state-of-the-art pre-trained language models and (2) Analytical Reasoning Machine (ARM), a logical-level reasoning framework extracting symbolic knowledge (e.g, participants, facts, logical functions) to deduce legitimate solutions. In our experiments, we find that the Transformer-based models struggle to solve this task as their performance is close to random guess and ARM achieves better performance by leveraging symbolic knowledge and interpretable reasoning steps. Results show that both methods still lag far behind human performance, which leave further space for future research.

Although contemporary large language models (LMs) demonstrate impressive question-answering capabilities, their answers are typically the product of a single call to the model. This entails an unwelcome degree of opacity and compromises performance, especially on problems that are inherently multi-step. To address these limitations, we show how LMs can be made to perform faithful multi-step reasoning via a process whose causal structure mirrors the underlying logical structure of the problem. Our approach works by chaining together reasoning steps, where each step results from calls to two fine-tuned LMs, one for selection and one for inference, to produce a valid reasoning trace. Our method carries out a beam search through the space of reasoning traces to improve reasoning quality. We demonstrate the effectiveness of our model on multi-step logical deduction and scientific question-answering, showing that it outperforms baselines on final answer accuracy, and generates humanly interpretable reasoning traces whose validity can be checked by the user.

Large Language Models (LLMs) have succeeded remarkably in various natural language processing (NLP) tasks, yet their reasoning capabilities remain a fundamental challenge. While LLMs exhibit impressive fluency and factual recall, their ability to perform complex reasoning-spanning logical deduction, mathematical problem-solving, commonsense inference, and multi-step reasoning-often falls short of human expectations. This survey provides a comprehensive review of emerging techniques enhancing reasoning in LLMs. We categorize existing methods into key approaches, including prompting strategies (e.g., Chain-of-Thought reasoning, Self-Consistency, and Tree-of-Thought reasoning), architectural innovations (e.g., retrieval-augmented models, modular reasoning networks, and neuro-symbolic integration), and learning paradigms (e.g., fine-tuning with reasoning-specific datasets, reinforcement learning, and self-supervised reasoning objectives). Additionally, we explore evaluation frameworks used to assess reasoning in LLMs and highlight open challenges, such as hallucinations, robustness, and reasoning generalization across diverse tasks. By synthesizing recent advancements, this survey aims to provide insights into promising directions for future research and practical applications of reasoning-augmented LLMs.

Studies have underscored how, regardless of the recent breakthrough and swift advances in AI research, even state-of-the-art Large Language models (LLMs) continue to struggle when performing logical and mathematical reasoning. The results seem to suggest that LLMs still work as (highly advanced) data pattern identifiers, scoring poorly when attempting to generalise and solve reasoning problems the models have never previously seen or that are not close to samples presented in their training data. To address this compelling concern, this paper makes use of the notion of critical questions from the literature on argumentation theory, focusing in particular on Toulmin's model of argumentation. We show that employing these critical questions can improve the reasoning capabilities of LLMs. By probing the rationale behind the models' reasoning process, the LLM can assess whether some logical mistake is occurring and correct it before providing the final reply to the user prompt. The underlying idea is drawn from the gold standard of any valid argumentative procedure: the conclusion is valid if it is entailed by accepted premises. Or, to paraphrase such Aristotelian principle in a real-world approximation, characterised by incomplete information and presumptive logic, the conclusion is valid if not proved otherwise. This approach successfully steers the models' output through a reasoning pipeline, resulting in better performance against the baseline and its Chain-of-Thought (CoT) implementation. To this end, an extensive evaluation of the proposed approach on the MT-Bench Reasoning and Math tasks across a range of LLMs is provided.

Large language models (LLMs) have shown remarkable reasoning capabilities, especially when prompted to generate intermediate reasoning steps (e.g., Chain-of-Thought, CoT). However, LLMs can still struggle with problems that are easy for humans, such as generating action plans for executing tasks in a given environment, or performing complex math, logical, and commonsense reasoning. The deficiency stems from the key fact that LLMs lack an internal world model to predict the world state (e.g., environment status, intermediate variable values) and simulate long-term outcomes of actions. This prevents LLMs from performing deliberate planning akin to human brains, which involves exploring alternative reasoning paths, anticipating future states and rewards, and iteratively refining existing reasoning steps. To overcome the limitations, we propose a new LLM reasoning framework, Reasoning via Planning (RAP). RAP repurposes the LLM as both a world model and a reasoning agent, and incorporates a principled planning algorithm (based on Monto Carlo Tree Search) for strategic exploration in the vast reasoning space. During reasoning, the LLM (as agent) incrementally builds a reasoning tree under the guidance of the LLM (as world model) and task-specific rewards, and obtains a high-reward reasoning path efficiently with a proper balance between exploration vs. exploitation. We apply RAP to a variety of challenging reasoning problems including plan generation, math reasoning, and logical inference. Empirical results on these tasks demonstrate the superiority of RAP over various strong baselines, including CoT and least-to-most prompting with self-consistency. RAP on LLAMA-33B surpasses CoT on GPT-4 with 33% relative improvement in a plan generation setting.

Deductive reasoning plays a pivotal role in the formulation of sound and cohesive arguments. It allows individuals to draw conclusions that logically follow, given the truth value of the information provided. Recent progress in the domain of large language models (LLMs) has showcased their capability in executing deductive reasoning tasks. Nonetheless, a significant portion of research primarily assesses the accuracy of LLMs in solving such tasks, often overlooking a deeper analysis of their reasoning behavior. In this study, we draw upon principles from cognitive psychology to examine inferential strategies employed by LLMs, through a detailed evaluation of their responses to propositional logic problems. Our findings indicate that LLMs display reasoning patterns akin to those observed in humans, including strategies like supposition following or chain construction. Moreover, our research demonstrates that the architecture and scale of the model significantly affect its preferred method of reasoning, with more advanced models tending to adopt strategies more frequently than less sophisticated ones. Importantly, we assert that a model's accuracy, that is the correctness of its final conclusion, does not necessarily reflect the validity of its reasoning process. This distinction underscores the necessity for more nuanced evaluation procedures in the field.

Recent scholarship on reasoning in LLMs has supplied evidence of impressive performance and flexible adaptation to machine generated or human feedback. Nonmonotonic reasoning, crucial to human cognition for navigating the real world, remains a challenging, yet understudied task. In this work, we study nonmonotonic reasoning capabilities of seven state-of-the-art LLMs in one abstract and one commonsense reasoning task featuring generics, such as 'Birds fly', and exceptions, 'Penguins don't fly' (see Fig. 1). While LLMs exhibit reasoning patterns in accordance with human nonmonotonic reasoning abilities, they fail to maintain stable beliefs on truth conditions of generics at the addition of supporting examples ('Owls fly') or unrelated information ('Lions have manes'). Our findings highlight pitfalls in attributing human reasoning behaviours to LLMs, as well as assessing general capabilities, while consistent reasoning remains elusive.

Chain of Thought (CoT) is significant in improving the reasoning abilities of large language models (LLMs). However, the correlation between the effectiveness of CoT and the length of reasoning steps in prompts remains largely unknown. To shed light on this, we have conducted several empirical experiments to explore the relations. Specifically, we design experiments that expand and compress the rationale reasoning steps within CoT demonstrations, while keeping all other factors constant. We have the following key findings. First, the results indicate that lengthening the reasoning steps in prompts, even without adding new information into the prompt, considerably enhances LLMs' reasoning abilities across multiple datasets. Alternatively, shortening the reasoning steps, even while preserving the key information, significantly diminishes the reasoning abilities of models. This finding highlights the importance of the number of steps in CoT prompts and provides practical guidance to make better use of LLMs' potential in complex problem-solving scenarios. Second, we also investigated the relationship between the performance of CoT and the rationales used in demonstrations. Surprisingly, the result shows that even incorrect rationales can yield favorable outcomes if they maintain the requisite length of inference. Third, we observed that the advantages of increasing reasoning steps are task-dependent: simpler tasks require fewer steps, whereas complex tasks gain significantly from longer inference sequences.

Recently, with the chain of thought (CoT) prompting, large language models (LLMs), e.g., GPT-3, have shown strong reasoning ability in several natural language processing tasks such as arithmetic, commonsense, and logical reasoning. However, LLMs with CoT require multi-step prompting and multi-token prediction, which is highly sensitive to individual mistakes and vulnerable to error accumulation. The above issues make the LLMs need the ability to verify the answers. In fact, after inferring conclusions in some thinking decision tasks, people often check them by re-verifying steps to avoid some mistakes. In this paper, we propose and prove that LLMs also have similar self-verification abilities. We take the conclusion obtained by CoT as one of the conditions for solving the original problem. By taking turns masking the original conditions and predicting their results, we calculate an explainable answer verification score based on whether the re-predicted conditions are correct. Experimental results demonstrate that the proposed method can improve the reasoning performance on various arithmetic, commonsense, and logical reasoning datasets. Our code is publicly available at: https://github.com/WENGSYX/Self-Verification.

Modern large language models (LLMs) employ various forms of logical inference, both implicitly and explicitly, when addressing reasoning tasks. Understanding how to optimally leverage these inference paradigms is critical for advancing LLMs' reasoning capabilities. This paper adopts an exploratory approach by introducing a controlled evaluation environment for analogical reasoning -- a fundamental cognitive task -- that is systematically parameterized across three dimensions: modality (textual, visual, symbolic), difficulty (easy, medium, hard), and task format (multiple-choice or free-text generation). We analyze the comparative dynamics of inductive, abductive, and deductive inference pipelines across these dimensions, and demonstrate that our findings generalize to broader in-context learning tasks. Additionally, we investigate advanced paradigms such as hypothesis selection, verification, and refinement, revealing their potential to scale up logical inference in LLM reasoning. This exploratory study provides a foundation for future research in enhancing LLM reasoning through systematic logical inference strategies.

Reasoning is a fundamental capability for solving complex multi-step problems, particularly in visual contexts where sequential step-wise understanding is essential. Existing approaches lack a comprehensive framework for evaluating visual reasoning and do not emphasize step-wise problem-solving. To this end, we propose a comprehensive framework for advancing step-by-step visual reasoning in large language models (LMMs) through three key contributions. First, we introduce a visual reasoning benchmark specifically designed to evaluate multi-step reasoning tasks. The benchmark presents a diverse set of challenges with eight different categories ranging from complex visual perception to scientific reasoning with over 4k reasoning steps in total, enabling robust evaluation of LLMs' abilities to perform accurate and interpretable visual reasoning across multiple steps. Second, we propose a novel metric that assesses visual reasoning quality at the granularity of individual steps, emphasizing both correctness and logical coherence. The proposed metric offers deeper insights into reasoning performance compared to traditional end-task accuracy metrics. Third, we present a new multimodal visual reasoning model, named LlamaV-o1, trained using a multi-step curriculum learning approach, where tasks are progressively organized to facilitate incremental skill acquisition and problem-solving. The proposed LlamaV-o1 is designed for multi-step reasoning and learns step-by-step through a structured training paradigm. Extensive experiments show that our LlamaV-o1 outperforms existing open-source models and performs favorably against close-source proprietary models. Compared to the recent Llava-CoT, our LlamaV-o1 achieves an average score of 67.3 with an absolute gain of 3.8\% across six benchmarks while being 5 times faster during inference scaling. Our benchmark, model, and code are publicly available.

Recent developments, particularly OpenAI's O1 model, have demonstrated the remarkable potential of Large Language Models (LLMs) for complex reasoning tasks. Through analysis of O1's outputs and provided sample Chain-of-Thought (CoT) demonstrations, we observe that it approaches problem-solving in a distinctly human-like manner, systematically brainstorming ideas, testing hypotheses, verifying results, and planning comprehensive solutions. These sophisticated reasoning capabilities remain notably absent in other state-of-the-art language models. In this paper, we hypothesize that this performance gap stems from the limited availability of high-quality reasoning process data in current training sets. We demonstrate that by constructing a specialized dataset focused on explicit problem-solving workflows ("worked solutions"), we can elicit substantially improved planning capabilities from existing models. Additionally, we propose the Reasoning Enhancement Loop (REL), a method for generating synthetic worked solutions.

The rapid advancement of large language models (LLMs) has significantly enhanced their reasoning abilities, enabling increasingly complex tasks. However, these capabilities often diminish in smaller, more computationally efficient models like GPT-2. Recent research shows that reasoning distillation can help small models acquire reasoning capabilities, but most existing methods focus primarily on improving teacher-generated reasoning paths. Our observations reveal that small models can generate high-quality reasoning paths during sampling, even without chain-of-thought prompting, though these paths are often latent due to their low probability under standard decoding strategies. To address this, we propose Self-Enhanced Reasoning Training (SERT), which activates and leverages latent reasoning capabilities in small models through self-training on filtered, self-generated reasoning paths under zero-shot conditions. Experiments using OpenAI's GPT-3.5 as the teacher model and GPT-2 models as the student models demonstrate that SERT enhances the reasoning abilities of small models, improving their performance in reasoning distillation.

To augment language models with the ability to reason, researchers usually prompt or finetune them to produce chain of thought reasoning steps before producing the final answer. However, although people use natural language to reason effectively, it may be that LMs could reason more effectively with some intermediate computation that is not in natural language. In this work, we explore an alternative reasoning approach: instead of explicitly producing the chain of thought reasoning steps, we use the language model's internal hidden states to perform implicit reasoning. The implicit reasoning steps are distilled from a teacher model trained on explicit chain-of-thought reasoning, and instead of doing reasoning "horizontally" by producing intermediate words one-by-one, we distill it such that the reasoning happens "vertically" among the hidden states in different layers. We conduct experiments on a multi-digit multiplication task and a grade school math problem dataset and find that this approach enables solving tasks previously not solvable without explicit chain-of-thought, at a speed comparable to no chain-of-thought.

Recent studies on transformer-based language models show that they can answer questions by reasoning over knowledge provided as part of the context (i.e., in-context reasoning). However, since the available knowledge is often not filtered for a particular question, in-context reasoning can be sensitive to distractor facts, additional content that is irrelevant to a question but that may be relevant for a different question (i.e., not necessarily random noise). In these situations, the model fails to distinguish the knowledge that is necessary to answer the question, leading to spurious reasoning and degraded performance. This reasoning failure contrasts with the model's apparent ability to distinguish its contextual knowledge from all the knowledge it has memorized during pre-training. Following this observation, we propose teaching the model to reason more robustly by folding the provided contextual knowledge into the model's parameters before presenting it with a question. Our method, RECKONING, is a bi-level learning algorithm that teaches language models to reason by updating their parametric knowledge through back-propagation, allowing them to then answer questions using the updated parameters. During training, the inner loop rapidly adapts a copy of the model weights to encode contextual knowledge into its parameters. In the outer loop, the model learns to use the updated weights to reproduce and answer reasoning questions about the memorized knowledge. Our experiments on two multi-hop reasoning datasets show that RECKONING's performance improves over the in-context reasoning baseline (by up to 4.5%). We also find that compared to in-context reasoning, RECKONING generalizes better to longer reasoning chains unseen during training, is more robust to distractors in the context, and is more computationally efficient when multiple questions are asked about the same knowledge.

Chain of Thought (CoT) of multi-step benefits from the logical structure of the reasoning steps and task-specific actions, significantly enhancing the mathematical reasoning capabilities of large language models. As the prevalence of long CoT, the number of reasoning steps exceeds manageable token limits and leads to higher computational demands. Inspired by the fundamental logic of human cognition, ``derive, then reduce'', we conceptualize the standard multi-step CoT as a novel Markov Chain of Thought (MCoT). In this study, we consider the mathematical reasoning task, defining each reasoning step as text accompanied by a Python code snippet. To facilitate a longer reasoning path, self-correction is enabled through interactions with the code interpreter. Our MCoT aims to compress previous reasoning steps into a simplified question, enabling efficient next-step inference without relying on a lengthy KV cache. In our experiments, we curate the MCoTInstruct dataset, and the empirical results indicate that MCoT not only significantly enhances efficiency but also maintains comparable accuracy. While much remains to be explored, this work paves the way for exploring the long CoT reasoning abilities of LLMs.

With recent advancements in large language models, methods like chain-of-thought prompting to elicit reasoning chains have been shown to improve results on reasoning tasks. However, tasks that require multiple steps of reasoning still pose significant challenges to state-of-the-art models. Drawing inspiration from the beam search algorithm, we propose PathFinder, a tree-search-based reasoning path generation approach. It enhances diverse branching and multi-hop reasoning through the integration of dynamic decoding, enabled by varying sampling methods and parameters. Using constrained reasoning, PathFinder integrates novel quality constraints, pruning, and exploration methods to enhance the efficiency and the quality of generation. Moreover, it includes scoring and ranking features to improve candidate selection. Our approach outperforms competitive baselines on three complex arithmetic and commonsense reasoning tasks by 6% on average. Our model generalizes well to longer, unseen reasoning chains, reflecting similar complexities to beam search with large branching factors.

Logical reasoning is fundamental for humans yet presents a substantial challenge in the domain of Artificial Intelligence. Initially, researchers used Knowledge Representation and Reasoning (KR) systems that did not scale and required non trivial manual effort. Recently, the emergence of large language models (LLMs) has demonstrated the ability to overcome various limitations of formal Knowledge Representation (KR) systems. Consequently, there is a growing interest in using LLMs for logical reasoning via natural language. This work strives to understand the proficiency of LLMs in logical reasoning by offering a brief review of the latest progress in this area; with a focus on the logical reasoning datasets, tasks, and the methods adopted to utilize LLMs for reasoning. To offer a thorough analysis, we have compiled a benchmark titled LogiGLUE. This includes 24 varied datasets encompassing deductive, abductive, and inductive reasoning. We have standardized these datasets into Seq2Seq tasks to facilitate straightforward training and evaluation for future research. Utilizing LogiGLUE as a foundation, we have trained an instruction fine tuned language model, resulting in LogiT5. We study single task training, multi task training, and a chain of thought knowledge distillation fine tuning technique to assess the performance of model across the different logical reasoning categories. By this comprehensive process, we aim to shed light on the capabilities and potential pathways for enhancing logical reasoning proficiency in LLMs, paving the way for more advanced and nuanced developments in this critical field.

