Daily Papers

Self-training approach for large language models (LLMs) improves reasoning abilities by training the models on their self-generated rationales. Previous approaches have labeled rationales that produce correct answers for a given question as appropriate for training. However, a single measure risks misjudging rationale quality, leading the models to learn flawed reasoning patterns. To address this issue, we propose CREST (Consistency-driven Rationale Evaluation for Self-Training), a self-training framework that further evaluates each rationale through follow-up questions and leverages this evaluation to guide its training. Specifically, we introduce two methods: (1) filtering out rationales that frequently result in incorrect answers on follow-up questions and (2) preference learning based on mixed preferences from rationale evaluation results of both original and follow-up questions. Experiments on three question-answering datasets using open LLMs show that CREST not only improves the logical robustness and correctness of rationales but also improves reasoning abilities compared to previous self-training approaches.

Learning from preference feedback is a common practice for aligning large language models~(LLMs) with human value. Conventionally, preference data is learned and encoded into a scalar reward model that connects a value head with an LLM to produce a scalar score as preference or reward. However, scalar models lack interpretability and are known to be susceptible to biases in datasets. This paper investigates leveraging the generation capability of LLMs to address both limitations in one shot. Specifically, we prompt the pre-trained LLM to generate positive and negative judgments, both supported with rationales in natural language form. The self-generated contrastive judgment pairs are used to train the generative judge with Direct Preference Optimization (DPO). This proposal of training the generative Judge using self-generated Contrastive judgments (Con-J) ensures natural interpretability due to the generated rationales together with the judgments, as well as high robustness against bias without the need for an additional reward head. Experimental results show that the performance of Con-J is comparable to the scalar reward model trained on the same collection of preference data, and demonstrate its superior interpretability and robustness in encoding human preferences.

Large language models (LLMs) often generate inaccurate or fabricated information and generally fail to indicate their confidence, which limits their broader applications. Previous work elicits confidence from LLMs by direct or self-consistency prompting, or constructing specific datasets for supervised finetuning. The prompting-based approaches have inferior performance, and the training-based approaches are limited to binary or inaccurate group-level confidence estimates. In this work, we present the advanced SaySelf, a training framework that teaches LLMs to express more accurate fine-grained confidence estimates. In addition, beyond the confidence scores, SaySelf initiates the process of directing LLMs to produce self-reflective rationales that clearly identify gaps in their parametric knowledge and explain their uncertainty. This is achieved by using an LLM to automatically summarize the uncertainties in specific knowledge via natural language. The summarization is based on the analysis of the inconsistency in multiple sampled reasoning chains, and the resulting data is utilized for supervised fine-tuning. Moreover, we utilize reinforcement learning with a meticulously crafted reward function to calibrate the confidence estimates, motivating LLMs to deliver accurate, high-confidence predictions and to penalize overconfidence in erroneous outputs. Experimental results in both in-distribution and out-of-distribution datasets demonstrate the effectiveness of SaySelf in reducing the confidence calibration error and maintaining the task performance. We show that the generated self-reflective rationales are reasonable and can further contribute to the calibration. The code is made public at https://github.com/xu1868/SaySelf.

Multimodal reasoning is a challenging task that requires models to reason across multiple modalities to answer questions. Existing approaches have made progress by incorporating language and visual modalities into a two-stage reasoning framework, separating rationale generation from answer inference. However, these approaches often fall short due to the inadequate quality of the generated rationales. In this work, we delve into the importance of rationales in model reasoning. We observe that when rationales are completely accurate, the model's accuracy significantly improves, highlighting the need for high-quality rationale generation. Motivated by this, we propose MC-CoT, a self-consistency training strategy that generates multiple rationales and answers, subsequently selecting the most accurate through a voting process. This approach not only enhances the quality of generated rationales but also leads to more accurate and robust answers. Through extensive experiments, we demonstrate that our approach significantly improves model performance across various benchmarks. Remarkably, we show that even smaller base models, when equipped with our proposed approach, can achieve results comparable to those of larger models, illustrating the potential of our approach in harnessing the power of rationales for improved multimodal reasoning. The code is available at https://github.com/chengtan9907/mc-cot.

LLM-as-a-judge models have been used for evaluating both human and AI generated content, specifically by providing scores and rationales. Rationales, in addition to increasing transparency, help models learn to calibrate its judgments. Enhancing a model's rationale can therefore improve its calibration abilities and ultimately the ability to score content. We introduce Self-Rationalization, an iterative process of improving the rationales for the judge models, which consequently improves the score for fine-grained customizable scoring criteria (i.e., likert-scale scoring with arbitrary evaluation criteria). Self-rationalization works by having the model generate multiple judgments with rationales for the same input, curating a preference pair dataset from its own judgements, and iteratively fine-tuning the judge via DPO. Intuitively, this approach allows the judge model to self-improve by learning from its own rationales, leading to better alignment and evaluation accuracy. After just two iterations -- while only relying on examples in the training set -- human evaluation shows that our judge model learns to produce higher quality rationales, with a win rate of 62% on average compared to models just trained via SFT on rationale . This judge model also achieves high scoring accuracy on BigGen Bench and Reward Bench, outperforming even bigger sized models trained using SFT with rationale, self-consistency or best-of-N sampling by 3% to 9%.

Generating step-by-step "chain-of-thought" rationales improves language model performance on complex reasoning tasks like mathematics or commonsense question-answering. However, inducing language model rationale generation currently requires either constructing massive rationale datasets or sacrificing accuracy by using only few-shot inference. We propose a technique to iteratively leverage a small number of rationale examples and a large dataset without rationales, to bootstrap the ability to perform successively more complex reasoning. This technique, the "Self-Taught Reasoner" (STaR), relies on a simple loop: generate rationales to answer many questions, prompted with a few rationale examples; if the generated answers are wrong, try again to generate a rationale given the correct answer; fine-tune on all the rationales that ultimately yielded correct answers; repeat. We show that STaR significantly improves performance on multiple datasets compared to a model fine-tuned to directly predict final answers, and performs comparably to fine-tuning a 30times larger state-of-the-art language model on CommensenseQA. Thus, STaR lets a model improve itself by learning from its own generated reasoning.

Large language models (LMs) are capable of generating free-text rationales to aid question answering. However, prior work 1) suggests that useful self-rationalization is emergent only at significant scales (e.g., 175B parameter GPT-3); and 2) focuses largely on downstream performance, ignoring the semantics of the rationales themselves, e.g., are they faithful, true, and helpful for humans? In this work, we enable small-scale LMs (approx. 200x smaller than GPT-3) to generate rationales that not only improve downstream task performance, but are also more plausible, consistent, and diverse, assessed both by automatic and human evaluation. Our method, MaRio (Multi-rewArd RatIOnalization), is a multi-reward conditioned self-rationalization algorithm that optimizes multiple distinct properties like plausibility, diversity and consistency. Results on five difficult question-answering datasets StrategyQA, QuaRel, OpenBookQA, NumerSense and QASC show that not only does MaRio improve task accuracy, but it also improves the self-rationalization quality of small LMs across the aforementioned axes better than a supervised fine-tuning (SFT) baseline. Extensive human evaluations confirm that MaRio rationales are preferred vs. SFT rationales, as well as qualitative improvements in plausibility and consistency.