Generating accurate step-by-step reasoning is essential for Large Language Models (LLMs) to address complex problems and enhance robustness and interpretability. Despite the flux of research on developing advanced reasoning approaches, systematically analyzing the diverse LLMs and reasoning strategies in generating reasoning chains remains a significant challenge. The difficulties stem from the lack of two key elements: (1) an automatic method for evaluating the generated reasoning chains on different tasks, and (2) a unified formalism and implementation of the diverse reasoning approaches for systematic comparison. This paper aims to close the gap: (1) We introduce AutoRace for fully automated reasoning chain evaluation. Existing metrics rely on expensive human annotations or pre-defined LLM prompts not adaptable to different tasks. In contrast, AutoRace automatically creates detailed evaluation criteria tailored for each task, and uses GPT-4 for accurate evaluation following the criteria. (2) We develop LLM Reasoners, a library for standardized modular implementation of existing and new reasoning algorithms, under a unified formulation of the search, reward, and world model components. With the new evaluation and library, (3) we conduct extensive study of different reasoning approaches (e.g., CoT, ToT, RAP). The analysis reveals interesting findings about different factors contributing to reasoning, including the reward-guidance, breadth-vs-depth in search, world model, and prompt formats, etc.

Large language models (LLMs) often struggle with maintaining accuracy across a sequence of intermediate reasoning steps in mathematical reasoning, leading to error propagation that undermines the final result. The current methodology to mitigate this issue primarily involves using a verifier model to assess the correctness of generated solution candidates, focusing either on the overall reasoning path or on an incomplete reasoning path. By rethinking this approach, we argue that assessing potentials of incomplete reasoning paths could be more advantageous as it guides towards correct final answers, transforming the task into a planning problem. Our proposed verifier, the Outcome-supervision Value Model (OVM), employs outcome supervision for training, offering an efficient and intuitive method for planning by prioritizing steps that lead to accurate conclusions over mere per-step correctness. Furthermore, the OVM eschews the need for labor-intensive annotations on step-level correctness, enhancing its scalability. Our experiments on two multi-step mathematical reasoning datasets, GSM8K and Game of 24, demonstrate the superior performance of the OVM model. Notably, in GSM8K, our OVM-7B model achieves state-of-the-art results among LLMs up to 13B parameters; especially it does not utilize GPT-4 or code execution. These findings offer a novel perspective on the role of outcome supervision in training verifiers for multi-step reasoning tasks and provide theoretical justification for its advantage in value estimation for planning.

Cognitive textual and visual reasoning tasks, such as puzzles, series, and analogies, demand the ability to quickly reason, decipher, and evaluate patterns both textually and spatially. While LLMs and VLMs, through extensive training on large amounts of human-curated data, have attained a high level of pseudo-human intelligence in some common sense reasoning tasks, they still struggle with more complex reasoning tasks that require cognitive understanding. In this work, we introduce a new dataset, NTSEBench, designed to evaluate the cognitive multi-modal reasoning and problem-solving skills of large models. The dataset comprises 2,728 multiple-choice questions comprising of a total of 4,642 images across 26 categories sampled from the NTSE examination conducted nationwide in India, featuring both visual and textual general aptitude questions that do not rely on rote learning. We establish baselines on the dataset using state-of-the-art LLMs and VLMs. To facilitate a comparison between open source and propriety models, we propose four distinct modeling strategies to handle different modalities (text and images) in the dataset instances.

The reasoning abilities of large language models (LLMs) have improved with chain-of-thought (CoT) prompting, allowing models to solve complex tasks in a stepwise manner. However, training CoT capabilities requires detailed reasoning data, which is often scarce. The self-taught reasoner (STaR) framework addresses this by using reinforcement learning to automatically generate reasoning steps, reducing reliance on human-labeled data. Although STaR and its variants have demonstrated empirical success, a theoretical foundation explaining these improvements is lacking. This work provides a theoretical framework for understanding the effectiveness of reinforcement learning on CoT reasoning and STaR. Our contributions are: (1) an analysis of policy improvement, showing why LLM reasoning improves iteratively with STaR; (2) conditions for convergence to an optimal reasoning policy; (3) an examination of STaR's robustness, explaining how it can improve reasoning even when incorporating occasional incorrect steps; and (4) criteria for the quality of pre-trained models necessary to initiate effective reasoning improvement. This framework aims to bridge empirical findings with theoretical insights, advancing reinforcement learning approaches for reasoning in LLMs.

Multi-hop question answering (MHQA) requires a model to retrieve and integrate information from multiple passages to answer a complex question. Recent systems leverage the power of large language models and integrate evidence retrieval with reasoning prompts (e.g., chain-of-thought reasoning) for the MHQA task. However, the complexities in the question types (bridge v.s. comparison questions) and the reasoning types (sequential v.s. parallel reasonings) require more novel and fine-grained prompting methods to enhance the performance of MHQA under the zero-shot setting. In this paper, we propose STOC-TOT, a stochastic tree-of-thought reasoning prompting method with constrained decoding for MHQA and conduct a detailed comparison with other reasoning prompts on different question types and reasoning types. Specifically, we construct a tree-like reasoning structure by prompting the model to break down the original question into smaller sub-questions to form different reasoning paths. In addition, we prompt the model to provide a probability estimation for each reasoning path at each reasoning step. At answer time, we conduct constrained decoding on the model to generate more grounded answers and reduce hallucination. Experiments comparing STOC-TOT with two MHQA datasets and five large language models showed that our framework outperforms other reasoning prompts by a significant margin.

Chain-of-Thought (CoT) prompting can dramatically improve the multi-step reasoning abilities of large language models (LLMs). CoT explicitly encourages the LLM to generate intermediate rationales for solving a problem, by providing a series of reasoning steps in the demonstrations. Despite its success, there is still little understanding of what makes CoT prompting effective and which aspects of the demonstrated reasoning steps contribute to its performance. In this paper, we show that CoT reasoning is possible even with invalid demonstrations - prompting with invalid reasoning steps can achieve over 80-90% of the performance obtained using CoT under various metrics, while still generating coherent lines of reasoning during inference. Further experiments show that other aspects of the rationales, such as being relevant to the query and correctly ordering the reasoning steps, are much more important for effective CoT reasoning. Overall, these findings both deepen our understanding of CoT prompting, and open up new questions regarding LLMs' capability to learn to reason in context.

Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms to the conclusion, which suffers from a combinatorial explosion of the search space, and thus high failure rates for problems requiring longer chains of reasoning. The classical automated reasoning literature has shown that reasoning in the backward direction (i.e. from the intended conclusion to supporting axioms) is significantly more efficient at proof-finding. Importing this intuition into the LM setting, we develop a Backward Chaining algorithm, called LAMBADA, that decomposes reasoning into four sub-modules. These sub-modules are simply implemented by few-shot prompted LM inference. We show that LAMBADA achieves sizable accuracy boosts over state-of-the-art forward reasoning methods on challenging logical reasoning datasets, particularly when deep and accurate proof chains are required.

Reasoning is a distinctive human capacity, enabling us to address complex problems by breaking them down into a series of manageable cognitive steps. Yet, complex logical reasoning is still cumbersome for language models. Based on the dual process theory in cognitive science, we are the first to unravel the cognitive reasoning abilities of language models. Our framework employs an iterative methodology to construct a Cognitive Tree (CogTree). The root node of this tree represents the initial query, while the leaf nodes consist of straightforward questions that can be answered directly. This construction involves two main components: the implicit extraction module (referred to as the intuitive system) and the explicit reasoning module (referred to as the reflective system). The intuitive system rapidly generates multiple responses by utilizing in-context examples, while the reflective system scores these responses using comparative learning. The scores guide the intuitive system in its subsequent generation step. Our experimental results on two popular and challenging reasoning tasks indicate that it is possible to achieve a performance level comparable to that of GPT-3.5 (with 175B parameters), using a significantly smaller language model that contains fewer parameters (<=7B) than 5% of GPT-3.5.

Reasoning is a fundamental component for achieving language understanding. Among the multiple types of reasoning, conditional reasoning, the ability to draw different conclusions depending on some condition, has been understudied in large language models (LLMs). Recent prompting methods, such as chain of thought, have significantly improved LLMs on reasoning tasks. Nevertheless, there is still little understanding of what triggers reasoning abilities in LLMs. We hypothesize that code prompts can trigger conditional reasoning in LLMs trained on text and code. We propose a chain of prompts that transforms a natural language problem into code and prompts the LLM with the generated code. Our experiments find that code prompts exhibit a performance boost between 2.6 and 7.7 points on GPT 3.5 across multiple datasets requiring conditional reasoning. We then conduct experiments to discover how code prompts elicit conditional reasoning abilities and through which features. We observe that prompts need to contain natural language text accompanied by high-quality code that closely represents the semantics of the instance text. Furthermore, we show that code prompts are more efficient, requiring fewer demonstrations, and that they trigger superior state tracking of variables or key entities.

Recent work has shown that language models (LMs) have strong multi-step (i.e., procedural) reasoning capabilities. However, it is unclear whether LMs perform these tasks by cheating with answers memorized from pretraining corpus, or, via a multi-step reasoning mechanism. In this paper, we try to answer this question by exploring a mechanistic interpretation of LMs for multi-step reasoning tasks. Concretely, we hypothesize that the LM implicitly embeds a reasoning tree resembling the correct reasoning process within it. We test this hypothesis by introducing a new probing approach (called MechanisticProbe) that recovers the reasoning tree from the model's attention patterns. We use our probe to analyze two LMs: GPT-2 on a synthetic task (k-th smallest element), and LLaMA on two simple language-based reasoning tasks (ProofWriter & AI2 Reasoning Challenge). We show that MechanisticProbe is able to detect the information of the reasoning tree from the model's attentions for most examples, suggesting that the LM indeed is going through a process of multi-step reasoning within its architecture in many cases.

Large language models (LLMs) have demonstrated impressive reasoning abilities in complex tasks. However, they lack up-to-date knowledge and experience hallucinations during reasoning, which can lead to incorrect reasoning processes and diminish their performance and trustworthiness. Knowledge graphs (KGs), which capture vast amounts of facts in a structured format, offer a reliable source of knowledge for reasoning. Nevertheless, existing KG-based LLM reasoning methods only treat KGs as factual knowledge bases and overlook the importance of their structural information for reasoning. In this paper, we propose a novel method called reasoning on graphs (RoG) that synergizes LLMs with KGs to enable faithful and interpretable reasoning. Specifically, we present a planning-retrieval-reasoning framework, where RoG first generates relation paths grounded by KGs as faithful plans. These plans are then used to retrieve valid reasoning paths from the KGs for LLMs to conduct faithful reasoning. Furthermore, RoG not only distills knowledge from KGs to improve the reasoning ability of LLMs through training but also allows seamless integration with any arbitrary LLMs during inference. Extensive experiments on two benchmark KGQA datasets demonstrate that RoG achieves state-of-the-art performance on KG reasoning tasks and generates faithful and interpretable reasoning results.

Exploiting large language models (LLMs) to tackle deductive reasoning has garnered growing attention. It still remains highly challenging to achieve satisfactory results in complex deductive problems, characterized by plenty of premises (i.e., facts or rules) entailing intricate relationships among entities and requiring multi-hop reasoning. One intuitive solution is to decompose the original task into smaller sub-tasks, and then chain the multiple casual reasoning steps together in a forward (e.g., Selection-Inference) or backward (e.g., LAMBADA) direction. However, these techniques inevitably necessitate a large number of overall stages, leading to computationally expensive operations and a higher possibility of making misleading steps. In addition to stage-by-stage decomposition, we draw inspiration from another aspect of human problem-solving. Humans tend to distill the most relevant information and organize their thoughts systematically (e.g., creating mind maps), which assists them in answering questions or drawing conclusions precisely and quickly. In light of this, we propose a novel reasoning approach named Concise and Organized Perception (COP). COP carefully analyzes the given statements to efficiently identify the most pertinent information while eliminating redundancy. It then prompts the LLMs in a more organized form that adapts to the model's inference process. By perceiving concise and organized proofs, the deductive reasoning abilities of LLMs can be better elicited, and the risk of acquiring errors caused by excessive reasoning stages is mitigated. Furthermore, our approach can be combined with the aforementioned ones to further boost their performance. Extensive experimental results on three popular deductive benchmarks (i.e., ProofWriter, PrOntoQA and PrOntoQA-OOD) show that COP significantly outperforms previous state-of-the-art methods.

Recent research on Large Language Models (LLMs) has led to remarkable advancements in general NLP AI assistants. Some studies have further explored the use of LLMs for planning and invoking models or APIs to address more general multi-modal user queries. Despite this progress, complex visual-based tasks still remain challenging due to the diverse nature of visual tasks. This diversity is reflected in two aspects: 1) Reasoning paths. For many real-life applications, it is hard to accurately decompose a query simply by examining the query itself. Planning based on the specific visual content and the results of each step is usually required. 2) Flexible inputs and intermediate results. Input forms could be flexible for in-the-wild cases, and involves not only a single image or video but a mixture of videos and images, e.g., a user-view image with some reference videos. Besides, a complex reasoning process will also generate diverse multimodal intermediate results, e.g., video narrations, segmented video clips, etc. To address such general cases, we propose a multi-modal AI assistant, AssistGPT, with an interleaved code and language reasoning approach called Plan, Execute, Inspect, and Learn (PEIL) to integrate LLMs with various tools. Specifically, the Planner is capable of using natural language to plan which tool in Executor should do next based on the current reasoning progress. Inspector is an efficient memory manager to assist the Planner to feed proper visual information into a specific tool. Finally, since the entire reasoning process is complex and flexible, a Learner is designed to enable the model to autonomously explore and discover the optimal solution. We conducted experiments on A-OKVQA and NExT-QA benchmarks, achieving state-of-the-art results. Moreover, showcases demonstrate the ability of our system to handle questions far more complex than those found in the benchmarks.

The reasoning segmentation task, which demands a nuanced comprehension of intricate queries to accurately pinpoint object regions, is attracting increasing attention. However, Multi-modal Large Language Models (MLLM) often find it difficult to accurately localize the objects described in complex reasoning contexts. We believe that the act of reasoning segmentation should mirror the cognitive stages of human visual search, where each step is a progressive refinement of thought toward the final object. Thus we introduce the Chains of Reasoning and Segmenting (CoReS) and find this top-down visual hierarchy indeed enhances the visual search process. Specifically, we propose a dual-chain structure that generates multi-modal, chain-like outputs to aid the segmentation process. Furthermore, to steer the MLLM's outputs into this intended hierarchy, we incorporate in-context inputs as guidance. Extensive experiments demonstrate the superior performance of our CoReS, which surpasses the state-of-the-art method by 6.5\% on the ReasonSeg dataset. Project: https://chain-of-reasoning-and-segmentation.github.io/.

The integration of slow-thinking mechanisms into large language models (LLMs) offers a promising way toward achieving Level 2 AGI Reasoners, as exemplified by systems like OpenAI's o1. However, several significant challenges remain, including inefficient overthinking and an overreliance on auxiliary reward models. We point out that these limitations stem from LLMs' inability to internalize the search process, a key component of effective reasoning. A critical step toward addressing this issue is enabling LLMs to autonomously determine when and where to backtrack, a fundamental operation in traditional search algorithms. To this end, we propose a self-backtracking mechanism that equips LLMs with the ability to backtrack during both training and inference. This mechanism not only enhances reasoning ability but also efficiency by transforming slow-thinking processes into fast-thinking through self-improvement. Empirical evaluations demonstrate that our proposal significantly enhances the reasoning capabilities of LLMs, achieving a performance gain of over 40 percent compared to the optimal-path supervised fine-tuning method. We believe this study introduces a novel and promising pathway for developing more advanced and robust Reasoners.

Large language models (LLMs) have shown remarkable reasoning capabilities given chain-of-thought prompts (examples with intermediate reasoning steps). Existing benchmarks measure reasoning ability indirectly, by evaluating accuracy on downstream tasks such as mathematical reasoning. However, it is unclear how these models obtain the answers and whether they rely on simple heuristics rather than the generated chain-of-thought. To enable systematic exploration of the reasoning ability of LLMs, we present a new synthetic question-answering dataset called PrOntoQA, where each example is generated from a synthetic world model represented in first-order logic. This allows us to parse the generated chain-of-thought into symbolic proofs for formal analysis. Our analysis on InstructGPT and GPT-3 shows that LLMs are quite capable of making correct individual deduction steps, and so are generally capable of reasoning, even in fictional contexts. However, they have difficulty with proof planning: When multiple valid deduction steps are available, they are not able to systematically explore the different options.

The recent development of chain-of-thought (CoT) decoding has enabled large language models (LLMs) to generate explicit logical reasoning paths for complex problem-solving. However, research indicates that these paths are not always deliberate and optimal. The tree-of-thought (ToT) method employs tree-searching to extensively explore the reasoning space and find better reasoning paths that CoT decoding might overlook. This deliberation, however, comes at the cost of significantly increased inference complexity. In this work, we demonstrate that fine-tuning LLMs leveraging the search tree constructed by ToT allows CoT to achieve similar or better performance, thereby avoiding the substantial inference burden. This is achieved through Chain of Preference Optimization (CPO), where LLMs are fine-tuned to align each step of the CoT reasoning paths with those of ToT using the inherent preference information in the tree-search process. Extensive experimental results show that CPO significantly improves LLM performance in solving a variety of complex problems, including question answering, fact verification, and arithmetic reasoning, demonstrating its effectiveness. Our code is available at https://github.com/sail-sg/CPO.

Large language models (LLMs) have been routinely used to solve various tasks using step-by-step reasoning. However, the structure of intermediate reasoning steps, or thoughts, is rigid and unidirectional, such as chains, trees, or acyclic-directed graphs. Consequently, the resulting inflexible and forward-only reasoning may not address challenging tasks and fail when the LLM frequently gives false responses, i.e., ``hallucinations''. This paper proposes a new reasoning framework, called Thought Rollback (TR), allowing LLMs to adaptively build thought structure while maintaining effective reasoning toward problem-solving under ``hallucinations''. The core mechanism of TR is rolling back thoughts, which allows LLMs to perform error analysis on thoughts, and thus roll back to any previously mistaken thought for revision. Subsequently, by including such trial-and-error in the prompt to guide the LLM, each rollback leads to one more reliable reasoning path. Therefore, starting with a simple prompt without human annotations, LLM with TR adaptively and gradually explores thoughts for a correct solution. Comprehensive experiments on mathematical problems and multi-task reasoning demonstrate the state-of-the-art performance of TR in terms of problem-solving rate and interaction cost. For instance, the solving rate of GPT-4 with TR outperforms the current best by 9% on the MATH dataset.

Step-by-step reasoning is widely used to enhance the reasoning ability of large language models (LLMs) in complex problems. Evaluating the quality of reasoning traces is crucial for understanding and improving LLM reasoning. However, the evaluation criteria remain highly unstandardized, leading to fragmented efforts in developing metrics and meta-evaluation benchmarks. To address this gap, this survey provides a comprehensive overview of step-by-step reasoning evaluation, proposing a taxonomy of evaluation criteria with four top-level categories (groundedness, validity, coherence, and utility). We then categorize metrics based on their implementations, survey which metrics are used for assessing each criterion, and explore whether evaluator models can transfer across different criteria. Finally, we identify key directions for future research.

This paper introduces Typhoon T1, an open effort to develop an open Thai reasoning model. A reasoning model is a relatively new type of generative model built on top of large language models (LLMs). A reasoning model generates a long chain of thought before arriving at a final answer, an approach found to improve performance on complex tasks. However, details on developing such a model are limited, especially for reasoning models that can generate traces in a low-resource language. Typhoon T1 presents an open effort that dives into the details of developing a reasoning model in a more cost-effective way by leveraging supervised fine-tuning using open datasets, instead of reinforcement learning. This paper shares the details about synthetic data generation and training, as well as our dataset and model weights. Additionally, we provide insights gained from developing a reasoning model that generalizes across domains and is capable of generating reasoning traces in a low-resource language, using Thai as an example. We hope this open effort provides a foundation for further research in this field.

Large Language Models (LLMs) have achieved remarkable success in reasoning tasks with the development of prompting methods. However, existing prompting approaches cannot reuse insights of solving similar problems and suffer from accumulated errors in multi-step reasoning, since they prompt LLMs to reason from scratch. To address these issues, we propose \textit{Thought Propagation (TP)}, which explores the analogous problems and leverages their solutions to enhance the complex reasoning ability of LLMs. These analogous problems are related to the input one, with reusable solutions and problem-solving strategies. Thus, it is promising to propagate insights of solving previous analogous problems to inspire new problem-solving. To achieve this, TP first prompts LLMs to propose and solve a set of analogous problems that are related to the input one. Then, TP reuses the results of analogous problems to directly yield a new solution or derive a knowledge-intensive plan for execution to amend the initial solution obtained from scratch. TP is compatible with existing prompting approaches, allowing plug-and-play generalization and enhancement in a wide range of tasks without much labor in task-specific prompt engineering. Experiments across three challenging tasks demonstrate TP enjoys a substantial improvement over the baselines by an average of 12\% absolute increase in finding the optimal solutions in Shortest-path Reasoning, 13\% improvement of human preference in Creative Writing, and 15\% enhancement in the task completion rate of LLM-Agent Planning.

Large Language Models (LLMs) significantly benefit from Chain-of-Thought (CoT) prompting in performing various reasoning tasks. While CoT allows models to produce more comprehensive reasoning processes, its emphasis on intermediate reasoning steps can inadvertently introduce hallucinations and accumulated errors, thereby limiting models' ability to solve complex reasoning tasks. Inspired by how humans engage in careful and meticulous deductive logical reasoning processes to solve tasks, we seek to enable language models to perform explicit and rigorous deductive reasoning, and also ensure the trustworthiness of their reasoning process through self-verification. However, directly verifying the validity of an entire deductive reasoning process is challenging, even with advanced models like ChatGPT. In light of this, we propose to decompose a reasoning verification process into a series of step-by-step subprocesses, each only receiving their necessary context and premises. To facilitate this procedure, we propose Natural Program, a natural language-based deductive reasoning format. Our approach enables models to generate precise reasoning steps where subsequent steps are more rigorously grounded on prior steps. It also empowers language models to carry out reasoning self-verification in a step-by-step manner. By integrating this verification process into each deductive reasoning stage, we significantly enhance the rigor and trustfulness of generated reasoning steps. Along this process, we also improve the answer correctness on complex reasoning tasks. Code will be released at https://github.com/lz1oceani/verify_cot.

The field of natural language processing (NLP) has witnessed significant progress in recent years, with a notable focus on improving large language models' (LLM) performance through innovative prompting techniques. Among these, prompt engineering coupled with structures has emerged as a promising paradigm, with designs such as Chain-of-Thought, Tree of Thoughts, or Graph of Thoughts, in which the overall LLM reasoning is guided by a structure such as a graph. As illustrated with numerous examples, this paradigm significantly enhances the LLM's capability to solve numerous tasks, ranging from logical or mathematical reasoning to planning or creative writing. To facilitate the understanding of this growing field and pave the way for future developments, we devise a general blueprint for effective and efficient LLM reasoning schemes. For this, we conduct an in-depth analysis of the prompt execution pipeline, clarifying and clearly defining different concepts. We then build the first taxonomy of structure-enhanced LLM reasoning schemes. We focus on identifying fundamental classes of harnessed structures, and we analyze the representations of these structures, algorithms executed with these structures, and many others. We refer to these structures as reasoning topologies, because their representation becomes to a degree spatial, as they are contained within the LLM context. Our study compares existing prompting schemes using the proposed taxonomy, discussing how certain design choices lead to different patterns in performance and cost. We also outline theoretical underpinnings, relationships between prompting and others parts of the LLM ecosystem such as knowledge bases, and the associated research challenges. Our work will help to advance future prompt engineering techniques.

Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to compositional rules - rules consisting of multiple elements which form a complex logical expression. Reasoning about compositional rules is challenging because it requires multiple reasoning steps, and attending to the logical relationships between elements. We introduce a new prompting method, Chain of Logic, which elicits rule-based reasoning through decomposition (solving elements as independent threads of logic), and recomposition (recombining these sub-answers to resolve the underlying logical expression). This method was inspired by the IRAC (Issue, Rule, Application, Conclusion) framework, a sequential reasoning approach used by lawyers. We evaluate chain of logic across eight rule-based reasoning tasks involving three distinct compositional rules from the LegalBench benchmark and demonstrate it consistently outperforms other prompting methods, including chain of thought and self-ask, using open-source and commercial language models.

Composing knowledge from multiple pieces of texts is a key challenge in multi-hop question answering. We present a multi-hop reasoning dataset, Question Answering via Sentence Composition(QASC), that requires retrieving facts from a large corpus and composing them to answer a multiple-choice question. QASC is the first dataset to offer two desirable properties: (a) the facts to be composed are annotated in a large corpus, and (b) the decomposition into these facts is not evident from the question itself. The latter makes retrieval challenging as the system must introduce new concepts or relations in order to discover potential decompositions. Further, the reasoning model must then learn to identify valid compositions of these retrieved facts using common-sense reasoning. To help address these challenges, we provide annotation for supporting facts as well as their composition. Guided by these annotations, we present a two-step approach to mitigate the retrieval challenges. We use other multiple-choice datasets as additional training data to strengthen the reasoning model. Our proposed approach improves over current state-of-the-art language models by 11% (absolute). The reasoning and retrieval problems, however, remain unsolved as this model still lags by 20% behind human performance.

The context window of large language models (LLMs) has been extended significantly in recent years. However, while the context length that the LLM can process has grown, the capability of the model to accurately reason over that context degrades noticeably. This occurs because modern LLMs often become overwhelmed by the vast amount of information in the context; when answering questions, the model must identify and reason over relevant evidence sparsely distributed throughout the text. To alleviate the challenge of long-context reasoning, we develop a retrieve-then-reason framework, enabling LLMs to reason over relevant evidence collected during an intermediate retrieval step. We find that modern LLMs struggle to accurately retrieve relevant facts and instead, often hallucinate "retrieved facts", resulting in flawed reasoning and the production of incorrect answers. To address these issues, we introduce ALR^2, a method that augments the long-context reasoning capability of LLMs via an explicit two-stage procedure, i.e., aligning LLMs with the objectives of both retrieval and reasoning. We demonstrate the efficacy of ALR^2 for mitigating performance degradation in long-context reasoning tasks. Through extensive experiments on long-context QA benchmarks, we find our method to outperform competitive baselines by large margins, achieving at least 8.4 and 7.9 EM gains on the long-context versions of HotpotQA and SQuAD datasets, respectively.

Large language models (LLMs) are restricted to reason in the "language space", where they typically express the reasoning process with a chain-of-thought (CoT) to solve a complex reasoning problem. However, we argue that language space may not always be optimal for reasoning. For example, most word tokens are primarily for textual coherence and not essential for reasoning, while some critical tokens require complex planning and pose huge challenges to LLMs. To explore the potential of LLM reasoning in an unrestricted latent space instead of using natural language, we introduce a new paradigm Coconut (Chain of Continuous Thought). We utilize the last hidden state of the LLM as a representation of the reasoning state (termed "continuous thought"). Rather than decoding this into a word token, we feed it back to the LLM as the subsequent input embedding directly in the continuous space. Experiments show that Coconut can effectively augment the LLM on several reasoning tasks. This novel latent reasoning paradigm leads to emergent advanced reasoning patterns: the continuous thought can encode multiple alternative next reasoning steps, allowing the model to perform a breadth-first search (BFS) to solve the problem, rather than prematurely committing to a single deterministic path like CoT. Coconut outperforms CoT in certain logical reasoning tasks that require substantial backtracking during planning, with fewer thinking tokens during inference. These findings demonstrate the promise of latent reasoning and offer valuable insights for future research.

Large Language Models (LLMs) have showcased impressive reasoning capabilities, particularly when guided by specifically designed prompts in complex reasoning tasks such as math word problems. These models typically solve tasks using a chain-of-thought approach, which not only bolsters their reasoning abilities but also provides valuable insights into their problem-solving process. However, there is still significant room for enhancing the reasoning abilities of LLMs. Some studies suggest that the integration of an LLM output verifier can boost reasoning accuracy without necessitating additional model training. In this paper, we follow these studies and introduce a novel graph-based method to further augment the reasoning capabilities of LLMs. We posit that multiple solutions to a reasoning task, generated by an LLM, can be represented as a reasoning graph due to the logical connections between intermediate steps from different reasoning paths. Therefore, we propose the Reasoning Graph Verifier (RGV) to analyze and verify the solutions generated by LLMs. By evaluating these graphs, models can yield more accurate and reliable results.Our experimental results show that our graph-based verification method not only significantly enhances the reasoning abilities of LLMs but also outperforms existing verifier methods in terms of improving these models' reasoning performance.

Large Language Models (LLMs) were shown to struggle with long-term planning, which may be caused by the limited way in which they explore the space of possible solutions. We propose an architecture where a Reinforcement Learning (RL) Agent guides an LLM's space exploration: (1) the Agent has access to domain-specific information, and can therefore make decisions about the quality of candidate solutions based on specific and relevant metrics, which were not explicitly considered by the LLM's training objective; (2) the LLM can focus on generating immediate next steps, without the need for long-term planning. We allow non-linear reasoning by exploring alternative paths and backtracking. We evaluate this architecture on the program equivalence task, and compare it against Chain of Thought (CoT) and Tree of Thoughts (ToT). We assess both the downstream task, denoting the binary classification, and the intermediate reasoning steps. Our approach compares positively against CoT and ToT.

Chain-of-thought (CoT) reasoning has enabled large language models (LLMs) to utilize additional computation through intermediate tokens to solve complex tasks. However, we posit that typical reasoning traces contain many redundant tokens, incurring extraneous inference costs. Upon examination of the output distribution of current LLMs, we find evidence on their latent ability to reason more concisely, relative to their default behavior. To elicit this capability, we propose simple fine-tuning methods which leverage self-generated concise reasoning paths obtained by best-of-N sampling and few-shot conditioning, in task-specific settings. Our combined method achieves a 30% reduction in output tokens on average, across five model families on GSM8K and MATH, while maintaining average accuracy. By exploiting the fundamental stochasticity and in-context learning capabilities of LLMs, our self-training approach robustly elicits concise reasoning on a wide range of models, including those with extensive post-training. Code is available at https://github.com/TergelMunkhbat/concise-reasoning

We study whether Large Language Models (LLMs) latently perform multi-hop reasoning with complex prompts such as "The mother of the singer of 'Superstition' is". We look for evidence of a latent reasoning pathway where an LLM (1) latently identifies "the singer of 'Superstition'" as Stevie Wonder, the bridge entity, and (2) uses its knowledge of Stevie Wonder's mother to complete the prompt. We analyze these two hops individually and consider their co-occurrence as indicative of latent multi-hop reasoning. For the first hop, we test if changing the prompt to indirectly mention the bridge entity instead of any other entity increases the LLM's internal recall of the bridge entity. For the second hop, we test if increasing this recall causes the LLM to better utilize what it knows about the bridge entity. We find strong evidence of latent multi-hop reasoning for the prompts of certain relation types, with the reasoning pathway used in more than 80% of the prompts. However, the utilization is highly contextual, varying across different types of prompts. Also, on average, the evidence for the second hop and the full multi-hop traversal is rather moderate and only substantial for the first hop. Moreover, we find a clear scaling trend with increasing model size for the first hop of reasoning but not for the second hop. Our experimental findings suggest potential challenges and opportunities for future development and applications of LLMs.

Strategies such as chain-of-thought prompting improve the performance of large language models (LLMs) on complex reasoning tasks by decomposing input examples into intermediate steps. However, it remains unclear how to apply such methods to reason over long input documents, in which both the decomposition and the output of each intermediate step are non-trivial to obtain. In this work, we propose PEARL, a prompting framework to improve reasoning over long documents, which consists of three stages: action mining, plan formulation, and plan execution. More specifically, given a question about a long document, PEARL decomposes the question into a sequence of actions (e.g., SUMMARIZE, FIND_EVENT, FIND_RELATION) and then executes them over the document to obtain the answer. Each stage of PEARL is implemented via zero-shot or few-shot prompting of LLMs (in our work, GPT-4) with minimal human input. We evaluate PEARL on a challenging subset of the QuALITY dataset, which contains questions that require complex reasoning over long narrative texts. PEARL outperforms zero-shot and chain-of-thought prompting on this dataset, and ablation experiments show that each stage of PEARL is critical to its performance. Overall, PEARL is a first step towards leveraging LLMs to reason over long documents.

Large Language Models (LLMs) have shown potential in reasoning over structured environments, e.g., knowledge graph and table. Such tasks typically require multi-hop reasoning, i.e., match natural language utterance with instances in the environment. Previous methods leverage LLMs to incrementally build a reasoning path, where the LLMs either invoke tools or pick up schemas by step-by-step interacting with the environment. We propose Reasoning-Path-Editing (Readi), a novel framework where LLMs can efficiently and faithfully reason over structured environments. In Readi, LLMs initially generate a reasoning path given a query, and edit the path only when necessary. We instantiate the path on structured environments and provide feedback to edit the path if anything goes wrong. Experimental results on three KGQA and two TableQA datasets show the effectiveness of Readi, significantly surpassing previous LLM-based methods (by 9.1% Hit@1 on WebQSP, 12.4% on MQA-3H and 9.5% on WTQ), comparable with state-of-the-art fine-tuned methods (67% on CWQ and 74.7% on WebQSP) and substantially boosting the vanilla LLMs (by 14.9% on CWQ). Our code will be available on https://aka.ms/readi.

Large language models (LLMs) have shown increasing in-context learning capabilities through scaling up model and data size. Despite this progress, LLMs are still unable to solve algorithmic reasoning problems. While providing a rationale with the final answer has led to further improvements in multi-step reasoning problems, Anil et al. 2022 showed that even simple algorithmic reasoning tasks such as parity are far from solved. In this work, we identify and study four key stages for successfully teaching algorithmic reasoning to LLMs: (1) formulating algorithms as skills, (2) teaching multiple skills simultaneously (skill accumulation), (3) teaching how to combine skills (skill composition) and (4) teaching how to use skills as tools. We show that it is possible to teach algorithmic reasoning to LLMs via in-context learning, which we refer to as algorithmic prompting. We evaluate our approach on a variety of arithmetic and quantitative reasoning tasks, and demonstrate significant boosts in performance over existing prompting techniques. In particular, for long parity, addition, multiplication and subtraction, we achieve an error reduction of approximately 10x, 9x, 5x and 2x respectively compared to the best available baselines.

Current large language models can perform reasonably well on complex tasks that require step-by-step reasoning with few-shot learning. Are these models applying reasoning skills they have learnt during pre-training and reason outside of their training context, or are they simply memorizing their training corpus at finer granularity and have learnt to better understand their context? To tease apart these possibilities, we introduce ALERT, a benchmark and suite of analyses for assessing language models' reasoning ability comparing pre-trained and finetuned models on complex tasks that require reasoning skills to solve. ALERT provides a test bed to asses any language model on fine-grained reasoning skills, which spans over 20 datasets and covers 10 different reasoning skills. We leverage ALERT to further investigate the role of finetuning. With extensive empirical analysis we find that language models learn more reasoning skills such as textual entailment, abductive reasoning, and analogical reasoning during finetuning stage compared to pretraining state. We also find that when language models are finetuned they tend to overfit to the prompt template, which hurts the robustness of models causing generalization problems.

Spatial reasoning plays a vital role in both human cognition and machine intelligence, prompting new research into language models' (LMs) capabilities in this regard. However, existing benchmarks reveal shortcomings in evaluating qualitative spatial reasoning (QSR). These benchmarks typically present oversimplified scenarios or unclear natural language descriptions, hindering effective evaluation. We present a novel benchmark for assessing QSR in LMs, which is grounded in realistic 3D simulation data, offering a series of diverse room layouts with various objects and their spatial relationships. This approach provides a more detailed and context-rich narrative for spatial reasoning evaluation, diverging from traditional, toy-task-oriented scenarios. Our benchmark encompasses a broad spectrum of qualitative spatial relationships, including topological, directional, and distance relations. These are presented with different viewing points, varied granularities, and density of relation constraints to mimic real-world complexities. A key contribution is our logic-based consistency-checking tool, which enables the assessment of multiple plausible solutions, aligning with real-world scenarios where spatial relationships are often open to interpretation. Our benchmark evaluation of advanced LMs reveals their strengths and limitations in spatial reasoning. They face difficulties with multi-hop spatial reasoning and interpreting a mix of different view descriptions, pointing to areas for future improvement.

Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer language models (LMs) can reason according to logical rules. We ask whether those LMs can deduce theorems in propositional calculus and first-order logic; if their relative success in these problems reflects general logical capabilities; and which layers contribute the most to the task. First, we show for several encoder-only LMs that they can be trained, to a reasonable degree, to determine logical validity on various datasets. Next, by cross-probing fine-tuned models on these datasets, we show that LMs have difficulty in transferring their putative logical reasoning ability, which suggests that they may have learned dataset-specific features, instead of a general capability. Finally, we conduct a layerwise probing experiment, which shows that the hypothesis classification task is mostly solved through higher layers.