Large-scale high-quality training data is important for improving the performance of models. After trained with data that has rationales (reasoning steps), models gain reasoning capability. However, the dataset with high-quality rationales is relatively scarce due to the high annotation cost. To address this issue, we propose Self-motivated Learning framework. The framework motivates the model itself to automatically generate rationales on existing datasets. Based on the inherent rank from correctness across multiple rationales, the model learns to generate better rationales, leading to higher reasoning capability. Specifically, we train a reward model with the rank to evaluate the quality of rationales, and improve the performance of reasoning through reinforcement learning. Experiment results of Llama2 7B on multiple reasoning datasets show that our method significantly improves the reasoning ability of models, even outperforming text-davinci-002 in some datasets.

Incorporating natural language rationales in the prompt and In-Context Learning (ICL) has led to a significant improvement of Large Language Models (LLMs) performance. However, rationales currently require human-annotation or the use of auxiliary proxy models to target promising samples or generate high-quality rationales. In this work, we propose Self-AMPLIFY to generate automatically rationales from post hoc explanation methods applied to Small Language Models (SLMs) to improve their own performance. Self-AMPLIFY is a 3-step method that targets samples, generates rationales and builds a final prompt to leverage ICL. Self-AMPLIFY performance is evaluated on two SLMs and two datasets requiring reasoning abilities: these experiments show that Self-AMPLIFY achieves good results against competitors. Self-AMPLIFY is the first method to apply post hoc explanation methods to SLM to generate rationales to improve their own performance in a fully automated manner.

Large Language Models (LLMs) have achieved excellent performances in various tasks. However, fine-tuning an LLM requires extensive supervision. Human, on the other hand, may improve their reasoning abilities by self-thinking without external inputs. In this work, we demonstrate that an LLM is also capable of self-improving with only unlabeled datasets. We use a pre-trained LLM to generate "high-confidence" rationale-augmented answers for unlabeled questions using Chain-of-Thought prompting and self-consistency, and fine-tune the LLM using those self-generated solutions as target outputs. We show that our approach improves the general reasoning ability of a 540B-parameter LLM (74.4%->82.1% on GSM8K, 78.2%->83.0% on DROP, 90.0%->94.4% on OpenBookQA, and 63.4%->67.9% on ANLI-A3) and achieves state-of-the-art-level performance, without any ground truth label. We conduct ablation studies and show that fine-tuning on reasoning is critical for self-improvement.

The deployment of large language models (LLMs) faces considerable challenges concerning resource constraints and inference efficiency. Recent research has increasingly focused on smaller, task-specific models enhanced by distilling knowledge from LLMs. However, prior studies have often overlooked the diversity and quality of knowledge, especially the untapped potential of negative knowledge. Constructing effective negative knowledge remains severely understudied. In this paper, we introduce a novel framework called quality-guided contrastive rationale distillation aimed at enhancing reasoning capabilities through contrastive knowledge learning. For positive knowledge, we enrich its diversity through temperature sampling and employ self-consistency for further denoising and refinement. For negative knowledge, we propose an innovative self-adversarial approach that generates low-quality rationales by sampling previous iterations of smaller language models, embracing the idea that one can learn from one's own weaknesses. A contrastive loss is developed to distill both positive and negative knowledge into smaller language models, where an online-updating discriminator is integrated to assess qualities of rationales and assign them appropriate weights, optimizing the training process. Through extensive experiments across multiple reasoning tasks, we demonstrate that our method consistently outperforms existing distillation techniques, yielding higher-quality rationales.

The self-rationalising capabilities of large language models (LLMs) have been explored in restricted settings, using task/specific data sets. However, current LLMs do not (only) rely on specifically annotated data; nonetheless, they frequently explain their outputs. The properties of the generated explanations are influenced by the pre-training corpus and by the target data used for instruction fine-tuning. As the pre-training corpus includes a large amount of human-written explanations "in the wild", we hypothesise that LLMs adopt common properties of human explanations. By analysing the outputs for a multi-domain instruction fine-tuning data set, we find that generated explanations show selectivity and contain illustrative elements, but less frequently are subjective or misleading. We discuss reasons and consequences of the properties' presence or absence. In particular, we outline positive and negative implications depending on the goals and user groups of the self-rationalising system.

Self-improvement methods enable large language models (LLMs) to generate solutions themselves and iteratively train on filtered, high-quality rationales. This process proves effective and reduces the reliance on human supervision in LLMs' reasoning, but the performance soon plateaus. We delve into the process and find that models tend to over-sample on easy queries and under-sample on queries they have yet to master. As iterations proceed, this imbalance in sampling is exacerbated, leading to a long-tail distribution where solutions to difficult queries almost diminish. This phenomenon limits the performance gain of self-improving models. A straightforward solution is brute-force sampling to balance the distribution, which significantly raises computational costs. In this paper, we introduce Guided Self-Improvement (GSI), a strategy aimed at improving the efficiency of sampling challenging heavy-tailed data. It leverages Socratic-style guidance signals to help LLM reasoning with complex queries, reducing the exploration effort and minimizing computational overhead. Experiments on four models across diverse mathematical tasks show that GSI strikes a balance between performance and efficiency, while also being effective on held-out tasks.

The key components of machine learning are data samples for training, model for learning patterns, and loss function for optimizing accuracy. Analogously, unlearning can potentially be achieved through anti-data samples (or anti-samples), unlearning method, and reversed loss function. While prior research has explored unlearning methods and reversed loss functions, the potential of anti-samples remains largely untapped. In this paper, we introduce UnSTAR: Unlearning with Self-Taught Anti-Sample Reasoning for large language models (LLMs). Our contributions are threefold; first, we propose a novel concept of anti-sample-induced unlearning; second, we generate anti-samples by leveraging misleading rationales, which help reverse learned associations and accelerate the unlearning process; and third, we enable fine-grained targeted unlearning, allowing for the selective removal of specific associations without impacting related knowledge - something not achievable by previous works. Results demonstrate that anti-samples offer an efficient, targeted unlearning strategy for LLMs, opening new avenues for privacy-preserving machine learning and model modification.

Automated rationale generation is an approach for real-time explanation generation whereby a computational model learns to translate an autonomous agent's internal state and action data representations into natural language. Training on human explanation data can enable agents to learn to generate human-like explanations for their behavior. In this paper, using the context of an agent that plays Frogger, we describe (a) how to collect a corpus of explanations, (b) how to train a neural rationale generator to produce different styles of rationales, and (c) how people perceive these rationales. We conducted two user studies. The first study establishes the plausibility of each type of generated rationale and situates their user perceptions along the dimensions of confidence, humanlike-ness, adequate justification, and understandability. The second study further explores user preferences between the generated rationales with regard to confidence in the autonomous agent, communicating failure and unexpected behavior. Overall, we find alignment between the intended differences in features of the generated rationales and the perceived differences by users. Moreover, context permitting, participants preferred detailed rationales to form a stable mental model of the agent's behavior.