This study focuses on improving the performance of lightweight Large Language Models (LLMs) in mathematical reasoning tasks. We introduce a novel method for measuring mathematical logic similarity and design an automatic screening mechanism to construct a set of reference problems that integrate both semantic and logical similarity. By employing carefully crafted positive and negative example prompts, we guide the model towards adopting sound reasoning logic. To the best of our knowledge, this is the first attempt to utilize retrieval-enhanced generation for mathematical problem-solving. Experimental results demonstrate that our method achieves a 15.8% improvement over the Chain of Thought approach on the SVAMP dataset and a 21.5 % improvement on the GSM8K dataset. Further application of this method to a large-scale model with 175 billion parameters yields performance comparable to the best results on both aforementioned datasets. Finally, we conduct an analysis of errors during the reasoning process, providing valuable insights and directions for future research on reasoning tasks using large language models.

Chain-of-thought reasoning, a cognitive process fundamental to human intelligence, has garnered significant attention in the realm of artificial intelligence and natural language processing. However, there still remains a lack of a comprehensive survey for this arena. To this end, we take the first step and present a thorough survey of this research field carefully and widely. We use X-of-Thought to refer to Chain-of-Thought in a broad sense. In detail, we systematically organize the current research according to the taxonomies of methods, including XoT construction, XoT structure variants, and enhanced XoT. Additionally, we describe XoT with frontier applications, covering planning, tool use, and distillation. Furthermore, we address challenges and discuss some future directions, including faithfulness, multi-modal, and theory. We hope this survey serves as a valuable resource for researchers seeking to innovate within the domain of chain-of-thought reasoning.

State-of-the-art Large Language Models (LLMs) are accredited with an increasing number of different capabilities, ranging from reading comprehension, over advanced mathematical and reasoning skills to possessing scientific knowledge. In this paper we focus on their multi-hop reasoning capability: the ability to identify and integrate information from multiple textual sources. Given the concerns with the presence of simplifying cues in existing multi-hop reasoning benchmarks, which allow models to circumvent the reasoning requirement, we set out to investigate, whether LLMs are prone to exploiting such simplifying cues. We find evidence that they indeed circumvent the requirement to perform multi-hop reasoning, but they do so in more subtle ways than what was reported about their fine-tuned pre-trained language model (PLM) predecessors. Motivated by this finding, we propose a challenging multi-hop reasoning benchmark, by generating seemingly plausible multi-hop reasoning chains, which ultimately lead to incorrect answers. We evaluate multiple open and proprietary state-of-the-art LLMs, and find that their performance to perform multi-hop reasoning is affected, as indicated by up to 45% relative decrease in F1 score when presented with such seemingly plausible alternatives. We conduct a deeper analysis and find evidence that while LLMs tend to ignore misleading lexical cues, misleading reasoning paths indeed present a significant challenge.

Large Language Models (LLMs) have demonstrated strong performance in handling complex tasks requiring both extensive knowledge and reasoning abilities. However, the existing LLM inference pipeline operates as an opaque process without explicit separation between knowledge retrieval and reasoning steps, making the model's decision-making process unclear and disorganized. This ambiguity can lead to issues such as hallucinations and knowledge forgetting, which significantly impact the reliability of LLMs in high-stakes domains. In this paper, we propose a new inference paradigm that decomposes the complex inference process into two distinct and clear actions: (1) memory recall: which retrieves relevant knowledge, and (2) reasoning: which performs logical steps based on the recalled knowledge. To facilitate this decomposition, we introduce two special tokens memory and reason, guiding the model to distinguish between steps that require knowledge retrieval and those that involve reasoning. Our experiment results show that this decomposition not only improves model performance but also enhances the interpretability of the inference process, enabling users to identify sources of error and refine model responses effectively. The code is available at https://github.com/MingyuJ666/Disentangling-Memory-and-Reasoning.

In enhancing the reasoning capabilities of large language models (LLMs), prior research primarily focuses on specific prompting techniques such as few-shot or zero-shot chain-of-thought (CoT) prompting. These methods, while effective, often involve manually intensive prompt engineering. Our study takes a novel approach by asking: Can LLMs reason effectively without prompting? Our findings reveal that, intriguingly, CoT reasoning paths can be elicited from pre-trained LLMs by simply altering the decoding process. Rather than conventional greedy decoding, we investigate the top-k alternative tokens, uncovering that CoT paths are frequently inherent in these sequences. This approach not only bypasses the confounders of prompting but also allows us to assess the LLMs' intrinsic reasoning abilities. Moreover, we observe that the presence of a CoT in the decoding path correlates with a higher confidence in the model's decoded answer. This confidence metric effectively differentiates between CoT and non-CoT paths. Extensive empirical studies on various reasoning benchmarks show that the proposed CoT-decoding substantially outperforms the standard greedy decoding.

Large language models (LLMs) are capable of answering knowledge-intensive complex questions with chain-of-thought (CoT) reasoning. However, they tend to generate factually incorrect reasoning steps when the required knowledge is not available or up-to-date in models' parameters. Recent works turn to retrieving external knowledge to augment CoT reasoning. Despite being promising, these chain-based methods suffer from: 1) Negative retrieval. Unnecessary or incorrect retrieval may mislead the reasoning; 2) Limited sight. Lacking the ability to look backward or forward, a local error in one step will propagate along the chain. In this paper, we propose a novel approach: Probabilistic Tree-of-thought Reasoning (ProbTree). First, LLMs translate a complex question into a query tree, in which each non-root node denotes a sub-question of its parent node. Then, probabilistic reasoning is conducted over the tree, by solving questions from leaf to root considering the confidence of both question decomposing and answering. During reasoning, for leaf nodes, LLMs choose a more confident answer from Closed-book QA that employs parametric knowledge and Open-book QA that employs retrieved external knowledge, thus eliminating the negative retrieval problem. For non-leaf nodes, with the hierarchical structure, LLMs have broader sights and are able to globally reason with the information from child nodes, thus recovering from local errors. The experiments on three Complex QA datasets under the open-domain setting show that our approach outperforms SOTA methods significantly, demonstrating the effect of probabilistic tree-of-thought reasoning.

Large Language Models (LLMs) have shown remarkable reasoning capabilities on complex tasks, but they still suffer from out-of-date knowledge, hallucinations, and opaque decision-making. In contrast, Knowledge Graphs (KGs) can provide explicit and editable knowledge for LLMs to alleviate these issues. Existing paradigm of KG-augmented LLM manually predefines the breadth of exploration space and requires flawless navigation in KGs. However, this paradigm cannot adaptively explore reasoning paths in KGs based on the question semantics and self-correct erroneous reasoning paths, resulting in a bottleneck in efficiency and effect. To address these limitations, we propose a novel self-correcting adaptive planning paradigm for KG-augmented LLM named Plan-on-Graph (PoG), which first decomposes the question into several sub-objectives and then repeats the process of adaptively exploring reasoning paths, updating memory, and reflecting on the need to self-correct erroneous reasoning paths until arriving at the answer. Specifically, three important mechanisms of Guidance, Memory, and Reflection are designed to work together, to guarantee the adaptive breadth of self-correcting planning for graph reasoning. Finally, extensive experiments on three real-world datasets demonstrate the effectiveness and efficiency of PoG.

Reasoning system dynamics is one of the most important analytical approaches for many scientific studies. With the initial state of a system as input, the recent graph neural networks (GNNs)-based methods are capable of predicting the future state distant in time with high accuracy. Although these methods have diverse designs in modeling the coordinates and interacting forces of the system, we show that they actually share a common paradigm that learns the integration of the velocity over the interval between the initial and terminal coordinates. However, their integrand is constant w.r.t. time. Inspired by this observation, we propose a new approach to predict the integration based on several velocity estimations with Newton-Cotes formulas and prove its effectiveness theoretically. Extensive experiments on several benchmarks empirically demonstrate consistent and significant improvement compared with the state-of-the-art methods.

We endow Large Language Models (LLMs) with fine-grained self-evaluation to refine multi-step reasoning inference. We propose an effective prompting approach that integrates self-evaluation guidance through stochastic beam search. Our approach explores the reasoning search space using a well-calibrated automatic criterion. This enables an efficient search to produce higher-quality final predictions. With the self-evaluation guided stochastic beam search, we also balance the quality-diversity trade-off in the generation of reasoning chains. This allows our approach to adapt well with majority voting and surpass the corresponding Codex-backboned baselines by 6.34%, 9.56%, and 5.46% on the GSM8K, AQuA, and StrategyQA benchmarks, respectively, in few-shot accuracy. Analysis of our decompositional reasoning finds it pinpoints logic failures and leads to higher consistency and robustness. Our code is publicly available at https://github.com/YuxiXie/SelfEval-Guided-Decoding.

Reasoning language models (RLMs), also known as Large Reasoning Models (LRMs), such as OpenAI's o1 and o3, DeepSeek-V3, and Alibaba's QwQ, have redefined AI's problem-solving capabilities by extending large language models (LLMs) with advanced reasoning mechanisms. Yet, their high costs, proprietary nature, and complex architectures - uniquely combining Reinforcement Learning (RL), search heuristics, and LLMs - present accessibility and scalability challenges. To address these, we propose a comprehensive blueprint that organizes RLM components into a modular framework, based on a survey and analysis of all RLM works. This blueprint incorporates diverse reasoning structures (chains, trees, graphs, and nested forms), reasoning strategies (e.g., Monte Carlo Tree Search, Beam Search), RL concepts (policy, value models and others), and supervision schemes (Output-Based and Process-Based Supervision). We also provide detailed mathematical formulations and algorithmic specifications to simplify RLM implementation. By showing how schemes like LLaMA-Berry, QwQ, Journey Learning, and Graph of Thoughts fit as special cases, we demonstrate the blueprint's versatility and unifying potential. To illustrate its utility, we introduce x1, a modular implementation for rapid RLM prototyping and experimentation. Using x1 and a literature review, we provide key insights, such as multi-phase training for policy and value models, and the importance of familiar training distributions. Finally, we outline how RLMs can integrate with a broader LLM ecosystem, including tools and databases. Our work demystifies RLM construction, democratizes advanced reasoning capabilities, and fosters innovation, aiming to mitigate the gap between "rich AI" and "poor AI" by lowering barriers to RLM development and experimentation.

Large language models (LLMs) have demonstrated impressive capabilities in various reasoning tasks, aided by techniques like chain-of-thought (CoT) prompting that elicits verbalized reasoning. However, LLMs often generate text with obvious mistakes and contradictions, raising doubts about their ability to robustly process and utilize generated rationales. In this work, we investigate CoT reasoning in LLMs through the lens of internal representations, focusing on how these representations are influenced by generated rationales. Our preliminary analysis reveals that while generated rationales improve answer accuracy, inconsistencies emerge between the model's internal representations in middle layers and those in final layers, potentially undermining the reliability of their reasoning processes. To address this, we propose internal consistency as a measure of the model's confidence by examining the agreement of latent predictions decoded from intermediate layers. Extensive empirical studies across different models and datasets demonstrate that internal consistency effectively distinguishes between correct and incorrect reasoning paths. Motivated by this, we propose a new approach to calibrate CoT reasoning by up-weighting reasoning paths with high internal consistency, resulting in a significant boost in reasoning performance. Further analysis uncovers distinct patterns in attention and feed-forward modules across layers, providing insights into the emergence of internal inconsistency. In summary, our results demonstrate the potential of using internal representations for self-evaluation of LLMs.

When writing and talking, people sometimes pause to think. Although reasoning-focused works have often framed reasoning as a method of answering questions or completing agentic tasks, reasoning is implicit in almost all written text. For example, this applies to the steps not stated between the lines of a proof or to the theory of mind underlying a conversation. In the Self-Taught Reasoner (STaR, Zelikman et al. 2022), useful thinking is learned by inferring rationales from few-shot examples in question-answering and learning from those that lead to a correct answer. This is a highly constrained setting -- ideally, a language model could instead learn to infer unstated rationales in arbitrary text. We present Quiet-STaR, a generalization of STaR in which LMs learn to generate rationales at each token to explain future text, improving their predictions. We address key challenges, including 1) the computational cost of generating continuations, 2) the fact that the LM does not initially know how to generate or use internal thoughts, and 3) the need to predict beyond individual next tokens. To resolve these, we propose a tokenwise parallel sampling algorithm, using learnable tokens indicating a thought's start and end, and an extended teacher-forcing technique. Encouragingly, generated rationales disproportionately help model difficult-to-predict tokens and improve the LM's ability to directly answer difficult questions. In particular, after continued pretraining of an LM on a corpus of internet text with Quiet-STaR, we find zero-shot improvements on GSM8K (5.9%rightarrow10.9%) and CommonsenseQA (36.3%rightarrow47.2%) and observe a perplexity improvement of difficult tokens in natural text. Crucially, these improvements require no fine-tuning on these tasks. Quiet-STaR marks a step towards LMs that can learn to reason in a more general and scalable way.

Large language models (LLMs) have accomplished remarkable reasoning performance in various domains. However, in the domain of reasoning tasks, we discover a frailty: LLMs are surprisingly brittle to the ordering of the premises, despite the fact that such ordering does not alter the underlying task. In particular, we observe that LLMs achieve the best performance when the premise order aligns with the context required in intermediate reasoning steps. For example, in deductive reasoning tasks, presenting the premises in the same order as the ground truth proof in the prompt (as opposed to random ordering) drastically increases the model's accuracy. We first examine the effect of premise ordering on deductive reasoning on a variety of LLMs, and our evaluation shows that permuting the premise order can cause a performance drop of over 30%. In addition, we release the benchmark R-GSM, based on GSM8K, to examine the ordering effect for mathematical problem-solving, and we again observe a significant drop in accuracy, relative to the original GSM8K benchmark.

As large language models (LLMs) perform more difficult tasks, it becomes harder to verify the correctness and safety of their behavior. One approach to help with this issue is to prompt LLMs to externalize their reasoning, e.g., by having them generate step-by-step reasoning as they answer a question (Chain-of-Thought; CoT). The reasoning may enable us to check the process that models use to perform tasks. However, this approach relies on the stated reasoning faithfully reflecting the model's actual reasoning, which is not always the case. To improve over the faithfulness of CoT reasoning, we have models generate reasoning by decomposing questions into subquestions. Decomposition-based methods achieve strong performance on question-answering tasks, sometimes approaching that of CoT while improving the faithfulness of the model's stated reasoning on several recently-proposed metrics. By forcing the model to answer simpler subquestions in separate contexts, we greatly increase the faithfulness of model-generated reasoning over CoT, while still achieving some of the performance gains of CoT. Our results show it is possible to improve the faithfulness of model-generated reasoning; continued improvements may lead to reasoning that enables us to verify the correctness and safety of LLM behavior.

Recently, Chain-of-Thought (CoT) prompting has delivered success on complex reasoning tasks, which aims at designing a simple prompt like ``Let's think step by step'' or multiple in-context exemplars with well-designed rationales to elicit Large Language Models (LLMs) to generate intermediate reasoning steps. However, the generated rationales often come with mistakes, making unfactual and unfaithful reasoning chains. To mitigate this brittleness, we propose a novel Chain-of-Knowledge (CoK) prompting, where we aim at eliciting LLMs to generate explicit pieces of knowledge evidence in the form of structure triple. This is inspired by our human behaviors, i.e., we can draw a mind map or knowledge map as the reasoning evidence in the brain before answering a complex question. Benefiting from CoK, we additionally introduce a F^2-Verification method to estimate the reliability of the reasoning chains in terms of factuality and faithfulness. For the unreliable response, the wrong evidence can be indicated to prompt the LLM to rethink. Extensive experiments demonstrate that our method can further improve the performance of commonsense, factual, symbolic, and arithmetic reasoning tasks.

Leveraging the autonomous decision-making capabilities of large language models (LLMs) demonstrates superior performance in reasoning tasks. Despite the successes of iterative or recursive retrieval-augmented generation (RAG), they often are trapped in a single solution space when confronted with complex tasks. In this paper, we propose a novel thinking pattern in RAG which integrates system analysis with efficient reasoning actions, significantly activating intrinsic reasoning capabilities and expanding the solution space of specific tasks via Monte Carlo Tree Search (MCTS), dubbed AirRAG. Specifically, our approach designs five fundamental reasoning actions that are expanded to a wide tree-based reasoning spaces using MCTS. The extension also uses self-consistency verification to explore potential reasoning paths and implement inference scaling. In addition, computationally optimal strategies are used to apply more inference computation to key actions to achieve further performance improvements. Experimental results demonstrate the effectiveness of AirRAG through considerable performance gains over complex QA datasets. Furthermore, AirRAG is flexible and lightweight, making it easy to integrate with other advanced technologies.

A prominent challenge for modern language understanding systems is the ability to answer implicit reasoning questions, where the required reasoning steps for answering the question are not mentioned in the text explicitly. In this work, we investigate why current models struggle with implicit reasoning question answering (QA) tasks, by decoupling inference of reasoning steps from their execution. We define a new task of implicit relation inference and construct a benchmark, IMPLICITRELATIONS, where given a question, a model should output a list of concept-relation pairs, where the relations describe the implicit reasoning steps required for answering the question. Using IMPLICITRELATIONS, we evaluate models from the GPT-3 family and find that, while these models struggle on the implicit reasoning QA task, they often succeed at inferring implicit relations. This suggests that the challenge in implicit reasoning questions does not stem from the need to plan a reasoning strategy alone, but to do it while also retrieving and reasoning over relevant information.

Recent works have shown that chain-of-thought (CoT) prompting can elicit language models to solve complex reasoning tasks, step-by-step. However, prompt-based CoT methods are dependent on very large models such as GPT-3 175B which are prohibitive to deploy at scale. In this paper, we use these large models as reasoning teachers to enable complex reasoning in smaller models and reduce model size requirements by several orders of magnitude. We propose Fine-tune-CoT, a method that generates reasoning samples from very large teacher models to fine-tune smaller models. We evaluate our method on a wide range of public models and complex tasks. We find that Fine-tune-CoT enables substantial reasoning capability in small models, far outperforming prompt-based baselines and even the teacher model in many tasks. Additionally, we extend our method by leveraging the teacher model's ability to generate multiple distinct rationales for each original sample. Enriching the fine-tuning data with such diverse reasoning results in a substantial performance boost across datasets, even for very small models. We conduct ablations and sample studies to understand the emergence of reasoning capabilities of student models. Our code implementation and data are available at https://github.com/itsnamgyu/reasoning-teacher.

In this paper, we propose an autonomous information seeking visual question answering framework, AVIS. Our method leverages a Large Language Model (LLM) to dynamically strategize the utilization of external tools and to investigate their outputs, thereby acquiring the indispensable knowledge needed to provide answers to the posed questions. Responding to visual questions that necessitate external knowledge, such as "What event is commemorated by the building depicted in this image?", is a complex task. This task presents a combinatorial search space that demands a sequence of actions, including invoking APIs, analyzing their responses, and making informed decisions. We conduct a user study to collect a variety of instances of human decision-making when faced with this task. This data is then used to design a system comprised of three components: an LLM-powered planner that dynamically determines which tool to use next, an LLM-powered reasoner that analyzes and extracts key information from the tool outputs, and a working memory component that retains the acquired information throughout the process. The collected user behavior serves as a guide for our system in two key ways. First, we create a transition graph by analyzing the sequence of decisions made by users. This graph delineates distinct states and confines the set of actions available at each state. Second, we use examples of user decision-making to provide our LLM-powered planner and reasoner with relevant contextual instances, enhancing their capacity to make informed decisions. We show that AVIS achieves state-of-the-art results on knowledge-intensive visual question answering benchmarks such as Infoseek and OK-VQA.

Large Language Models (LLMs) have shown outstanding performance across wide range of downstream tasks. This competency is attributed to their substantial parameter size and pre-training on extensive corpus. Moreover, LLMs have exhibited enhanced reasoning capabilities in tackling complex reasoning tasks, owing to the utilization of a method named ``Chain-of-Thought (CoT) prompting''. This method is designed to generate intermediate reasoning steps that guide the inference of the final answer. However, it is essential to highlight that these advanced reasoning abilities appear to emerge in models with a minimum of 10 billion parameters, thereby limiting its efficacy in situations where computational resources are constrained. In this paper, we investigate the possibility of transferring the reasoning capabilities of LLMs to smaller models via knowledge distillation. Specifically, we propose Sci-CoT, a two-stage framework that separates the processes of generating rationales and inferring answers. This method enables a more efficient use of rationales during the answer inference stage, leading to improved performance on scientific question-answering tasks. Utilizing Sci-CoT, our 80-million parameter model is able to exceed the performance of BLOOM-176B in the ARC-Easy dataset under the few shot setting.

In most current research, large language models (LLMs) are able to perform reasoning tasks by generating chains of thought through the guidance of specific prompts. However, there still exists a significant discrepancy between their capability in solving complex reasoning problems and that of humans. At present, most approaches focus on chains of thought (COT) and tool use, without considering the adoption and application of human cognitive frameworks. It is well-known that when confronting complex reasoning challenges, humans typically employ various cognitive abilities, and necessitate interaction with all aspects of tools, knowledge, and the external environment information to accomplish intricate tasks. This paper introduces a novel intelligent framework, referred to as OlaGPT. OlaGPT carefully studied a cognitive architecture framework, and propose to simulate certain aspects of human cognition. The framework involves approximating different cognitive modules, including attention, memory, reasoning, learning, and corresponding scheduling and decision-making mechanisms. Inspired by the active learning mechanism of human beings, it proposes a learning unit to record previous mistakes and expert opinions, and dynamically refer to them to strengthen their ability to solve similar problems. The paper also outlines common effective reasoning frameworks for human problem-solving and designs Chain-of-Thought (COT) templates accordingly. A comprehensive decision-making mechanism is also proposed to maximize model accuracy. The efficacy of OlaGPT has been stringently evaluated on multiple reasoning datasets, and the experimental outcomes reveal that OlaGPT surpasses state-of-the-art benchmarks, demonstrating its superior performance. Our implementation of OlaGPT is available on GitHub: https://github.com/oladata-team/OlaGPT.

Large language models' reasoning abilities benefit from methods that organize their thought processes, such as chain-of-thought prompting, which employs a sequential structure to guide the reasoning process step-by-step. However, existing approaches focus primarily on organizing the sequence of thoughts, leaving structure in individual thought steps underexplored. To address this gap, we propose Table as Thought, a framework inspired by cognitive neuroscience theories on human thought. Table as Thought organizes reasoning within a tabular schema, where rows represent sequential thought steps and columns capture critical constraints and contextual information to enhance reasoning. The reasoning process iteratively populates the table until self-verification ensures completeness and correctness. Our experiments show that Table as Thought excels in planning tasks and demonstrates a strong potential for enhancing LLM performance in mathematical reasoning compared to unstructured thought baselines. This work provides a novel exploration of refining thought representation within LLMs, paving the way for advancements in reasoning and AI cognition.

Large language model (LLM) performance on reasoning problems typically does not generalize out of distribution. Previous work has claimed that this can be mitigated by modifying prompts to include examples with chains of thought--demonstrations of solution procedures--with the intuition that it is possible to in-context teach an LLM an algorithm for solving the problem. This paper presents a case study of chain of thought on problems from Blocksworld, a classical planning domain, and examine the performance of two state-of-the-art LLMs across two axes: generality of examples given in prompt, and complexity of problems queried with each prompt. While our problems are very simple, we only find meaningful performance improvements from chain of thought prompts when those prompts are exceedingly specific to their problem class, and that those improvements quickly deteriorate as the size n of the query-specified stack grows past the size of stacks shown in the examples. Our results hint that, contrary to previous claims in the literature, CoT's performance improvements do not stem from the model learning general algorithmic procedures via demonstrations and depend on carefully engineering highly problem specific prompts. This spotlights drawbacks of chain of thought, especially because of the sharp tradeoff between possible performance gains and the amount of human labor necessary to generate examples with correct reasoning traces.

Recent advancements in large language models (LLMs) have propelled Artificial Intelligence (AI) to new heights, enabling breakthroughs in various tasks such as writing assistance, code generation, and machine translation. A significant distinction of advanced LLMs, such as ChatGPT, is their demonstrated ability to "reason." However, evaluating the reasoning ability of LLMs remains a challenge as most existing evaluations focus on their accuracy on the downstream tasks rather than directly assessing their reasoning processes. Efforts have been made to develop benchmarks and metrics to assess reasoning in LLMs, but they suffer from data leakage or limited scope. In this paper, we introduce LogicAsker, an automatic approach that comprehensively evaluates and improves the logical reasoning abilities of LLMs under a set of atomic reasoning skills based on propositional and predicate logic. The results provide insights into LLMs' reasoning abilities and reveal the logical rules the LLMs did not learn well. We evaluate LogicAsker on six widely deployed LLMs, including GPT-3, ChatGPT, GPT-4, Bard, Vicuna, and Guanaco. The results show that test cases from LogicAsker can find logical reasoning failures in different LLMs with a rate of 25\% - 94\%. In addition, the test cases of LogicAsker can be further used to design demonstration examples for in-context learning, which effectively improves the logical reasoning ability of LLMs, e.g., 10\% for GPT-4. As far as we know, our work is the first to create prompts based on testing results to improve LLMs' formal reasoning ability effectively. All the code, data, and results will be released for reproduction and future research.

To enable Large Language Models (LLMs) to function as conscious agents with generalizable reasoning capabilities, it is crucial that they possess the reasoning ability to comprehend situational changes (transitions) in distribution triggered by environmental factors or actions from other agents. Despite its fundamental significance, this ability remains underexplored due to the complexity of modeling infinite possible changes in an event and their associated distributions, coupled with the lack of benchmark data with situational transitions. Addressing these gaps, we propose a novel formulation of reasoning with distributional changes as a three-step discriminative process, termed as MetAphysical ReaSoning. We then introduce the first-ever benchmark, MARS, comprising three tasks corresponding to each step. These tasks systematically assess LLMs' capabilities in reasoning the plausibility of (i) changes in actions, (ii) states caused by changed actions, and (iii) situational transitions driven by changes in action. Extensive evaluations with 20 (L)LMs of varying sizes and methods indicate that all three tasks in this process pose significant challenges, even for state-of-the-art LLMs and LMs after fine-tuning. Further analyses reveal potential causes for the underperformance of LLMs and demonstrate that pre-training them on large-scale conceptualization taxonomies can potentially enhance their metaphysical reasoning capabilities. Our data and models are publicly accessible at https://github.com/HKUST-KnowComp/MARS.

This paper investigates the mathematical reasoning capabilities of large language models (LLMs) using 50 newly constructed high-school-level word problems. Unlike prior studies that focus solely on answer correctness, we rigorously analyze both final answers and solution steps to identify reasoning failures. Evaluating eight state-of-the-art models - including Mixtral, Llama, Gemini, GPT-4o, and OpenAI's o1 variants - we find that while newer models (e.g., o3-mini, deepseek-r1) achieve higher accuracy, all models exhibit errors in spatial reasoning, strategic planning, and arithmetic, sometimes producing correct answers through flawed logic. Common failure modes include unwarranted assumptions, over-reliance on numerical patterns, and difficulty translating physical intuition into mathematical steps. Manual analysis reveals that models struggle with problems requiring multi-step deduction or real-world knowledge, despite possessing broad mathematical knowledge. Our results underscore the importance of evaluating reasoning processes, not just answers, and caution against overestimating LLMs' problem-solving proficiency. The study highlights persistent gaps in LLMs' generalization abilities, emphasizing the need for targeted improvements in structured reasoning and constraint handling.

Large language models (LLMs) have dramatically enhanced the field of language intelligence, as demonstrably evidenced by their formidable empirical performance across a spectrum of complex reasoning tasks. Additionally, theoretical proofs have illuminated their emergent reasoning capabilities, providing a compelling showcase of their advanced cognitive abilities in linguistic contexts. Critical to their remarkable efficacy in handling complex reasoning tasks, LLMs leverage the intriguing chain-of-thought (CoT) reasoning techniques, obliging them to formulate intermediate steps en route to deriving an answer. The CoT reasoning approach has not only exhibited proficiency in amplifying reasoning performance but also in enhancing interpretability, controllability, and flexibility. In light of these merits, recent research endeavors have extended CoT reasoning methodologies to nurture the development of autonomous language agents, which adeptly adhere to language instructions and execute actions within varied environments. This survey paper orchestrates a thorough discourse, penetrating vital research dimensions, encompassing: (i) the foundational mechanics of CoT techniques, with a focus on elucidating the circumstances and justification behind its efficacy; (ii) the paradigm shift in CoT; and (iii) the burgeoning of language agents fortified by CoT approaches. Prospective research avenues envelop explorations into generalization, efficiency, customization, scaling, and safety. This paper caters to a wide audience, including beginners seeking comprehensive knowledge of CoT reasoning and language agents, as well as experienced researchers interested in foundational mechanics and engaging in cutting-edge discussions on these topics. A repository for the related papers is available at https://github.com/Zoeyyao27/CoT-Igniting-Agent.

Mathematical reasoning is a crucial capability for Large Language Models (LLMs), yet generating detailed and accurate reasoning traces remains a significant challenge. This paper introduces a novel approach to produce high-quality reasoning traces for LLM fine-tuning using online learning Flows. Our method employs an incremental output production Flow, where component LLMs collaboratively construct solutions through iterative communication. We train the Flow using online Direct Preference Optimization (DPO) learning with rollouts, generating DPO pairs for each training example and updating models in real-time. We directly compare the quality of reasoning traces generated by our method with those produced through direct model inference, demonstrating the effectiveness of our approach in improving LLM performance in mathematical reasoning tasks.

Pre-trained language models (PLMs) have shown impressive performance in various language tasks. However, they are prone to spurious correlations, and often generate illusory information. In real-world applications, PLMs should justify decisions with formalized, coherent reasoning chains, but this challenge remains under-explored. Cognitive psychology theorizes that humans are capable of utilizing fast and intuitive heuristic thinking to make decisions based on past experience, then rationalizing the decisions through slower and deliberative analytic reasoning. We incorporate these interlinked dual processes in fine-tuning and in-context learning with PLMs, applying them to two language understanding tasks that require coherent physical commonsense reasoning. We show that our proposed Heuristic-Analytic Reasoning (HAR) strategies drastically improve the coherence of rationalizations for model decisions, yielding state-of-the-art results on Tiered Reasoning for Intuitive Physics (TRIP). We also find that this improved coherence is a direct result of more faithful attention to relevant language context in each step of reasoning. Our findings suggest that human-like reasoning strategies can effectively improve the coherence and reliability of PLM reasoning.

Traditional methods for reasoning segmentation rely on supervised fine-tuning with categorical labels and simple descriptions, limiting its out-of-domain generalization and lacking explicit reasoning processes. To address these limitations, we propose Seg-Zero, a novel framework that demonstrates remarkable generalizability and derives explicit chain-of-thought reasoning through cognitive reinforcement. Seg-Zero introduces a decoupled architecture consisting of a reasoning model and a segmentation model. The reasoning model interprets user intentions, generates explicit reasoning chains, and produces positional prompts, which are subsequently used by the segmentation model to generate precious pixel-level masks. We design a sophisticated reward mechanism that integrates both format and accuracy rewards to effectively guide optimization directions. Trained exclusively via reinforcement learning with GRPO and without explicit reasoning data, Seg-Zero achieves robust zero-shot generalization and exhibits emergent test-time reasoning capabilities. Experiments show that Seg-Zero-7B achieves a zero-shot performance of 57.5 on the ReasonSeg benchmark, surpassing the prior LISA-7B by 18\%. This significant improvement highlights Seg-Zero's ability to generalize across domains while presenting an explicit reasoning process. Code is available at https://github.com/dvlab-research/Seg-Zero.

We introduce Diagram of Thought (DoT), a framework that models iterative reasoning in large language models (LLMs) as the construction of a directed acyclic graph (DAG) within a single model. Unlike traditional approaches that represent reasoning as linear chains or trees, DoT organizes propositions, critiques, refinements, and verifications into a cohesive DAG structure, allowing the model to explore complex reasoning pathways while maintaining logical consistency. Each node in the diagram corresponds to a proposition that has been proposed, critiqued, refined, or verified, enabling the LLM to iteratively improve its reasoning through natural language feedback. By leveraging auto-regressive next-token prediction with role-specific tokens, DoT facilitates seamless transitions between proposing ideas and critically evaluating them, providing richer feedback than binary signals. Furthermore, we formalize the DoT framework using Topos Theory, providing a mathematical foundation that ensures logical consistency and soundness in the reasoning process. This approach enhances both the training and inference processes within a single LLM, eliminating the need for multiple models or external control mechanisms. DoT offers a conceptual framework for designing next-generation reasoning-specialized models, emphasizing training efficiency, robust reasoning capabilities, and theoretical grounding. The code is available at https://github.com/diagram-of-thought/diagram-of-thought.

While language models have demonstrated impressive capabilities across a range of tasks, they still struggle with tasks that require complex planning and reasoning. Recent studies have proposed training language models on search processes rather than optimal solutions, resulting in better generalization performance even though search processes are noisy and even suboptimal. However, these studies overlook the value of optimal solutions, which can serve as step-by-step landmarks to guide more effective search. In this work, we explore how to leverage optimal solutions to enhance the search and planning abilities of language models. To this end, we propose guided stream of search (GSoS), which seamlessly incorporates optimal solutions into the self-generation process in a progressive manner, producing high-quality search trajectories. These trajectories are then distilled into the pre-trained model via supervised fine-tuning. Our approach significantly enhances the search and planning abilities of language models on Countdown, a simple yet challenging mathematical reasoning task. Notably, combining our method with RL fine-tuning yields further improvements, whereas previous supervised fine-tuning methods do not benefit from RL. Furthermore, our approach exhibits greater effectiveness than leveraging optimal solutions in the form of subgoal rewards.

In order to build artificial intelligence systems that can perceive and reason with human behavior in the real world, we must first design models that conduct complex spatio-temporal reasoning over motion sequences. Moving towards this goal, we propose the HumanMotionQA task to evaluate complex, multi-step reasoning abilities of models on long-form human motion sequences. We generate a dataset of question-answer pairs that require detecting motor cues in small portions of motion sequences, reasoning temporally about when events occur, and querying specific motion attributes. In addition, we propose NSPose, a neuro-symbolic method for this task that uses symbolic reasoning and a modular design to ground motion through learning motion concepts, attribute neural operators, and temporal relations. We demonstrate the suitability of NSPose for the HumanMotionQA task, outperforming all baseline methods.

Reasoning is most powerful when an LLM accurately aggregates relevant information. We examine the critical role of information aggregation in reasoning by requiring the LLM to analyze sports narratives. To succeed at this task, an LLM must infer points from actions, identify related entities, attribute points accurately to players and teams, and compile key statistics to draw conclusions. We conduct comprehensive experiments with real NBA basketball data and present SportsGen, a new method to synthesize game narratives. By synthesizing data, we can rigorously evaluate LLMs' reasoning capabilities under complex scenarios with varying narrative lengths and density of information. Our findings show that most models, including GPT-4o, often fail to accurately aggregate basketball scores due to frequent scoring patterns. Open-source models like Llama-3 further suffer from significant score hallucinations. Finally, the effectiveness of reasoning is influenced by narrative complexity, information density, and domain-specific terms, highlighting the challenges in analytical reasoning tasks.

In this work, we use large language models (LLMs) to augment and accelerate research on the P versus NP problem, one of the most important open problems in theoretical computer science and mathematics. Specifically, we propose Socratic reasoning, a general framework that promotes in-depth thinking with LLMs for complex problem-solving. Socratic reasoning encourages LLMs to recursively discover, solve, and integrate problems while facilitating self-evaluation and refinement. Our pilot study on the P vs. NP problem shows that GPT-4 successfully produces a proof schema and engages in rigorous reasoning throughout 97 dialogue turns, concluding "P neq NP", which is in alignment with (Xu and Zhou, 2023). The investigation uncovers novel insights within the extensive solution space of LLMs, shedding light on LLM for Science.