We study self-rewarding reasoning large language models (LLMs), which can simultaneously generate step-by-step reasoning and evaluate the correctness of their outputs during the inference time-without external feedback. This integrated approach allows a single model to independently guide its reasoning process, offering computational advantages for model deployment. We particularly focus on the representative task of self-correction, where models autonomously detect errors in their responses, revise outputs, and decide when to terminate iterative refinement loops. To enable this, we propose a two-staged algorithmic framework for constructing self-rewarding reasoning models using only self-generated data. In the first stage, we employ sequential rejection sampling to synthesize long chain-of-thought trajectories that incorporate both self-rewarding and self-correction mechanisms. Fine-tuning models on these curated data allows them to learn the patterns of self-rewarding and self-correction. In the second stage, we further enhance the models' ability to assess response accuracy and refine outputs through reinforcement learning with rule-based signals. Experiments with Llama-3 and Qwen-2.5 demonstrate that our approach surpasses intrinsic self-correction capabilities and achieves performance comparable to systems that rely on external reward models.

A major issue with using deep learning models in sensitive applications is that they provide no explanation for their output. To address this problem, unsupervised selective rationalization produces rationales alongside predictions by chaining two jointly-trained components, a rationale generator and a predictor. Although this architecture guarantees that the prediction relies solely on the rationale, it does not ensure that the rationale contains a plausible explanation for the prediction. We introduce a novel training technique that effectively limits generation of implausible rationales by injecting noise between the generator and the predictor. Furthermore, we propose a new benchmark for evaluating unsupervised selective rationalization models using movie reviews from existing datasets. We achieve sizeable improvements in rationale plausibility and task accuracy over the state-of-the-art across a variety of tasks, including our new benchmark, while maintaining or improving model faithfulness.

Training on large amounts of rationales (i.e., CoT Fine-tuning) is effective at improving the reasoning capabilities of large language models (LLMs). However, acquiring human-authored rationales or augmenting rationales from proprietary models is costly and not scalable. In this paper, we study the problem of whether LLMs could self-improve their reasoning capabilities. To this end, we propose Self-Explore, where the LLM is tasked to explore the first wrong step (i.e., the first pit) within the rationale and use such signals as fine-grained rewards for further improvement. On the GSM8K and MATH test set, Self-Explore achieves 11.57% and 2.89% improvement on average across three LLMs compared to supervised fine-tuning (SFT). Our code is available at https://github.com/hbin0701/Self-Explore.

Generating rationales that justify scoring decisions has been a promising way to facilitate explainability in automated scoring systems. However, existing methods do not match the accuracy of classifier-based methods. Plus, the generated rationales often contain hallucinated information. To address these issues, we propose a novel framework capable of generating more faithful rationales and, more importantly, matching performance with classifier-based black-box scoring systems. We first mimic the human assessment process by querying Large Language Models (LLMs) to generate a thought tree. We then summarise intermediate assessment decisions from each thought tree path for creating synthetic rationale data and rationale preference data. Finally, we utilise the generated synthetic data to calibrate LLMs through a two-step training process: supervised fine-tuning and preference optimization. Extensive experimental results demonstrate that our framework achieves a 38% assessment performance improvement in the QWK score compared to prior work while producing higher-quality rationales, as recognised by human evaluators and LLMs. Our work sheds light on the effectiveness of performing preference optimization using synthetic preference data obtained from thought tree paths.

Neural language models (LMs) have achieved impressive results on various language-based reasoning tasks by utilizing latent knowledge encoded in their own pretrained parameters. To make this reasoning process more explicit, recent works retrieve a rationalizing LM's internal knowledge by training or prompting it to generate free-text rationales, which can be used to guide task predictions made by either the same LM or a separate reasoning LM. However, rationalizing LMs require expensive rationale annotation and/or computation, without any assurance that their generated rationales improve LM task performance or faithfully reflect LM decision-making. In this paper, we propose PINTO, an LM pipeline that rationalizes via prompt-based learning, and learns to faithfully reason over rationales via counterfactual regularization. First, PINTO maps out a suitable reasoning process for the task input by prompting a frozen rationalizing LM to generate a free-text rationale. Second, PINTO's reasoning LM is fine-tuned to solve the task using the generated rationale as context, while regularized to output less confident predictions when the rationale is perturbed. Across four datasets, we show that PINTO significantly improves the generalization ability of the reasoning LM, yielding higher performance on both in-distribution and out-of-distribution test sets. Also, we find that PINTO's rationales are more faithful to its task predictions than those generated by competitive baselines.

Solving algebraic word problems requires executing a series of arithmetic operations---a program---to obtain a final answer. However, since programs can be arbitrarily complicated, inducing them directly from question-answer pairs is a formidable challenge. To make this task more feasible, we solve these problems by generating answer rationales, sequences of natural language and human-readable mathematical expressions that derive the final answer through a series of small steps. Although rationales do not explicitly specify programs, they provide a scaffolding for their structure via intermediate milestones. To evaluate our approach, we have created a new 100,000-sample dataset of questions, answers and rationales. Experimental results show that indirect supervision of program learning via answer rationales is a promising strategy for inducing arithmetic programs.

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.

We introduce AI rationalization, an approach for generating explanations of autonomous system behavior as if a human had performed the behavior. We describe a rationalization technique that uses neural machine translation to translate internal state-action representations of an autonomous agent into natural language. We evaluate our technique in the Frogger game environment, training an autonomous game playing agent to rationalize its action choices using natural language. A natural language training corpus is collected from human players thinking out loud as they play the game. We motivate the use of rationalization as an approach to explanation generation and show the results of two experiments evaluating the effectiveness of rationalization. Results of these evaluations show that neural machine translation is able to accurately generate rationalizations that describe agent behavior, and that rationalizations are more satisfying to humans than other alternative methods of explanation.

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.

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.

The reasoning steps generated by LLMs might be incomplete, as they mimic logical leaps common in everyday communication found in their pre-training data: underlying rationales are frequently left implicit (unstated). To address this challenge, we introduce RATIONALYST, a model for process-supervision of reasoning based on pre-training on a vast collection of rationale annotations extracted from unlabeled data. We extract 79k rationales from web-scale unlabelled dataset (the Pile) and a combination of reasoning datasets with minimal human intervention. This web-scale pre-training for reasoning allows RATIONALYST to consistently generalize across diverse reasoning tasks, including mathematical, commonsense, scientific, and logical reasoning. Fine-tuned from LLaMa-3-8B, RATIONALYST improves the accuracy of reasoning by an average of 3.9% on 7 representative reasoning benchmarks. It also demonstrates superior performance compared to significantly larger verifiers like GPT-4 and similarly sized models fine-tuned on matching training sets.

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.

The ability of large language models to solve complex mathematical problems has progressed significantly, particularly for tasks requiring advanced reasoning. However, the scarcity of sufficiently challenging problems, particularly at the Olympiad level, hinders further advancements. In this work, we introduce PromptCoT, a novel approach for automatically generating high-quality Olympiad-level math problems. The proposed method synthesizes complex problems based on mathematical concepts and the rationale behind problem construction, emulating the thought processes of experienced problem designers. We provide a theoretical analysis demonstrating that an optimal rationale should maximize both the likelihood of rationale generation given the associated concepts and the likelihood of problem generation conditioned on both the rationale and the concepts. Our method is evaluated on standard benchmarks including GSM8K, MATH-500, and AIME2024, where it consistently outperforms existing problem generation methods. Furthermore, we demonstrate that PromptCoT exhibits superior data scalability, consistently maintaining high performance as the dataset size increases, outperforming the baselines. The implementation is available at https://github.com/zhaoxlpku/PromptCoT.