While Chain of Thought (CoT) prompting approaches have significantly consolidated the reasoning capabilities of large language models (LLMs), they still face limitations that require extensive human effort or have performance needs to be improved. Existing endeavors have focused on bridging these gaps; however, these approaches either hinge on external data and cannot completely eliminate manual effort, or they fall short in effectively directing LLMs to generate high-quality exemplary prompts. To address the said pitfalls, we propose a novel prompt approach for automatic reasoning named LBS3, inspired by curriculum learning which better reflects human learning habits. Specifically, LBS3 initially steers LLMs to recall easy-to-hard proxy queries that are pertinent to the target query. Following this, it invokes a progressive strategy that utilizes exemplary prompts stemmed from easy-proxy queries to direct LLMs in solving hard-proxy queries, enabling the high-quality of the proxy solutions. Finally, our extensive experiments in various reasoning-intensive tasks with varying open- and closed-source LLMs show that LBS3 achieves strongly competitive performance compared to the SOTA baselines.

This paper proposes a research direction to advance AI which draws inspiration from cognitive theories of human decision making. The premise is that if we gain insights about the causes of some human capabilities that are still lacking in AI (for instance, adaptability, generalizability, common sense, and causal reasoning), we may obtain similar capabilities in an AI system by embedding these causal components. We hope that the high-level description of our vision included in this paper, as well as the several research questions that we propose to consider, can stimulate the AI research community to define, try and evaluate new methodologies, frameworks, and evaluation metrics, in the spirit of achieving a better understanding of both human and machine intelligence.

In human cognition theory, human thinking is governed by two systems: the fast and intuitive System 1 and the slower but more deliberative System 2. Recent studies have shown that incorporating System 2 process into Transformers including large language models (LLMs), significantly enhances their reasoning capabilities. Nevertheless, models that purely resemble System 2 thinking require substantially higher computational costs and are much slower to respond. To address this challenge, we present Dualformer, a single Transformer model that seamlessly integrates both the fast and slow reasoning modes. Dualformer is obtained by training on data with randomized reasoning traces, where different parts of the traces are dropped during training. The dropping strategies are specifically tailored according to the trace structure, analogous to analyzing our thinking process and creating shortcuts with patterns. At inference time, our model can be configured to output only the solutions (fast mode) or both the reasoning chain and the final solution (slow mode), or automatically decide which mode to engage (auto mode). In all cases, Dualformer outperforms the corresponding baseline models in both performance and computational efficiency: (1) in slow mode, Dualformer optimally solves unseen 30 x 30 maze navigation tasks 97.6% of the time, surpassing the Searchformer (trained on data with complete reasoning traces) baseline performance of 93.3%, while only using 45.5% fewer reasoning steps; (2) in fast mode, Dualformer completes those tasks with an 80% optimal rate, significantly outperforming the Solution-Only model (trained on solution-only data), which has an optimal rate of only 30%. For math problems, our techniques have also achieved improved performance with LLM fine-tuning, showing its generalization beyond task-specific models.

Large Language Models (LLMs) have revolutionized natural language processing and hold immense potential for advancing Artificial Intelligence. However, the core architecture of most mainstream LLMs -- the Transformer -- has inherent limitations in computational depth, rendering them theoretically incapable of solving many reasoning tasks that demand increasingly deep computations. Chain of Thought (CoT) prompting has emerged as a technique to address these architectural limitations, as evidenced by several theoretical studies. It offers a promising approach to solving complex reasoning tasks that were previously beyond the capabilities of these models. Despite its successes, CoT and its variants (such as Tree of Thought, Graph of Thought, etc.) rely on a "one-prompt-for-all" approach, using a single prompt structure (e.g., "think step by step") for a wide range of tasks -- from counting and sorting to solving mathematical and algorithmic problems. This approach poses significant challenges for models to generate the correct reasoning steps, as the model must navigate through a vast prompt template space to find the appropriate template for each task. In this work, we build upon previous theoretical analyses of CoT to demonstrate how the one-prompt-for-all approach can negatively affect the computability of LLMs. We partition the solution search space into two: the prompt space and the answer space. Our findings show that task-specific supervision is essential for navigating the prompt space accurately and achieving optimal performance. Through experiments with state-of-the-art LLMs, we reveal a gap in reasoning performance when supervision is applied versus when it is not.

Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation rules. In this paper, we present a new challenge for the evaluation (and eventually the design) of neural architectures and similar system, developing a task suite of mathematics problems involving sequential questions and answers in a free-form textual input/output format. The structured nature of the mathematics domain, covering arithmetic, algebra, probability and calculus, enables the construction of training and test splits designed to clearly illuminate the capabilities and failure-modes of different architectures, as well as evaluate their ability to compose and relate knowledge and learned processes. Having described the data generation process and its potential future expansions, we conduct a comprehensive analysis of models from two broad classes of the most powerful sequence-to-sequence architectures and find notable differences in their ability to resolve mathematical problems and generalize their knowledge.

Humans have a powerful and mysterious capacity to reason. By working through a series of purely mental steps, we can make inferences we would not be capable of making directly -- despite the fact that we get no additional data from the world. Similarly, when large language models generate a series of intermediate steps (a chain of thought) before answering a question, they often produce better answers than they otherwise would. We investigate why and how chain-of-thought reasoning is useful in language models, testing the hypothesis that reasoning is effective when training data consists of local clusters of variables that influence each other strongly. These training conditions enable the chaining of accurate local inferences in order to estimate relationships between variables that were not seen together in training. We prove that there will exist a "reasoning gap", where reasoning through intermediate variables improves inference, for the simple case of an autoregressive density estimator trained on local samples from a chain-structured probabilistic model. We then test our hypothesis empirically in more complex models, training an autoregressive language model on samples from Bayes nets but only including a subset of variables in each sample. We test language models' ability to match conditional probabilities with and without intermediate reasoning steps, finding that intermediate steps are only helpful when the training data is locally structured with respect to dependencies between variables and that the combination of locally-structured observations and reasoning is much more data-efficient than training on all variables. Our results illustrate how the effectiveness of reasoning step by step is rooted in the local statistical structure of the training data.

Enabling Large Language Models (LLMs) to handle a wider range of complex tasks (e.g., coding, math) has drawn great attention from many researchers. As LLMs continue to evolve, merely increasing the number of model parameters yields diminishing performance improvements and heavy computational costs. Recently, OpenAI's o1 model has shown that inference strategies (i.e., Test-time Compute methods) can also significantly enhance the reasoning capabilities of LLMs. However, the mechanisms behind these methods are still unexplored. In our work, to investigate the reasoning patterns of o1, we compare o1 with existing Test-time Compute methods (BoN, Step-wise BoN, Agent Workflow, and Self-Refine) by using OpenAI's GPT-4o as a backbone on general reasoning benchmarks in three domains (i.e., math, coding, commonsense reasoning). Specifically, first, our experiments show that the o1 model has achieved the best performance on most datasets. Second, as for the methods of searching diverse responses (e.g., BoN), we find the reward models' capability and the search space both limit the upper boundary of these methods. Third, as for the methods that break the problem into many sub-problems, the Agent Workflow has achieved better performance than Step-wise BoN due to the domain-specific system prompt for planning better reasoning processes. Fourth, it is worth mentioning that we have summarized six reasoning patterns of o1, and provided a detailed analysis on several reasoning benchmarks.

Understanding the abilities of LLMs to reason about natural language plans, such as instructional text and recipes, is critical to reliably using them in decision-making systems. A fundamental aspect of plans is the temporal order in which their steps needs to be executed, which reflects the underlying causal dependencies between them. We introduce CaT-Bench, a benchmark of Step Order Prediction questions, which test whether a step must necessarily occur before or after another in cooking recipe plans. We use this to evaluate how well frontier LLMs understand causal and temporal dependencies. We find that SOTA LLMs are underwhelming (best zero-shot is only 0.59 in F1), and are biased towards predicting dependence more often, perhaps relying on temporal order of steps as a heuristic. While prompting for explanations and using few-shot examples improve performance, the best F1 result is only 0.73. Further, human evaluation of explanations along with answer correctness show that, on average, humans do not agree with model reasoning. Surprisingly, we also find that explaining after answering leads to better performance than normal chain-of-thought prompting, and LLM answers are not consistent across questions about the same step pairs. Overall, results show that LLMs' ability to detect dependence between steps has significant room for improvement.

Abstract reasoning is a key ability for an intelligent system. Large language models achieve above-chance performance on abstract reasoning tasks, but exhibit many imperfections. However, human abstract reasoning is also imperfect, and depends on our knowledge and beliefs about the content of the reasoning problem. For example, humans reason much more reliably about logical rules that are grounded in everyday situations than arbitrary rules about abstract attributes. The training experiences of language models similarly endow them with prior expectations that reflect human knowledge and beliefs. We therefore hypothesized that language models would show human-like content effects on abstract reasoning problems. We explored this hypothesis across three logical reasoning tasks: natural language inference, judging the logical validity of syllogisms, and the Wason selection task (Wason, 1968). We find that state of the art large language models (with 7 or 70 billion parameters; Hoffman et al., 2022) reflect many of the same patterns observed in humans across these tasks -- like humans, models reason more effectively about believable situations than unrealistic or abstract ones. Our findings have implications for understanding both these cognitive effects, and the factors that contribute to language model performance.

Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving math problems and proving theorems has garnered significant interest in the fields of machine learning and natural language processing. For example, mathematics serves as a testbed for aspects of reasoning that are challenging for powerful deep learning models, driving new algorithmic and modeling advances. On the other hand, recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning. In this survey paper, we review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade. We also evaluate existing benchmarks and methods, and discuss future research directions in this domain.

Trained on vast corpora of human language, language models demonstrate emergent human-like reasoning abilities. Yet they are still far from true intelligence, which opens up intriguing opportunities to explore the parallels of humans and model behaviors. In this work, we study the ability to skip steps in reasoning - a hallmark of human expertise developed through practice. Unlike humans, who may skip steps to enhance efficiency or to reduce cognitive load, models do not inherently possess such motivations to minimize reasoning steps. To address this, we introduce a controlled framework that stimulates step-skipping behavior by iteratively refining models to generate shorter and accurate reasoning paths. Empirical results indicate that models can develop the step skipping ability under our guidance. Moreover, after fine-tuning on expanded datasets that include both complete and skipped reasoning sequences, the models can not only resolve tasks with increased efficiency without sacrificing accuracy, but also exhibit comparable and even enhanced generalization capabilities in out-of-domain scenarios. Our work presents the first exploration into human-like step-skipping ability and provides fresh perspectives on how such cognitive abilities can benefit AI models.

Algorithmic reasoning refers to the ability to understand the complex patterns behind the problem and decompose them into a sequence of reasoning steps towards the solution. Such nature of algorithmic reasoning makes it a challenge for large language models (LLMs), even though they have demonstrated promising performance in other reasoning tasks. Within this context, some recent studies use programming languages (e.g., Python) to express the necessary logic for solving a given instance/question (e.g., Program-of-Thought) as inspired by their strict and precise syntaxes. However, it is non-trivial to write an executable code that expresses the correct logic on the fly within a single inference call. Also, the code generated specifically for an instance cannot be reused for others, even if they are from the same task and might require identical logic to solve. This paper presents Think-and-Execute, a novel framework that decomposes the reasoning process of language models into two steps. (1) In Think, we discover a task-level logic that is shared across all instances for solving a given task and then express the logic with pseudocode; (2) In Execute, we further tailor the generated pseudocode to each instance and simulate the execution of the code. With extensive experiments on seven algorithmic reasoning tasks, we demonstrate the effectiveness of Think-and-Execute. Our approach better improves LMs' reasoning compared to several strong baselines performing instance-specific reasoning (e.g., CoT and PoT), suggesting the helpfulness of discovering task-level logic. Also, we show that compared to natural language, pseudocode can better guide the reasoning of LMs, even though they are trained to follow natural language instructions.

In their recent Nature Human Behaviour paper, "Emergent analogical reasoning in large language models," (Webb, Holyoak, and Lu, 2023) the authors argue that "large language models such as GPT-3 have acquired an emergent ability to find zero-shot solutions to a broad range of analogy problems." In this response, we provide counterexamples of the letter string analogies. In our tests, GPT-3 fails to solve even the easiest variants of the problems presented in the original paper. Zero-shot reasoning is an extraordinary claim that requires extraordinary evidence. We do not see that evidence in our experiments. To strengthen claims of humanlike reasoning such as zero-shot reasoning, it is important that the field develop approaches that rule out data memorization.

Reasoning is central to human intelligence. However, fallacious arguments are common, and some exacerbate problems such as spreading misinformation about climate change. In this paper, we propose the task of logical fallacy detection, and provide a new dataset (Logic) of logical fallacies generally found in text, together with an additional challenge set for detecting logical fallacies in climate change claims (LogicClimate). Detecting logical fallacies is a hard problem as the model must understand the underlying logical structure of the argument. We find that existing pretrained large language models perform poorly on this task. In contrast, we show that a simple structure-aware classifier outperforms the best language model by 5.46% on Logic and 4.51% on LogicClimate. We encourage future work to explore this task as (a) it can serve as a new reasoning challenge for language models, and (b) it can have potential applications in tackling the spread of misinformation. Our dataset and code are available at https://github.com/causalNLP/logical-fallacy

Large language models (LLMs) have shown impressive performance in various reasoning benchmarks with the emergence of Chain-of-Thought (CoT) and its derivative methods, particularly in tasks involving multi-choice questions (MCQs). However, current works all process data uniformly without considering the problem-solving difficulty, which means an excessive focus on simple questions while insufficient to intricate ones. To address this challenge, we inspired by humans using heuristic strategies to categorize tasks and handle them individually, propose to apply the Divide and Conquer to LLMs reasoning. First, we divide questions into different subsets based on the statistical confidence score (CS), then fix nearly resolved sets and conquer demanding nuanced process ones with elaborately designed methods, including Prior Knowledge based Reasoning (PKR) and Filter Choices based Reasoning (FCR), as well as their integration variants. Our experiments demonstrate that this proposed strategy significantly boosts the models' reasoning abilities across nine datasets involving arithmetic, commonsense, and logic tasks. For instance, compared to baseline, we make a striking improvement on low confidence subsets of 8.72\% for AQuA, 15.07\% for ARC Challenge and 7.71\% for RiddleSense. In addition, through extensive analysis on length of rationale and number of options, we verify that longer reasoning paths in PKR could prevent models from referring infer-harmful shortcuts, and also find that removing irrelevant choices in FCR would substantially avoid models' confusion. The code is at https://github.com/AiMijie/Divide-and-Conquer

Although planning is a crucial component of the autonomous driving stack, researchers have yet to develop robust planning algorithms that are capable of safely handling the diverse range of possible driving scenarios. Learning-based planners suffer from overfitting and poor long-tail performance. On the other hand, rule-based planners generalize well, but might fail to handle scenarios that require complex driving maneuvers. To address these limitations, we investigate the possibility of leveraging the common-sense reasoning capabilities of Large Language Models (LLMs) such as GPT4 and Llama2 to generate plans for self-driving vehicles. In particular, we develop a novel hybrid planner that leverages a conventional rule-based planner in conjunction with an LLM-based planner. Guided by commonsense reasoning abilities of LLMs, our approach navigates complex scenarios which existing planners struggle with, produces well-reasoned outputs while also remaining grounded through working alongside the rule-based approach. Through extensive evaluation on the nuPlan benchmark, we achieve state-of-the-art performance, outperforming all existing pure learning- and rule-based methods across most metrics. Our code will be available at https://llmassist.github.io.

The rapid progress of large language models (LLMs) has seen them excel and frequently surpass human performance on standard benchmarks. This has enabled many downstream applications, such as LLM agents, to rely on their sophisticated reasoning to navigate complex task requirements. However, LLMs are known to unexpectedly falter in simple tasks and under seemingly straightforward circumstances - underscoring the need for better and more diverse evaluation setups to measure their true capabilities. To this end, we choose to study compositional and conditional reasoning, two cornerstones of human cognition, and introduce GroundCocoa - a lexically diverse benchmark connecting these reasoning skills to the real-world problem of flight booking. Our task involves aligning detailed user preferences with available flight options presented in a multiple-choice format. Results indicate a significant disparity in performance among current state-of-the-art LLMs with even the best performing model, GPT-4 Turbo, not exceeding 67% accuracy despite advanced prompting techniques.

Despite superior reasoning prowess demonstrated by Large Language Models (LLMs) with Chain-of-Thought (CoT) prompting, a lack of understanding prevails around the internal mechanisms of the models that facilitate CoT generation. This work investigates the neural sub-structures within LLMs that manifest CoT reasoning from a mechanistic point of view. From an analysis of LLaMA-2 7B applied to multistep reasoning over fictional ontologies, we demonstrate that LLMs deploy multiple parallel pathways of answer generation for step-by-step reasoning. These parallel pathways provide sequential answers from the input question context as well as the generated CoT. We observe a striking functional rift in the middle layers of the LLM. Token representations in the initial half remain strongly biased towards the pretraining prior, with the in-context taking over abruptly in the later half. This internal phase shift manifests in different functional components: attention heads that write the answer token predominantly appear in the later half, attention heads that move information along ontological relationships appear exclusively in the initial half, and so on. To the best of our knowledge, this is the first attempt towards mechanistic investigation of CoT reasoning in LLMs.

Despite the success of chain of thought in enhancing language model reasoning, the underlying process remains less well understood. Although logically sound reasoning appears inherently crucial for chain of thought, prior studies surprisingly reveal minimal impact when using invalid demonstrations instead. Furthermore, the conventional chain of thought does not inform language models on what mistakes to avoid, which potentially leads to more errors. Hence, inspired by how humans can learn from both positive and negative examples, we propose contrastive chain of thought to enhance language model reasoning. Compared to the conventional chain of thought, our approach provides both valid and invalid reasoning demonstrations, to guide the model to reason step-by-step while reducing reasoning mistakes. To improve generalization, we introduce an automatic method to construct contrastive demonstrations. Our experiments on reasoning benchmarks demonstrate that contrastive chain of thought can serve as a general enhancement of chain-of-thought prompting.

Large language models (LLMs) have demonstrated remarkable success across a wide range of tasks; however, they still encounter challenges in reasoning tasks that require understanding and inferring relationships between distinct pieces of information within text sequences. This challenge is particularly pronounced in tasks involving multi-step processes, such as logical reasoning and multi-hop question answering, where understanding implicit relationships between entities and leveraging multi-hop connections in the given context are crucial. Graphs, as fundamental data structures, explicitly represent pairwise relationships between entities, thereby offering the potential to enhance LLMs' reasoning capabilities. External graphs have proven effective in supporting LLMs across multiple tasks. However, in many reasoning tasks, no pre-existing graph structure is provided. Can we structure implicit knowledge derived from context into graphs to assist LLMs in reasoning? In this paper, we propose Reasoning with Graphs (RwG) by first constructing explicit graphs from the context and then leveraging these graphs to enhance LLM reasoning performance on reasoning tasks. Extensive experiments demonstrate the effectiveness of the proposed method in improving both logical reasoning and multi-hop question answering tasks.