Self-correction is a novel method that can stimulate the potential reasoning abilities of large language models (LLMs). It involves detecting and correcting errors during the inference process when LLMs solve reasoning problems. However, recent works do not regard self-correction as a spontaneous and intrinsic capability of LLMs. Instead, such correction is achieved through post-hoc generation, external knowledge introduction, multi-model collaboration, and similar techniques. In this paper, we propose a series of mathematical LLMs called S^3c-Math, which are able to perform Spontaneous Step-level Self-correction for Mathematical reasoning. This capability helps LLMs to recognize whether their ongoing inference tends to contain errors and simultaneously correct these errors to produce a more reliable response. We proposed a method, which employs a step-level sampling approach to construct step-wise self-correction data for achieving such ability. Additionally, we implement a training strategy that uses above constructed data to equip LLMs with spontaneous step-level self-correction capacities. Our data and methods have been demonstrated to be effective across various foundation LLMs, consistently showing significant progress in evaluations on GSM8K, MATH, and other mathematical benchmarks. To the best of our knowledge, we are the first to introduce the spontaneous step-level self-correction ability of LLMs in mathematical reasoning.

Eliciting feedback from end users of NLP models can be beneficial for improving models. However, how should we present model responses to users so they are most amenable to be corrected from user feedback? Further, what properties do users value to understand and trust responses? We answer these questions by analyzing the effect of rationales (or explanations) generated by QA models to support their answers. We specifically consider decomposed QA models that first extract an intermediate rationale based on a context and a question and then use solely this rationale to answer the question. A rationale outlines the approach followed by the model to answer the question. Our work considers various formats of these rationales that vary according to well-defined properties of interest. We sample rationales from language models using few-shot prompting for two datasets, and then perform two user studies. First, we present users with incorrect answers and corresponding rationales in various formats and ask them to provide natural language feedback to revise the rationale. We then measure the effectiveness of this feedback in patching these rationales through in-context learning. The second study evaluates how well different rationale formats enable users to understand and trust model answers, when they are correct. We find that rationale formats significantly affect how easy it is (1) for users to give feedback for rationales, and (2) for models to subsequently execute this feedback. In addition, formats with attributions to the context and in-depth reasoning significantly enhance user-reported understanding and trust of model outputs.

Large language models (LLMs) have demonstrated outstanding performance across various tasks, yet they still exhibit limitations such as hallucination, unfaithful reasoning, and toxic content. One potential approach to mitigate these issues is learning from human or external feedback (e.g. tools). In this paper, we introduce an intrinsic self-correct reasoning framework for LLMs that eliminates the need for human feedback, external tools, and handcraft prompts. The proposed framework, based on a multi-step reasoning paradigm Learning from Correctness (LeCo), improves reasoning performance without needing to learn from errors. This paradigm prioritizes learning from correct reasoning steps, and a unique method to measure confidence for each reasoning step based on generation logits. Experimental results across various multi-step reasoning tasks demonstrate the effectiveness of the framework in improving reasoning performance with reduced token consumption.

Recent research has shown that rationales, or step-by-step chains of thought, can be used to improve performance in multi-step reasoning tasks. We reconsider rationale-augmented prompting for few-shot in-context learning, where (input -> output) prompts are expanded to (input, rationale -> output) prompts. For rationale-augmented prompting we demonstrate how existing approaches, which rely on manual prompt engineering, are subject to sub-optimal rationales that may harm performance. To mitigate this brittleness, we propose a unified framework of rationale-augmented ensembles, where we identify rationale sampling in the output space as the key component to robustly improve performance. This framework is general and can easily be extended to common natural language processing tasks, even those that do not traditionally leverage intermediate steps, such as question answering, word sense disambiguation, and sentiment analysis. We demonstrate that rationale-augmented ensembles achieve more accurate and interpretable results than existing prompting approaches--including standard prompting without rationales and rationale-based chain-of-thought prompting--while simultaneously improving interpretability of model predictions through the associated rationales.

Self-correction has emerged as a promising solution to boost the reasoning performance of large language models (LLMs), where LLMs refine their solutions using self-generated critiques that pinpoint the errors. This work explores whether smaller-size (<= 13B) language models (LMs) have the ability of self-correction on reasoning tasks with minimal inputs from stronger LMs. We propose a novel pipeline that prompts smaller LMs to collect self-correction data that supports the training of self-refinement abilities. First, we leverage correct solutions to guide the model in critiquing their incorrect responses. Second, the generated critiques, after filtering, are used for supervised fine-tuning of the self-correcting reasoner through solution refinement. Our experimental results show improved self-correction abilities of two models on five datasets spanning math and commonsense reasoning, with notable performance gains when paired with a strong GPT-4-based verifier, though limitations are identified when using a weak self-verifier for determining when to correct.

Rationality is the quality of being guided by reason, characterized by decision-making that aligns with evidence and logical principles. It plays a crucial role in reliable problem-solving by ensuring well-grounded and consistent solutions. While large language models (LLMs) have made significant progress in generating human-like text, they still exhibit limitations such as bounded knowledge space and inconsistent outputs. In response, recent efforts have shifted toward developing multimodal and multi-agent systems, as well as integrating modules like external tools, programming codes, symbolic reasoners, utility function, and conformal risk controls rather than relying solely on a single LLM for decision-making. This paper surveys the state-of-the-art advancements in language and multimodal agents, evaluates how they contribute to make intelligent agents more rational, and identifies open challenges and future research directions. We maintain an open repository at https://github.com/bowen-upenn/Agent_Rationality.

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.

Chain-of-thought (CoT) has proven to improve the reasoning capability of large language models (LLMs). However, due to the complexity of multimodal scenarios and the difficulty in collecting high-quality CoT data, CoT reasoning in multimodal LLMs has been largely overlooked. To this end, we propose a simple yet effective self-training framework, R3V, which iteratively enhances the model's Vision-language Reasoning by Reflecting on CoT Rationales. Our framework consists of two interleaved parts: (1) iteratively bootstrapping positive and negative solutions for reasoning datasets, and (2) reflection on rationale for learning from mistakes. Specifically, we introduce the self-refine and self-select losses, enabling the model to refine flawed rationale and derive the correct answer by comparing rationale candidates. Experiments on a wide range of vision-language tasks show that R3V consistently improves multimodal LLM reasoning, achieving a relative improvement of 23 to 60 percent over GPT-distilled baselines. Additionally, our approach supports self-reflection on generated solutions, further boosting performance through test-time computation.

Prompting methods such as Chain-of-Thought (CoT) have shed new light on enhancing the reasoning capabilities of large language models, and researchers have extensively explored the generation process of rationales and answers. However, they have overlooked the potential challenges posed by the poor quality of reasoning problems, which may influence the reasoning performance significantly. In this work, we propose Self-Polish (SP), a novel method that facilitates the model's problem-solving process by prompting them to progressively refine the given problems to be more comprehensible and solvable. Specifically, the method teaches models to eliminate irrelevant information, rearrange the logic structure and organize local conditions into new ones parallelly. SP is orthogonal to all other prompting methods, making it convenient to integrate with state-of-the-art techniques for further improvement. We conduct thorough experiments on five benchmarks to illustrate the effectiveness of the proposed method. For example, with Text-davinci-003, our method boosts the performance of standard few-shot prompting by 8.0% on GSM8K and 17.8% on MultiArith; it also improves the performance of CoT by 6.0% on GSM8K and 6.0% on MathQA, respectively. Furthermore, our method also showcases impressive performance on robustness evaluation.

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.

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.

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.

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.

Analogical reasoning is a unique ability of humans to address unfamiliar challenges by transferring strategies from relevant past experiences. One key finding in psychology is that compared with irrelevant past experiences, recalling relevant ones can help humans better handle new tasks. Coincidentally, the NLP community has also recently found that self-generating relevant examples in the context can help large language models (LLMs) better solve a given problem than hand-crafted prompts. However, it is yet not clear whether relevance is the key factor eliciting such capability, i.e., can LLMs benefit more from self-generated relevant examples than irrelevant ones? In this work, we systematically explore whether LLMs can truly perform analogical reasoning on a diverse set of reasoning tasks. With extensive experiments and analysis, we show that self-generated random examples can surprisingly achieve comparable or even better performance, e.g., 4% performance boost on GSM8K with random biological examples. We find that the accuracy of self-generated examples is the key factor and subsequently design two improved methods with significantly reduced inference costs. Overall, we aim to advance a deeper understanding of LLM analogical reasoning and hope this work stimulates further research in the design of self-generated contexts.

Large Language Models (LLMs) are deployed as powerful tools for several natural language processing (NLP) applications. Recent works show that modern LLMs can generate self-explanations (SEs), which elicit their intermediate reasoning steps for explaining their behavior. Self-explanations have seen widespread adoption owing to their conversational and plausible nature. However, there is little to no understanding of their faithfulness. In this work, we discuss the dichotomy between faithfulness and plausibility in SEs generated by LLMs. We argue that while LLMs are adept at generating plausible explanations -- seemingly logical and coherent to human users -- these explanations do not necessarily align with the reasoning processes of the LLMs, raising concerns about their faithfulness. We highlight that the current trend towards increasing the plausibility of explanations, primarily driven by the demand for user-friendly interfaces, may come at the cost of diminishing their faithfulness. We assert that the faithfulness of explanations is critical in LLMs employed for high-stakes decision-making. Moreover, we urge the community to identify the faithfulness requirements of real-world applications and ensure explanations meet those needs. Finally, we propose some directions for future work, emphasizing the need for novel methodologies and frameworks that can enhance the faithfulness of self-explanations without compromising their plausibility, essential for the transparent deployment of LLMs in diverse high-stakes domains.

Recent advancements in prompt engineering strategies, such as Chain-of-Thought (CoT) and Self-Discover, have demonstrated significant potential in improving the reasoning abilities of Large Language Models (LLMs). However, these state-of-the-art (SOTA) prompting strategies rely on single or fixed set of static seed reasoning modules like "think step by step" or "break down this problem" intended to simulate human approach to problem-solving. This constraint limits the flexibility of models in tackling diverse problems effectively. In this paper, we introduce Auto-Evolve, a novel framework that enables LLMs to self-create dynamic reasoning modules and downstream action plan, resulting in significant improvements over current SOTA methods. We evaluate Auto-Evolve on the challenging BigBench-Hard (BBH) dataset with Claude 2.0, Claude 3 Sonnet, Mistral Large, and GPT 4, where it consistently outperforms the SOTA prompt strategies. Auto-Evolve outperforms CoT by up to 10.4% and on an average by 7% across these four models. Our framework introduces two innovations: a) Auto-Evolve dynamically generates reasoning modules for each task while aligning with human reasoning paradigm, thus eliminating the need for predefined templates. b) We introduce an iterative refinement component, that incrementally refines instruction guidance for LLMs and helps boost performance by average 2.8% compared to doing it in a single step.

We introduce self-invoking code generation, a new task designed to evaluate the progressive reasoning and problem-solving capabilities of LLMs. In this task, models are presented with a base problem and a related, more complex problem. They must solve the base problem and then utilize its solution to address the more complex one. This work features three key contributions. First, we propose a general recipe for generating more challenging versions of existing benchmarks, resulting in three new benchmarks: HumanEval Pro, MBPP Pro, and BigCodeBench-Lite Pro, specifically designed to assess LLMs on self-invoking code generation. Second, from the analysis of experimental results over twenty LLMs on our benchmarks, we have two important observations: (i) Most LLMs excel in traditional code generation benchmarks like HumanEval and MBPP, but their performance declines on self-invoking tasks. For example, o1-mini achieves 96.2% pass@1 on HumanEval but only 76.2% on HumanEval Pro. (ii) On self-invoking code generation task, the instruction-tuned models demonstrate only marginal improvements compared to the base models. Third, we disclose the types of failure modes that exist in our evaluation results. All these results underscore the need for further advancements in self-invoking code generation tasks and provide a new direction for future research on enhancing LLMs' code reasoning capabilities.

Sequence models are a critical component of modern NLP systems, but their predictions are difficult to explain. We consider model explanations though rationales, subsets of context that can explain individual model predictions. We find sequential rationales by solving a combinatorial optimization: the best rationale is the smallest subset of input tokens that would predict the same output as the full sequence. Enumerating all subsets is intractable, so we propose an efficient greedy algorithm to approximate this objective. The algorithm, which is called greedy rationalization, applies to any model. For this approach to be effective, the model should form compatible conditional distributions when making predictions on incomplete subsets of the context. This condition can be enforced with a short fine-tuning step. We study greedy rationalization on language modeling and machine translation. Compared to existing baselines, greedy rationalization is best at optimizing the combinatorial objective and provides the most faithful rationales. On a new dataset of annotated sequential rationales, greedy rationales are most similar to human rationales.

We introduce a novel framework, LM-Guided CoT, that leverages a lightweight (i.e., <1B) language model (LM) for guiding a black-box large (i.e., >10B) LM in reasoning tasks. Specifically, the lightweight LM first generates a rationale for each input instance. The Frozen large LM is then prompted to predict a task output based on the rationale generated by the lightweight LM. Our approach is resource-efficient in the sense that it only requires training the lightweight LM. We optimize the model through 1) knowledge distillation and 2) reinforcement learning from rationale-oriented and task-oriented reward signals. We assess our method with multi-hop extractive question answering (QA) benchmarks, HotpotQA, and 2WikiMultiHopQA. Experimental results show that our approach outperforms all baselines regarding answer prediction accuracy. We also find that reinforcement learning helps the model to produce higher-quality rationales with improved QA performance.

In the absence of extensive human-annotated data for complex reasoning tasks, self-improvement -- where models are trained on their own outputs -- has emerged as a primary method for enhancing performance. However, the critical factors underlying the mechanism of these iterative self-improving methods remain poorly understood, such as under what conditions self-improvement is effective, and what are the bottlenecks in the current iterations. In this work, we identify and propose methods to monitor two pivotal factors in this iterative process: (1) the model's ability to generate sufficiently diverse responses (exploration); and (2) the effectiveness of external rewards in distinguishing high-quality candidates from lower-quality ones (exploitation). Using mathematical reasoning as a case study, we begin with a quantitative analysis to track the dynamics of exploration and exploitation, discovering that a model's exploratory capabilities rapidly deteriorate over iterations, and the effectiveness of exploiting external rewards diminishes as well. Motivated by these findings, we introduce B-STaR, a Self-Taught Reasoning framework that autonomously adjusts configurations across iterations to Balance exploration and exploitation, thereby optimizing the self-improving effectiveness based on the current policy model and available rewards. Our experiments on mathematical reasoning, coding, and commonsense reasoning demonstrate that B-STaR not only enhances the model's exploratory capabilities throughout training but also achieves a more effective balance between exploration and exploitation, leading to superior performance.