This study presents a novel learning approach designed to enhance both mathematical reasoning and problem-solving abilities of Large Language Models (LLMs). We focus on integrating the Chain-of-Thought (CoT) and the Program-of-Thought (PoT) learning, hypothesizing that prioritizing the learning of mathematical reasoning ability is helpful for the amplification of problem-solving ability. Thus, the initial learning with CoT is essential for solving challenging mathematical problems. To this end, we propose a sequential learning approach, named SAAS (Solving Ability Amplification Strategy), which strategically transitions from CoT learning to PoT learning. Our empirical study, involving an extensive performance comparison using several benchmarks, demonstrates that our SAAS achieves state-of-the-art (SOTA) performance. The results underscore the effectiveness of our sequential learning approach, marking a significant advancement in the field of mathematical reasoning in LLMs.

Reasoning presents a significant and challenging issue for Large Language Models (LLMs). The predominant focus of research has revolved around developing diverse prompting strategies to guide and structure the reasoning processes of LLMs. However, these approaches based on decoder-only causal language models often operate the input question in a single forward pass, potentially missing the rich, back-and-forth interactions inherent in human reasoning. Scant attention has been paid to a critical dimension, i.e., the input question itself embedded within the prompts. In response, we introduce a deceptively simple yet highly effective prompting strategy, termed question "re-reading". Drawing inspiration from human learning and problem-solving, re-reading entails revisiting the question information embedded within input prompts. This approach aligns seamlessly with the cognitive principle of reinforcement, enabling LLMs to extract deeper insights, identify intricate patterns, establish more nuanced connections, and ultimately enhance their reasoning capabilities across various tasks. Experiments conducted on a series of reasoning benchmarks serve to underscore the effectiveness and generality of our method. Moreover, our findings demonstrate that our approach seamlessly integrates with various language models, though-eliciting prompting methods, and ensemble techniques, further underscoring its versatility and compatibility in the realm of LLMs.

Statutory reasoning refers to the application of legislative provisions to a series of case facts described in natural language. We re-frame statutory reasoning as an analogy task, where each instance of the analogy task involves a combination of two instances of statutory reasoning. This increases the dataset size by two orders of magnitude, and introduces an element of interpretability. We show that this task is roughly as difficult to Natural Language Processing models as the original task. Finally, we come back to statutory reasoning, solving it with a combination of a retrieval mechanism and analogy models, and showing some progress on prior comparable work.

When presented with questions involving visual thinking, humans naturally switch reasoning modalities, often forming mental images or drawing visual aids. Large language models have shown promising results in arithmetic and symbolic reasoning by expressing intermediate reasoning in text as a chain of thought, yet struggle to extend this capability to answer text queries that are easily solved by visual reasoning, even with extensive multimodal pretraining. We introduce a simple method, whiteboard-of-thought prompting, to unlock the visual reasoning capabilities of multimodal large language models across modalities. Whiteboard-of-thought prompting provides multimodal large language models with a metaphorical `whiteboard' to draw out reasoning steps as images, then returns these images back to the model for further processing. We find this can be accomplished with no demonstrations or specialized modules, instead leveraging models' existing ability to write code with libraries such as Matplotlib and Turtle. This simple approach shows state-of-the-art results on four difficult natural language tasks that involve visual and spatial reasoning. We identify multiple settings where GPT-4o using chain-of-thought fails dramatically, including more than one where it achieves 0% accuracy, while whiteboard-of-thought enables up to 92% accuracy in these same settings. We present a detailed exploration of where the technique succeeds as well as its sources of error.

Large language models (LLMs) have demonstrated impressive performance in various natural language processing tasks, yet their ability to perform multi-step logical reasoning remains an open challenge. Although Chain-of-Thought prompting has improved logical reasoning by enabling models to generate intermediate steps, it lacks mechanisms to assess the coherence of these logical transitions. In this paper, we propose a novel, lightweight evaluation strategy for logical reasoning that uses query-key alignments inside transformer attention heads. By computing a single forward pass and extracting a "QK-score" from carefully chosen heads, our method reveals latent representations that reliably separate valid from invalid inferences, offering a scalable alternative to traditional ablation-based techniques. We also provide an empirical validation on multiple logical reasoning benchmarks, demonstrating improved robustness of our evaluation method against distractors and increased reasoning depth. The experiments were conducted on a diverse set of models, ranging from 1.5B to 70B parameters.

Chain-of-Thought significantly enhances a model's reasoning capability, but it also comes with a considerable increase in inference costs due to long chains. With the observation that the reasoning path can be easily compressed under easy tasks but struggle on hard tasks, we explore the feasibility of elastically controlling the length of reasoning paths with only one model, thereby reducing the inference overhead of reasoning models dynamically based on task difficulty. We introduce a new tuning and inference strategy named CoT-Valve, designed to allow models to generate reasoning chains of varying lengths. To achieve this, we propose to identify a direction in the parameter space that, when manipulated, can effectively control the length of generated CoT. Moreover, we show that this property is valuable for compressing the reasoning chain. We construct datasets with chains from long to short for the same questions and explore two enhanced strategies for CoT-Valve: (1) a precise length-compressible CoT tuning method, and (2) a progressive chain length compression approach. Our experiments show that CoT-Valve successfully enables controllability and compressibility of the chain and shows better performance than the prompt-based control. We applied this method to QwQ-32B-Preview, reducing reasoning chains on GSM8K from 741 to 225 tokens with a minor performance drop (95.07% to 94.92%) and on AIME from 6827 to 4629 tokens, with only one additional incorrect answer.

Recent advancements in large language models have showcased their remarkable generalizability across various domains. However, their reasoning abilities still have significant room for improvement, especially when confronted with scenarios requiring multi-step reasoning. Although large language models possess extensive knowledge, their behavior, particularly in terms of reasoning, often fails to effectively utilize this knowledge to establish a coherent thinking paradigm. Generative language models sometimes show hallucinations as their reasoning procedures are unconstrained by logical principles. Aiming to improve the zero-shot chain-of-thought reasoning ability of large language models, we propose Logical Chain-of-Thought (LogiCoT), a neurosymbolic framework that leverages principles from symbolic logic to verify and revise the reasoning processes accordingly. Experimental evaluations conducted on language tasks in diverse domains, including arithmetic, commonsense, symbolic, causal inference, and social problems, demonstrate the efficacy of the enhanced reasoning paradigm by logic.

This paper presents a novel framework for enhancing reasoning capabilities in large language models (LLMs) by leveraging iterative reasoning and feedback-driven methodologies. Building on the limitations identified in the SimpleBench benchmark, a dataset designed to evaluate logical coherence and real-world reasoning, we propose a multi-step prompting strategy coupled with global consistency checks to improve model accuracy and robustness. Through comparative analysis of state-of-the-art models, including Claude 3 Opus, Claude 3.5, GPT- 4o, and o1-preview, we demonstrate that iterative reasoning significantly enhances model performance, with improvements observed in both standard accuracy metrics (AVG@5) and a newly introduced metric, Extreme Averaging (EAG@5). Our results reveal model-specific strengths: Claude excels in maintaining logical consistency, while GPT-4o exhibits exploratory creativity but struggles with ambiguous prompts. By analyzing case studies and identifying gaps in spatial and temporal reasoning, we highlight areas for further refinement. The findings underscore the potential of structured reasoning frameworks to address inherent model limitations, irrespective of pretraining methodologies. This study lays the groundwork for integrating dynamic feedback mechanisms, adaptive restart strategies, and diverse evaluation metrics to advance LLM reasoning capabilities across complex and multi-domain problem spaces.

Large language models (LLMs) have a substantial capacity for high-level analogical reasoning: reproducing patterns in linear text that occur in their training data (zero-shot evaluation) or in the provided context (few-shot in-context learning). However, recent studies show that even the more advanced LLMs fail in scenarios that require reasoning over multiple objects or facts and making sequences of logical deductions. We propose a two-stage probabilistic inference paradigm, ThinkSum, which reasons over sets of objects or facts in a structured manner. In the first stage (Think - retrieval of associations), a LLM is queried in parallel over a set of phrases extracted from the prompt or an auxiliary model call. In the second stage (Sum - probabilistic inference or reasoning), the results of these queries are aggregated to make the final prediction. We demonstrate the possibilities and advantages of ThinkSum on the BIG-bench suite of LLM evaluation tasks, achieving improvements over the state of the art using GPT-family models on thirteen difficult tasks, often with far smaller model variants. We also compare and contrast ThinkSum with other proposed modifications to direct prompting of LLMs, such as variants of chain-of-thought prompting. Our results suggest that because the probabilistic inference in ThinkSum is performed outside of calls to the LLM, ThinkSum is less sensitive to prompt design, yields more interpretable predictions, and can be flexibly combined with latent variable models to extract structured knowledge from LLMs. Overall, our proposed paradigm represents a promising approach for enhancing the reasoning capabilities of LLMs.

Chain of Thought (CoT) was introduced in recent research as a method for improving step-by-step reasoning in Large Language Models. However, CoT has limited applications such as its need for hand-crafted few-shot exemplar prompts and no capability to adjust itself to different queries. In this work, we propose a system to automatically generate rationales using CoT. Our method improves multi-step implicit reasoning capabilities by decomposing the implicit query into several explicit questions. This provides interpretability for the model, improving reasoning in weaker LLMs. We test our approach with two Q\&A datasets: StrategyQA and HotpotQA. We show an increase in accuracy with both, especially on StrategyQA. To facilitate further research in this field, the complete source code for this study has been made publicly available on GitHub: https://github.com/miralab-ai/autoreason.

Large language models have shown impressive results for multi-hop mathematical reasoning when the input question is only textual. Many mathematical reasoning problems, however, contain both text and image. With the ever-increasing adoption of vision language models (VLMs), understanding their reasoning abilities for such problems is crucial. In this paper, we evaluate the reasoning capabilities of VLMs along various axes through the lens of geometry problems. We procedurally create a synthetic dataset of geometry questions with controllable difficulty levels along multiple axes, thus enabling a systematic evaluation. The empirical results obtained using our benchmark for state-of-the-art VLMs indicate that these models are not as capable in subjects like geometry (and, by generalization, other topics requiring similar reasoning) as suggested by previous benchmarks. This is made especially clear by the construction of our benchmark at various depth levels, since solving higher-depth problems requires long chains of reasoning rather than additional memorized knowledge. We release the dataset for further research in this area.

The chain-of-though (CoT) prompting methods were successful in various natural language processing (NLP) tasks thanks to their ability to unveil the underlying complex reasoning processes. Such reasoning processes typically exhibit implicitly structured steps. Recent efforts also started investigating methods to encourage more explicitly structured reasoning procedures to be captured. In this work, we propose Tab-CoT, a novel tabular-format CoT prompting method, which allows the complex reasoning process to be explicitly modelled in a highly structured manner. Despite its simplicity, we show that our approach is capable of performing reasoning across multiple dimensions (i.e., both rows and columns). We demonstrate our approach's strong zero-shot and few-shot capabilities through extensive experiments on a range of reasoning tasks.

We propose a novel Chain Guided Retriever-reader ({\tt CGR}) framework to model the reasoning chain for multi-hop Science Question Answering. Our framework is capable of performing explainable reasoning without the need of any corpus-specific annotations, such as the ground-truth reasoning chain, or human-annotated entity mentions. Specifically, we first generate reasoning chains from a semantic graph constructed by Abstract Meaning Representation of retrieved evidence facts. A Chain-aware loss, concerning both local and global chain information, is also designed to enable the generated chains to serve as distant supervision signals for training the retriever, where reinforcement learning is also adopted to maximize the utility of the reasoning chains. Our framework allows the retriever to capture step-by-step clues of the entire reasoning process, which is not only shown to be effective on two challenging multi-hop Science QA tasks, namely OpenBookQA and ARC-Challenge, but also favors explainability.

Large language models (LLMs) have revolutionized many areas (e.g. natural language processing, software engineering, etc.) by achieving state-of-the-art performance on extensive downstream tasks. Aiming to achieve robust and general artificial intelligence, there has been a surge of interest in investigating the reasoning ability of the LLMs. Whereas the textual and numerical reasoning benchmarks adopted by previous works are rather shallow and simple, it is hard to conclude that the LLMs possess strong reasoning ability by merely achieving positive results on these benchmarks. Recent efforts have demonstrated that the LLMs are poor at solving sequential decision-making problems that require common-sense planning by evaluating their performance on the reinforcement learning benchmarks. In this work, we conduct an in-depth assessment of several state-of-the-art LLMs' reasoning ability based on the inductive logic programming (ILP) benchmark, which is broadly recognized as a representative and challenging measurement for evaluating logic program induction/synthesis systems as it requires inducing strict cause-effect logic to achieve robust deduction on independent and identically distributed (IID) and out-of-distribution (OOD) test samples. Our evaluations illustrate that compared with the neural program induction systems which are much smaller in model size, the state-of-the-art LLMs are much poorer in terms of reasoning ability by achieving much lower performance and generalization using either natural language prompting or truth-value matrix prompting.

Chain-of-Thought(CoT) prompting and its variants explore equipping large language models (LLMs) with high-level reasoning abilities by emulating human-like linear cognition and logic. However, the human mind is complicated and mixed with both linear and nonlinear thinking. In this work, we propose Inferential Exclusion Prompting (IEP), a novel prompting that combines the principles of elimination and inference in order to guide LLMs to think non-linearly. IEP guides LLMs to plan and then utilize Natural Language Inference (NLI) to deduce each possible solution's entailment relation with context, commonsense, or facts, therefore yielding a broader perspective by thinking back for inferring. This forward planning and backward eliminating process allows IEP to better simulate the complex human thinking processes compared to other CoT-based methods, which only reflect linear cognitive processes. We conducted a series of empirical studies and have corroborated that IEP consistently outperforms CoT across various tasks. Additionally, we observe that integrating IEP and CoT further improves the LLMs' performance on certain tasks, highlighting the necessity of equipping LLMs with mixed logic processes. Moreover, to better evaluate comprehensive features inherent in human logic, we introduce Mental-Ability Reasoning Benchmark (MARB). The benchmark comprises six novel subtasks with a total of 9,115 questions, among which 1,685 are developed with hand-crafted rationale references. We believe both IEP and MARB can serve as a promising direction for unveiling LLMs' logic and verbal reasoning abilities and drive further advancements. MARB will be available at ~anonymity link soon.

Recent advancements in Chain-of-Thought prompting have facilitated significant breakthroughs for Large Language Models (LLMs) in complex reasoning tasks. Current research enhances the reasoning performance of LLMs by sampling multiple reasoning chains and ensembling based on the answer frequency. However, this approach fails in scenarios where the correct answers are in the minority. We identify this as a primary factor constraining the reasoning capabilities of LLMs, a limitation that cannot be resolved solely based on the predicted answers. To address this shortcoming, we introduce a hierarchical reasoning aggregation framework AoR (Aggregation of Reasoning), which selects answers based on the evaluation of reasoning chains. Additionally, AoR incorporates dynamic sampling, adjusting the number of reasoning chains in accordance with the complexity of the task. Experimental results on a series of complex reasoning tasks show that AoR outperforms prominent ensemble methods. Further analysis reveals that AoR not only adapts various LLMs but also achieves a superior performance ceiling when compared to current methods.

Few-shot Chain-of-Thought (CoT) prompting has demonstrated strong performance in improving the reasoning capabilities of large language models (LLMs). While theoretical investigations have been conducted to understand CoT, the underlying transformer used in these studies isolates the CoT reasoning process into separated in-context learning steps (Stepwise ICL). In this work, we theoretically show that, compared to Stepwise ICL, the transformer gains better error correction ability and more accurate predictions if the reasoning from earlier steps (Coherent CoT) is integrated. Given that this coherent reasoning changes the behavior of the transformer, we further investigate the sensitivity of the transformer with Coherent CoT when the demonstration examples are corrupted at the inference stage. Our theoretical results indicate that the transformer is more sensitive to errors in intermediate reasoning steps than the final outcome. Building upon this observation, we propose an improvement on CoT by incorporating both correct and incorrect reasoning paths in the demonstration. Our experiments validate the effectiveness of the proposed approach.

Chain-of-Thought (CoT) prompting reveals that large language models are capable of performing complex reasoning via intermediate steps. CoT prompting is primarily categorized into three approaches. The first approach utilizes straightforward prompts like ``Let's think step by step'' to generate a sequential thought process before yielding an answer. The second approach makes use of human-crafted, step-by-step demonstrations to guide the model's reasoning process. The third automates the generation of reasoned demonstrations with the 'Let's think step by step'.This approach sometimes leads to reasoning errors, highlighting the need to diversify demonstrations to mitigate its misleading effects. However, diverse demonstrations pose challenges for effective representations. In this work, we propose ECHO, a self-harmonized chain-of-thought prompting method. It consolidates diverse solution paths into a uniform and effective solution pattern.ECHO demonstrates the best overall performance across three reasoning domains.

Existing benchmarks for frontier models often test specialized, ``PhD-level'' knowledge that is difficult for non-experts to grasp. In contrast, we present a benchmark based on the NPR Sunday Puzzle Challenge that requires only general knowledge. Our benchmark is challenging for both humans and models, however correct solutions are easy to verify, and models' mistakes are easy to spot. Our work reveals capability gaps that are not evident in existing benchmarks: OpenAI o1 significantly outperforms other reasoning models that are on par on benchmarks that test specialized knowledge. Furthermore, our analysis of reasoning outputs uncovers new kinds of failures. DeepSeek R1, for instance, often concedes with ``I give up'' before providing an answer that it knows is wrong. R1 can also be remarkably ``uncertain'' in its output and in rare cases, it does not ``finish thinking,'' which suggests the need for an inference-time technique to ``wrap up'' before the context window limit is reached. We also quantify the effectiveness of reasoning longer with R1 and Gemini Thinking to identify the point beyond which more reasoning is unlikely to improve accuracy on our benchmark.