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.

A computational ethics framework is essential for AI and autonomous systems operating in complex, real-world environments. Existing approaches often lack the adaptability needed to integrate ethical principles into dynamic and ambiguous contexts, limiting their effectiveness across diverse scenarios. To address these challenges, we outline the necessary ingredients for building a holistic, meta-level framework that combines intermediate representations, probabilistic reasoning, and knowledge representation. The specifications therein emphasize scalability, supporting ethical reasoning at both individual decision-making levels and within the collective dynamics of multi-agent systems. By integrating theoretical principles with contextual factors, it facilitates structured and context-aware decision-making, ensuring alignment with overarching ethical standards. We further explore proposed theorems outlining how ethical reasoners should operate, offering a foundation for practical implementation. These constructs aim to support the development of robust and ethically reliable AI systems capable of navigating the complexities of real-world moral decision-making scenarios.

Despite the promising few-shot ability of large language models (LLMs), the standard paradigm of In-context Learning (ICL) suffers the disadvantages of susceptibility to selected demonstrations and the intricacy to generate these demonstrations. In this paper, we raise the fundamental question that whether human-generated demonstrations are necessary for ICL. To answer this question, we propose self-contemplation prompting strategy (SEC), a paradigm free from human-crafted demonstrations. The key point of SEC is that, instead of using hand-crafted examples as demonstrations in ICL, SEC asks LLMs to first create demonstrations on their own, based on which the final output is generated. SEC is a flexible framework and can be adapted to both the vanilla ICL and the chain-of-thought (CoT), but with greater ease: as the manual-generation process of both examples and rationale can be saved. Extensive experiments in arithmetic reasoning, commonsense reasoning, multi-task language understanding, and code generation benchmarks, show that SEC, which does not require hand-crafted demonstrations, significantly outperforms the zero-shot learning strategy, and achieves comparable results to ICL with hand-crafted demonstrations. This demonstrates that, for many tasks, contemporary LLMs possess a sufficient level of competence to exclusively depend on their own capacity for decision making, removing the need for external training data. Code is available at https://github.com/ruili33/SEC.

Tasks requiring deductive reasoning, especially those involving multiple steps, often demand adaptive strategies such as intermediate generation of rationales or programs, as no single approach is universally optimal. While Language Models (LMs) can enhance their outputs through iterative self-refinement and strategy adjustments, they frequently fail to apply the most effective strategy in their first attempt. This inefficiency raises the question: Can LMs learn to select the optimal strategy in the first attempt, without a need for refinement? To address this challenge, we introduce SMART (Self-learning Meta-strategy Agent for Reasoning Tasks), a novel framework that enables LMs to autonomously learn and select the most effective strategies for various reasoning tasks. We model the strategy selection process as a Markov Decision Process and leverage reinforcement learning-driven continuous self-improvement to allow the model to find the suitable strategy to solve a given task. Unlike traditional self-refinement methods that rely on multiple inference passes or external feedback, SMART allows an LM to internalize the outcomes of its own reasoning processes and adjust its strategy accordingly, aiming for correct solutions on the first attempt. Our experiments across various reasoning datasets and with different model architectures demonstrate that SMART significantly enhances the ability of models to choose optimal strategies without external guidance (+15 points on the GSM8K dataset). By achieving higher accuracy with a single inference pass, SMART not only improves performance but also reduces computational costs for refinement-based strategies, paving the way for more efficient and intelligent reasoning in LMs.

Rationale discovery is defined as finding a subset of the input data that maximally supports the prediction of downstream tasks. In graph machine learning context, graph rationale is defined to locate the critical subgraph in the given graph topology, which fundamentally determines the prediction results. In contrast to the rationale subgraph, the remaining subgraph is named the environment subgraph. Graph rationalization can enhance the model performance as the mapping between the graph rationale and prediction label is viewed as invariant, by assumption. To ensure the discriminative power of the extracted rationale subgraphs, a key technique named "intervention" is applied. The core idea of intervention is that given any changing environment subgraphs, the semantics from the rationale subgraph is invariant, which guarantees the correct prediction result. However, most, if not all, of the existing rationalization works on graph data develop their intervention strategies on the graph level, which is coarse-grained. In this paper, we propose well-tailored intervention strategies on graph data. Our idea is driven by the development of Transformer models, whose self-attention module provides rich interactions between input nodes. Based on the self-attention module, our proposed invariant graph Transformer (IGT) can achieve fine-grained, more specifically, node-level and virtual node-level intervention. Our comprehensive experiments involve 7 real-world datasets, and the proposed IGT shows significant performance advantages compared to 13 baseline methods.

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.

Reasoning ability is essential for Large Multimodal Models (LMMs). In the absence of multimodal chain-of-thought annotated data, self-evolving training, where the model learns from its own outputs, has emerged as an effective and scalable approach for enhancing reasoning abilities. Despite its growing usage, a comprehensive understanding of self-evolving training, particularly in the context of multimodal reasoning, remains limited. In this paper, we delve into the intricacies of self-evolving training for multimodal reasoning, pinpointing three key factors: Training Method, Reward Model, and Prompt Variation. We systematically examine each factor and explore how various configurations affect the training's effectiveness. Our analysis leads to a set of best practices for each factor, aimed at optimizing multimodal reasoning. Furthermore, we explore the Self-Evolution Dynamics during training and the impact of automatic balancing mechanisms in boosting performance. After all the investigations, we present a final recipe for self-evolving training in multimodal reasoning, encapsulating these design choices into a framework we call MSTaR (Multimodal Self-evolving Training for Reasoning), which is universally effective for models with different sizes on various benchmarks, e.g., surpassing the pre-evolved model significantly on 5 multimodal reasoning benchmarks without using additional human annotations, as demonstrated on MiniCPM-V-2.5 (8B), Phi-3.5-Vision (4B) and InternVL2 (2B). We believe this study fills a significant gap in the understanding of self-evolving training for multimodal reasoning and offers a robust framework for future research. Our policy and reward models, as well as the collected data, is released to facilitate further investigation in multimodal reasoning.

The remarkable success in neural networks provokes the selective rationalization. It explains the prediction results by identifying a small subset of the inputs sufficient to support them. Since existing methods still suffer from adopting the shortcuts in data to compose rationales and limited large-scale annotated rationales by human, in this paper, we propose a Shortcuts-fused Selective Rationalization (SSR) method, which boosts the rationalization by discovering and exploiting potential shortcuts. Specifically, SSR first designs a shortcuts discovery approach to detect several potential shortcuts. Then, by introducing the identified shortcuts, we propose two strategies to mitigate the problem of utilizing shortcuts to compose rationales. Finally, we develop two data augmentations methods to close the gap in the number of annotated rationales. Extensive experimental results on real-world datasets clearly validate the effectiveness of our proposed method.

The remarkable performance of models like the OpenAI o1 can be attributed to their ability to emulate human-like long-time thinking during inference. These models employ extended chain-of-thought (CoT) processes, exploring multiple strategies to enhance problem-solving capabilities. However, a critical question remains: How to intelligently and efficiently scale computational resources during testing. This paper presents the first comprehensive study on the prevalent issue of overthinking in these models, where excessive computational resources are allocated for simple problems with minimal benefit. We introduce novel efficiency metrics from both outcome and process perspectives to evaluate the rational use of computational resources by o1-like models. Using a self-training paradigm, we propose strategies to mitigate overthinking, streamlining reasoning processes without compromising accuracy. Experimental results show that our approach successfully reduces computational overhead while preserving model performance across a range of testsets with varying difficulty levels, such as GSM8K, MATH500, GPQA, and AIME.

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.

Free-text rationales justify model decisions in natural language and thus become likable and accessible among approaches to explanation across many tasks. However, their effectiveness can be hindered by misinterpretation and hallucination. As a perturbation test, we investigate how large language models (LLMs) perform rationale generation under the effects of readability level control, i.e., being prompted for an explanation targeting a specific expertise level, such as sixth grade or college. We find that explanations are adaptable to such instruction, though the requested readability is often misaligned with the measured text complexity according to traditional readability metrics. Furthermore, the generated rationales tend to feature medium level complexity, which correlates with the measured quality using automatic metrics. Finally, our human annotators confirm a generally satisfactory impression on rationales at all readability levels, with high-school-level readability being most commonly perceived and favored.

Accurate mathematical reasoning with Large Language Models (LLMs) is crucial in revolutionizing domains that heavily rely on such reasoning. However, LLMs often encounter difficulties in certain aspects of mathematical reasoning, leading to flawed reasoning and erroneous results. To mitigate these issues, we introduce a novel mechanism, the Chain of Self-Correction (CoSC), specifically designed to embed self-correction as an inherent ability in LLMs, enabling them to validate and rectify their own results. The CoSC mechanism operates through a sequence of self-correction stages. In each stage, the LLMs generate a program to address a given problem, execute this program using program-based tools to obtain an output, subsequently verify this output. Based on the verification, the LLMs either proceed to the next correction stage or finalize the answer. This iterative self-correction process allows the LLMs to refine their reasoning steps and improve the accuracy of their mathematical reasoning. To enable the CoSC mechanism at a low cost, we employ a two-phase finetuning approach. In the first phase, the LLMs are trained with a relatively small volume of seeding data generated from GPT-4, establishing an initial CoSC capability. In the second phase, the CoSC capability is further enhanced by training with a larger volume of self-generated data using the trained model in the first phase, without relying on the paid GPT-4. Our comprehensive experiments demonstrate that CoSC significantly improves performance on traditional mathematical datasets among existing open-source LLMs. Notably, our CoSC-Code-34B model achieved a 53.5% score on MATH, the most challenging mathematical reasoning dataset in the public domain, surpassing the performance of well-established models such as ChatGPT, GPT-4, and even multi-modal LLMs like GPT-4V, Gemini-1.0 Pro, and Gemini-1.0 Ultra.

Reinforcement learning from human feedback plays a crucial role in aligning language models towards human preferences, traditionally represented through comparisons between pairs or sets of responses within a given context. While many studies have enhanced algorithmic techniques to optimize learning from such data, this work shifts focus to improving preference learning through a data-centric approach. Specifically, we propose enriching existing preference datasets with machine-generated rationales that explain the reasons behind choices. We develop a simple and principled framework to augment current preference learning methods with rationale information. Our comprehensive analysis highlights how rationales enhance learning efficiency. Extensive experiments reveal that rationale-enriched preference learning offers multiple advantages: it improves data efficiency, accelerates convergence to higher-performing models, and reduces verbosity bias and hallucination. Furthermore, this framework is versatile enough to integrate with various preference optimization algorithms. Overall, our findings highlight the potential of re-imagining data design for preference learning, demonstrating that even freely available machine-generated rationales can significantly boost performance across multiple dimensions. The code repository is available at https: //github.com/reds-lab/preference-learning-with-rationales

Chain-of-thought prompting combined with pre-trained large language models has achieved encouraging results on complex reasoning tasks. In this paper, we propose a new decoding strategy, self-consistency, to replace the naive greedy decoding used in chain-of-thought prompting. It first samples a diverse set of reasoning paths instead of only taking the greedy one, and then selects the most consistent answer by marginalizing out the sampled reasoning paths. Self-consistency leverages the intuition that a complex reasoning problem typically admits multiple different ways of thinking leading to its unique correct answer. Our extensive empirical evaluation shows that self-consistency boosts the performance of chain-of-thought prompting with a striking margin on a range of popular arithmetic and commonsense reasoning benchmarks, including GSM8K (+17.9%), SVAMP (+11.0%), AQuA (+12.2%), StrategyQA (+6.4%) and ARC-challenge (+3.9%).

Large Language Models have demonstrated outstanding performance across various downstream tasks and have been widely applied in multiple scenarios. Human-annotated preference data is used for training to further improve LLMs' performance, which is constrained by the upper limit of human performance. Therefore, Self-Rewarding method has been proposed, where LLMs generate training data by rewarding their own outputs. However, the existing self-rewarding paradigm is not effective in mathematical reasoning scenarios and may even lead to a decline in performance. In this work, we propose the Process-based Self-Rewarding pipeline for language models, which introduces long-thought reasoning, step-wise LLM-as-a-Judge, and step-wise preference optimization within the self-rewarding paradigm. Our new paradigm successfully enhances the performance of LLMs on multiple mathematical reasoning benchmarks through iterative Process-based Self-Rewarding, demonstrating the immense potential of self-rewarding to achieve LLM reasoning that may surpass human capabilities.

The recent release of OpenAI's o1 models and other similar frameworks showcasing test-time scaling laws has demonstrated their exceptional capability to tackle complex reasoning tasks. Inspired by this, subsequent research has revealed that such test-time scaling laws hinge on the model's ability to search both within a single response (intra-response) and across multiple responses (inter-response) during training. Crucially, beyond selecting a single optimal response, the model must also develop robust self-correction capabilities within its own outputs. However, training models to achieve effective self-evaluation and self-correction remains a significant challenge, heavily dependent on the quality of self-reflection data. In this paper, we address this challenge by focusing on enhancing the quality of self-reflection data generation for complex problem-solving, which can subsequently improve the training of next-generation large language models (LLMs). Specifically, we explore how manually triggering a model's self-correction mechanisms can improve performance on challenging reasoning tasks. To this end, we propose a novel iterative deepening sampling algorithm framework designed to enhance self-correction and generate higher-quality samples. Through extensive experiments on Math500 and AIME benchmarks, we demonstrate that our method achieves a higher success rate on difficult tasks and provide detailed ablation studies to analyze its effectiveness across diverse settings.