Large language models show improved downstream task performance when prompted to generate step-by-step reasoning to justify their final answers. These reasoning steps greatly improve model interpretability and verification, but objectively studying their correctness (independent of the final answer) is difficult without reliable methods for automatic evaluation. We simply do not know how often the stated reasoning steps actually support the final end task predictions. In this work, we present ROSCOE, a suite of interpretable, unsupervised automatic scores that improve and extend previous text generation evaluation metrics. To evaluate ROSCOE against baseline metrics, we design a typology of reasoning errors and collect synthetic and human evaluation scores on commonly used reasoning datasets. In contrast with existing metrics, ROSCOE can measure semantic consistency, logicality, informativeness, fluency, and factuality - among other traits - by leveraging properties of step-by-step rationales. We empirically verify the strength of our metrics on five human annotated and six programmatically perturbed diagnostics datasets - covering a diverse set of tasks that require reasoning skills and show that ROSCOE can consistently outperform baseline metrics.

Large language models (LLMs) have gained enormous attention from both academia and industry, due to their exceptional ability in language generation and extremely powerful generalization. However, current LLMs still output unreliable content in practical reasoning tasks due to their inherent issues (e.g., hallucination). To better disentangle this problem, in this paper, we conduct an in-depth investigation to systematically explore the capability of LLMs in logical reasoning. More in detail, we first investigate the deficiency of LLMs in logical reasoning on different tasks, including event relation extraction and deductive reasoning. Our study demonstrates that LLMs are not good reasoners in solving tasks with rigorous reasoning and will produce counterfactual answers, which require us to iteratively refine. Therefore, we comprehensively explore different strategies to endow LLMs with logical reasoning ability, and thus enable them to generate more logically consistent answers across different scenarios. Based on our approach, we also contribute a synthesized dataset (LLM-LR) involving multi-hop reasoning for evaluation and pre-training. Extensive quantitative and qualitative analyses on different tasks also validate the effectiveness and necessity of teaching LLMs with logic and provide insights for solving practical tasks with LLMs in future work.

Commonsense causality reasoning (CCR) aims at identifying plausible causes and effects in natural language descriptions that are deemed reasonable by an average person. Although being of great academic and practical interest, this problem is still shadowed by the lack of a well-posed theoretical framework; existing work usually relies on deep language models wholeheartedly, and is potentially susceptible to confounding co-occurrences. Motivated by classical causal principles, we articulate the central question of CCR and draw parallels between human subjects in observational studies and natural languages to adopt CCR to the potential-outcomes framework, which is the first such attempt for commonsense tasks. We propose a novel framework, ROCK, to Reason O(A)bout Commonsense K(C)ausality, which utilizes temporal signals as incidental supervision, and balances confounding effects using temporal propensities that are analogous to propensity scores. The ROCK implementation is modular and zero-shot, and demonstrates good CCR capabilities.

Language models often achieve higher accuracy when reasoning step-by-step in complex tasks. However, their reasoning can be unsound, inconsistent, or rely on undesirable prior assumptions. To tackle these issues, we introduce a class of tools for language models called guides that use state and incremental constraints to guide generation. A guide can be invoked by the model to constrain its own generation to a set of valid statements given by the tool. In turn, the model's choices can change the guide's state. We show how a general system for logical reasoning can be used as a guide, which we call LogicGuide. Given a reasoning problem in natural language, a model can formalize its assumptions for LogicGuide and then guarantee that its reasoning steps are sound. In experiments with the PrOntoQA and ProofWriter reasoning datasets, LogicGuide significantly improves the performance of GPT-3, GPT-3.5 Turbo and LLaMA (accuracy gains up to 35%). LogicGuide also drastically reduces content effects: the interference of prior and current assumptions that both humans and language models have been shown to suffer from. Finally, we explore bootstrapping LLaMA 13B from its own reasoning and find that LogicGuide is critical: by training only on certified self-generated reasoning, LLaMA can self-improve, avoiding learning from its own hallucinations.

The capabilities and limitations of Large Language Models have been sketched out in great detail in recent years, providing an intriguing yet conflicting picture. On the one hand, LLMs demonstrate a general ability to solve problems. On the other hand, they show surprising reasoning gaps when compared to humans, casting doubt on the robustness of their generalisation strategies. The sheer volume of data used in the design of LLMs has precluded us from applying the method traditionally used to measure generalisation: train-test set separation. To overcome this, we study what kind of generalisation strategies LLMs employ when performing reasoning tasks by investigating the pretraining data they rely on. For two models of different sizes (7B and 35B) and 2.5B of their pretraining tokens, we identify what documents influence the model outputs for three simple mathematical reasoning tasks and contrast this to the data that are influential for answering factual questions. We find that, while the models rely on mostly distinct sets of data for each factual question, a document often has a similar influence across different reasoning questions within the same task, indicating the presence of procedural knowledge. We further find that the answers to factual questions often show up in the most influential data. However, for reasoning questions the answers usually do not show up as highly influential, nor do the answers to the intermediate reasoning steps. When we characterise the top ranked documents for the reasoning questions qualitatively, we confirm that the influential documents often contain procedural knowledge, like demonstrating how to obtain a solution using formulae or code. Our findings indicate that the approach to reasoning the models use is unlike retrieval, and more like a generalisable strategy that synthesises procedural knowledge from documents doing a similar form of reasoning.

Spatial reasoning is a crucial component of both biological and artificial intelligence. In this work, we present a comprehensive study of the capability of current state-of-the-art large language models (LLMs) on spatial reasoning. To support our study, we created and contribute a novel Spatial Reasoning Characterization (SpaRC) framework and Spatial Reasoning Paths (SpaRP) datasets, to enable an in-depth understanding of the spatial relations and compositions as well as the usefulness of spatial reasoning chains. We found that all the state-of-the-art LLMs do not perform well on the datasets -- their performances are consistently low across different setups. The spatial reasoning capability improves substantially as model sizes scale up. Finetuning both large language models (e.g., Llama-2-70B) and smaller ones (e.g., Llama-2-13B) can significantly improve their F1-scores by 7--32 absolute points. We also found that the top proprietary LLMs still significantly outperform their open-source counterparts in topological spatial understanding and reasoning.

Large language models (LLMs) are becoming increasingly important for machine learning applications. However, it can be challenging to align LLMs with our intent, particularly when we want to generate content that is preferable over others or when we want the LLM to respond in a certain style or tone that is hard to describe. To address this challenge, we propose an approach that uses contrastive examples to better describe our intent. This involves providing positive examples that illustrate the true intent, along with negative examples that show what characteristics we want LLMs to avoid. The negative examples can be retrieved from labeled data, written by a human, or generated by the LLM itself. Before generating an answer, we ask the model to analyze the examples to teach itself what to avoid. This reasoning step provides the model with the appropriate articulation of the user's need and guides it towards generting a better answer. We tested our approach on both synthesized and real-world datasets, including StackExchange and Reddit, and found that it significantly improves performance compared to standard few-shot prompting

Despite their tremendous success in many applications, large language models often fall short of consistent reasoning and planning in various (language, embodied, and social) scenarios, due to inherent limitations in their inference, learning, and modeling capabilities. In this position paper, we present a new perspective of machine reasoning, LAW, that connects the concepts of Language models, Agent models, and World models, for more robust and versatile reasoning capabilities. In particular, we propose that world and agent models are a better abstraction of reasoning, that introduces the crucial elements of deliberate human-like reasoning, including beliefs about the world and other agents, anticipation of consequences, goals/rewards, and strategic planning. Crucially, language models in LAW serve as a backend to implement the system or its elements and hence provide the computational power and adaptability. We review the recent studies that have made relevant progress and discuss future research directions towards operationalizing the LAW framework.

The reasoning performance of Large Language Models (LLMs) on a wide range of problems critically relies on chain-of-thought prompting, which involves providing a few chain of thought demonstrations as exemplars in prompts. Recent work, e.g., Tree of Thoughts, has pointed out the importance of exploration and self-evaluation in reasoning step selection for complex problem solving. In this paper, we present Boosting of Thoughts (BoT), an automated prompting framework for problem solving with LLMs by iteratively exploring and self-evaluating many trees of thoughts in order to acquire an ensemble of trial-and-error reasoning experiences, which will serve as a new form of prompting to solve the complex problem. Starting from a simple prompt without requiring examples, BoT iteratively explores and evaluates a large collection of reasoning steps, and more importantly, uses error analysis obtained from the LLM on them to explicitly revise prompting, which in turn enhances reasoning step generation, until a final answer is attained. Our experiments with GPT-4 and Llama2 across extensive complex mathematical problems demonstrate that BoT consistently achieves higher or comparable problem-solving rates than other advanced prompting approaches.

Chain-of-Thought (CoT) prompting has proven to be effective in enhancing the reasoning capabilities of Large Language Models (LLMs) with at least 100 billion parameters. However, it is ineffective or even detrimental when applied to reasoning tasks in Smaller Language Models (SLMs) with less than 10 billion parameters. To address this limitation, we introduce Dialogue-guided Chain-of-Thought (DialCoT) which employs a dialogue format to generate intermediate reasoning steps, guiding the model toward the final answer. Additionally, we optimize the model's reasoning path selection using the Proximal Policy Optimization (PPO) algorithm, further enhancing its reasoning capabilities. Our method offers several advantages compared to previous approaches. Firstly, we transform the process of solving complex reasoning questions by breaking them down into a series of simpler sub-questions, significantly reducing the task difficulty and making it more suitable for SLMs. Secondly, we optimize the model's reasoning path selection through the PPO algorithm. We conduct comprehensive experiments on four arithmetic reasoning datasets, demonstrating that our method achieves significant performance improvements compared to state-of-the-art competitors.

Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the automated resolution of mathematical problems. However, the landscape of mathematical problem types is vast and varied, with LLM-oriented techniques undergoing evaluation across diverse datasets and settings. This diversity makes it challenging to discern the true advancements and obstacles within this burgeoning field. This survey endeavors to address four pivotal dimensions: i) a comprehensive exploration of the various mathematical problems and their corresponding datasets that have been investigated; ii) an examination of the spectrum of LLM-oriented techniques that have been proposed for mathematical problem-solving; iii) an overview of factors and concerns affecting LLMs in solving math; and iv) an elucidation of the persisting challenges within this domain. To the best of our knowledge, this survey stands as one of the first extensive examinations of the landscape of LLMs in the realm of mathematics, providing a holistic perspective on the current state, accomplishments, and future challenges in this rapidly evolving field.

Prompting language models to provide step-by-step answers (e.g., "Chain-of-Thought") is the prominent approach for complex reasoning tasks, where more accurate reasoning chains typically improve downstream task performance. Recent literature discusses automatic methods to verify reasoning steps to evaluate and improve their correctness. However, no fine-grained step-level datasets are available to enable thorough evaluation of such verification methods, hindering progress in this direction. We introduce Reveal: Reasoning Verification Evaluation, a new dataset to benchmark automatic verifiers of complex Chain-of-Thought reasoning in open-domain question answering settings. Reveal includes comprehensive labels for the relevance, attribution to evidence passages, and logical correctness of each reasoning step in a language model's answer, across a wide variety of datasets and state-of-the-art language models.

The development of large language models (LLM) has shown progress on reasoning, though studies have largely considered either English or simple reasoning tasks. To address this, we introduce a multilingual structured reasoning and explanation dataset, termed xSTREET, that covers four tasks across six languages. xSTREET exposes a gap in base LLM performance between English and non-English reasoning tasks. We then propose two methods to remedy this gap, building on the insight that LLMs trained on code are better reasoners. First, at training time, we augment a code dataset with multilingual comments using machine translation while keeping program code as-is. Second, at inference time, we bridge the gap between training and inference by employing a prompt structure that incorporates step-by-step code primitives to derive new facts and find a solution. Our methods show improved multilingual performance on xSTREET, most notably on the scientific commonsense reasoning subtask. Furthermore, the models show no regression on non-reasoning tasks, thus demonstrating our techniques maintain general-purpose abilities.

This survey paper proposes a clearer view of natural language reasoning in the field of Natural Language Processing (NLP), both conceptually and practically. Conceptually, we provide a distinct definition for natural language reasoning in NLP, based on both philosophy and NLP scenarios, discuss what types of tasks require reasoning, and introduce a taxonomy of reasoning. Practically, we conduct a comprehensive literature review on natural language reasoning in NLP, mainly covering classical logical reasoning, natural language inference, multi-hop question answering, and commonsense reasoning. The paper also identifies and views backward reasoning, a powerful paradigm for multi-step reasoning, and introduces defeasible reasoning as one of the most important future directions in natural language reasoning research. We focus on single-modality unstructured natural language text, excluding neuro-symbolic techniques and mathematical reasoning.

The reasoning abilities of Large Language Models (LLMs) remain a topic of debate. Some methods such as ReAct-based prompting, have gained popularity for claiming to enhance sequential decision-making abilities of agentic LLMs. However, it is unclear what is the source of improvement in LLM reasoning with ReAct based prompting. In this paper we examine these claims of ReAct based prompting in improving agentic LLMs for sequential decision-making. By introducing systematic variations to the input prompt we perform a sensitivity analysis along the claims of ReAct and find that the performance is minimally influenced by the "interleaving reasoning trace with action execution" or the content of the generated reasoning traces in ReAct, contrary to original claims and common usage. Instead, the performance of LLMs is driven by the similarity between input example tasks and queries, implicitly forcing the prompt designer to provide instance-specific examples which significantly increases the cognitive burden on the human. Our investigation shows that the perceived reasoning abilities of LLMs stem from the exemplar-query similarity and approximate retrieval rather than any inherent reasoning abilities.

Emergent chain-of-thought (CoT) reasoning capabilities promise to improve performance and explainability of large language models (LLMs). However, uncertainties remain about how reasoning strategies formulated for previous model generations generalize to new model generations and different datasets. In this small-scale study, we compare different reasoning strategies induced by zero-shot prompting across six recently released LLMs (davinci-002, davinci-003, GPT-3.5-turbo, GPT-4, Flan-T5-xxl and Cohere command-xlarge) on a mixture of six question-answering datasets, including datasets from scientific and medical domains. Our findings demonstrate that while some variations in effectiveness occur, gains from CoT reasoning strategies remain robust across different models and datasets. GPT-4 has the most benefit from current state-of-the-art reasoning strategies and exhibits the best performance by applying a prompt previously discovered through automated discovery.

Multi-hop reasoning (i.e., reasoning across two or more documents) is a key ingredient for NLP models that leverage large corpora to exhibit broad knowledge. To retrieve evidence passages, multi-hop models must contend with a fast-growing search space across the hops, represent complex queries that combine multiple information needs, and resolve ambiguity about the best order in which to hop between training passages. We tackle these problems via Baleen, a system that improves the accuracy of multi-hop retrieval while learning robustly from weak training signals in the many-hop setting. To tame the search space, we propose condensed retrieval, a pipeline that summarizes the retrieved passages after each hop into a single compact context. To model complex queries, we introduce a focused late interaction retriever that allows different parts of the same query representation to match disparate relevant passages. Lastly, to infer the hopping dependencies among unordered training passages, we devise latent hop ordering, a weak-supervision strategy in which the trained retriever itself selects the sequence of hops. We evaluate Baleen on retrieval for two-hop question answering and many-hop claim verification, establishing state-of-the-art performance.

Recent large language models (LLMs) have shown indications of mathematical reasoning ability. However it has not been clear how they would fare on more challenging competition-level problems. And while self-generated verbalizations of intermediate reasoning steps (i.e., chain-of-thought prompting) have been shown to be helpful, whether LLMs can make use of helpful side information such as problem-specific hints has not been investigated before. In this paper, we propose a challenging benchmark dataset for enabling such analyses. The Concept and Hint-Annotated Math Problems (CHAMP) consists of high school math competition problems, annotated with concepts, or general math facts, and hints, or problem-specific tricks. These annotations allow us to explore the effects of additional information, such as relevant hints, misleading concepts, or related problems. This benchmark is difficult, with the best model only scoring 58.1% in standard settings. With concepts and hints, performance sometimes improves, indicating that some models can make use of such side information. We further annotate model-generated solutions for their correctness. Using this corpus, we find that models often arrive at the correct final answer through wrong reasoning steps. In addition, we test whether models are able to verify these solutions, and find that most models struggle. The dataset and code are available on the project website.

Large language models (LLMs) have shown increasing capability in problem-solving and decision-making, largely based on the step-by-step chain-of-thought reasoning processes. However, it has been increasingly challenging to evaluate the reasoning capability of LLMs. Concretely, existing outcome-based benchmarks begin to saturate and become less sufficient to monitor the progress. To this end, we present a process-based benchmark MR-BEN that demands a meta reasoning skill, where LMs are asked to locate and analyse potential errors in automatically generated reasoning steps. MR-BEN is a comprehensive benchmark comprising 5,975 questions collected from human experts, covering various subjects such as physics, chemistry, logic, coding, and more. Through our designed metrics for assessing meta-reasoning on this benchmark, we identify interesting limitations and weaknesses of current LLMs (open-source and closed-source models). For example, open-source models are seemingly comparable to GPT-4 on outcome-based benchmarks, but they lag far behind on our benchmark, revealing the underlying reasoning capability gap between them. Our dataset and codes are available on https://randolph-zeng.github.io/Mr-Ben.github.io/.

The growing power of large language models (LLMs) has revolutionized how people access and utilize information. Notably, the LLMs excel at performing fine-grained data representation, which facilitates precise retrieval of information. They also generate high-quality answers based on external references, enabling the production of useful knowledge. The recent introduction of reasoning models, like OpenAI O1 and DeepSeek R1, marks another leap forward, highlighting LLMs' ability to think progressively before delivering final answers. This breakthrough significantly improves the ability to address complex tasks, e.g., coding and math proofs. Inspired by this progress, we aim to develop similar capabilities for retrieval models, which hold great promise for tackling critical challenges in the field, including multi-task retrieval, zero-shot retrieval, and tasks requiring intensive reasoning of complex relationships. With this motivation, we propose a novel approach called O1 Embedder, which generates useful thoughts for the input query before making retrieval for the target documents. To realize this objective, we conquer two technical difficulties. First, we design a data synthesis workflow, creating training signals for O1 Embedder by generating initial thoughts from an LLM-expert and subsequently refining them using a retrieval committee. Second, we optimize the training process, enabling a pre-trained model to be jointly fine-tuned to generate retrieval thoughts via behavior cloning and perform dense retrieval through contrastive learning. Our approach is evaluated by comprehensive experiments, where substantial improvements are achieved across 12 popular datasets, spanning both in-domain and out-of-domain scenarios. These results highlight O1 Embedder's remarkable accuracy and generalizability, paving the way for the development of next-generation IR foundation models.