A fundamental challenge in formal theorem proving by LLMs is the lack of high-quality training data. Although reinforcement learning or expert iteration partially mitigates this issue by alternating between LLM generating proofs and finetuning them on correctly generated ones, performance quickly plateaus due to the scarcity of correct proofs (sparse rewards). To keep improving the models with limited data, we draw inspiration from mathematicians, who continuously develop new results, partly by proposing novel conjectures or exercises (which are often variants of known results) and attempting to solve them. We design the Self-play Theorem Prover (STP) that simultaneously takes on two roles, conjecturer and prover, each providing training signals to the other. The conjecturer is trained iteratively on previously generated conjectures that are barely provable by the current prover, which incentivizes it to generate increasingly challenging conjectures over time. The prover attempts to prove the conjectures with standard expert iteration. We evaluate STP with both Lean and Isabelle formal versifiers. With 19.8 billion tokens generated during the training in Lean, STP proves 26.3% of the statements in the LeanWorkbook dataset, doubling the previous best result of 13.2% achieved through expert iteration. The final model achieves state-of-the-art performance among whole-proof generation methods on miniF2F-test (61.7%, pass@3200), Proofnet-test (23.1%, pass@3200) and PutnamBench (8/644, pass@3200).

Effective training of language models (LMs) for mathematical reasoning tasks demands high-quality supervised fine-tuning data. Besides obtaining annotations from human experts, a common alternative is sampling from larger and more powerful LMs. However, this knowledge distillation approach can be costly and unstable, particularly when relying on closed-source, proprietary LMs like GPT-4, whose behaviors are often unpredictable. In this work, we demonstrate that the reasoning abilities of small-scale LMs can be enhanced through self-training, a process where models learn from their own outputs. We also show that the conventional self-training can be further augmented by a preference learning algorithm called Direct Preference Optimization (DPO). By integrating DPO into self-training, we leverage preference data to guide LMs towards more accurate and diverse chain-of-thought reasoning. We evaluate our method across various mathematical reasoning tasks using different base models. Our experiments show that this approach not only improves LMs' reasoning performance but also offers a more cost-effective and scalable solution compared to relying on large proprietary LMs.

Chain-of-Thought (CoT) reasoning has been extensively explored in large models to tackle complex understanding tasks. However, it still remains an open question whether such strategies can be applied to verifying and reinforcing image generation scenarios. In this paper, we provide the first comprehensive investigation of the potential of CoT reasoning to enhance autoregressive image generation. We focus on three techniques: scaling test-time computation for verification, aligning model preferences with Direct Preference Optimization (DPO), and integrating these techniques for complementary effects. Our results demonstrate that these approaches can be effectively adapted and combined to significantly improve image generation performance. Furthermore, given the pivotal role of reward models in our findings, we propose the Potential Assessment Reward Model (PARM) and PARM++, specialized for autoregressive image generation. PARM adaptively assesses each generation step through a potential assessment approach, merging the strengths of existing reward models, and PARM++ further introduces a reflection mechanism to self-correct the generated unsatisfactory image. Using our investigated reasoning strategies, we enhance a baseline model, Show-o, to achieve superior results, with a significant +24% improvement on the GenEval benchmark, surpassing Stable Diffusion 3 by +15%. We hope our study provides unique insights and paves a new path for integrating CoT reasoning with autoregressive image generation. Code and models are released at https://github.com/ZiyuGuo99/Image-Generation-CoT

We introduce iterative reasoning through energy diffusion (IRED), a novel framework for learning to reason for a variety of tasks by formulating reasoning and decision-making problems with energy-based optimization. IRED learns energy functions to represent the constraints between input conditions and desired outputs. After training, IRED adapts the number of optimization steps during inference based on problem difficulty, enabling it to solve problems outside its training distribution -- such as more complex Sudoku puzzles, matrix completion with large value magnitudes, and pathfinding in larger graphs. Key to our method's success is two novel techniques: learning a sequence of annealed energy landscapes for easier inference and a combination of score function and energy landscape supervision for faster and more stable training. Our experiments show that IRED outperforms existing methods in continuous-space reasoning, discrete-space reasoning, and planning tasks, particularly in more challenging scenarios. Code and visualizations at https://energy-based-model.github.io/ired/

The rapid development of large language and vision models (LLVMs) has been driven by advances in visual instruction tuning. Recently, open-source LLVMs have curated high-quality visual instruction tuning datasets and utilized additional vision encoders or multiple computer vision models in order to narrow the performance gap with powerful closed-source LLVMs. These advancements are attributed to multifaceted information required for diverse capabilities, including fundamental image understanding, real-world knowledge about common-sense and non-object concepts (e.g., charts, diagrams, symbols, signs, and math problems), and step-by-step procedures for solving complex questions. Drawing from the multifaceted information, we present a new efficient LLVM, Mamba-based traversal of rationales (Meteor), which leverages multifaceted rationale to enhance understanding and answering capabilities. To embed lengthy rationales containing abundant information, we employ the Mamba architecture, capable of processing sequential data with linear time complexity. We introduce a new concept of traversal of rationale that facilitates efficient embedding of rationale. Subsequently, the backbone multimodal language model (MLM) is trained to generate answers with the aid of rationale. Through these steps, Meteor achieves significant improvements in vision language performances across multiple evaluation benchmarks requiring diverse capabilities, without scaling up the model size or employing additional vision encoders and computer vision models.

Traditional language model-based theorem proving assumes that by training on a sufficient amount of formal proof data, a model will learn to prove theorems. Our key observation is that a wealth of informal information that is not present in formal proofs can be useful for learning to prove theorems. For instance, humans think through steps of a proof, but this thought process is not visible in the resulting code. We present Lean-STaR, a framework for training language models to produce informal thoughts prior to each step of a proof, thereby boosting the model's theorem-proving capabilities. Lean-STaR uses retrospective ground-truth tactics to generate synthetic thoughts for training the language model. At inference time, the trained model directly generates the thoughts prior to the prediction of the tactics in each proof step. Building on the self-taught reasoner framework, we then apply expert iteration to further fine-tune the model on the correct proofs it samples and verifies using the Lean solver. Lean-STaR achieves state-of-the-art results on the miniF2F-test benchmark within the Lean theorem proving environment, significantly outperforming base models (43.4% rightarrow 46.3%, Pass@64). We also analyze the impact of the augmented thoughts on various aspects of the theorem proving process, providing insights into their effectiveness.

We introduce SELF-DISCOVER, a general framework for LLMs to self-discover the task-intrinsic reasoning structures to tackle complex reasoning problems that are challenging for typical prompting methods. Core to the framework is a self-discovery process where LLMs select multiple atomic reasoning modules such as critical thinking and step-by-step thinking, and compose them into an explicit reasoning structure for LLMs to follow during decoding. SELF-DISCOVER substantially improves GPT-4 and PaLM 2's performance on challenging reasoning benchmarks such as BigBench-Hard, grounded agent reasoning, and MATH, by as much as 32% compared to Chain of Thought (CoT). Furthermore, SELF-DISCOVER outperforms inference-intensive methods such as CoT-Self-Consistency by more than 20%, while requiring 10-40x fewer inference compute. Finally, we show that the self-discovered reasoning structures are universally applicable across model families: from PaLM 2-L to GPT-4, and from GPT-4 to Llama2, and share commonalities with human reasoning patterns.

Foundation model-enabled generative artificial intelligence facilitates the development and implementation of agents, which can leverage distinguished reasoning and language processing capabilities to takes a proactive, autonomous role to pursue users' goals. Nevertheless, there is a lack of systematic knowledge to guide practitioners in designing the agents considering challenges of goal-seeking (including generating instrumental goals and plans), such as hallucinations inherent in foundation models, explainability of reasoning process, complex accountability, etc. To address this issue, we have performed a systematic literature review to understand the state-of-the-art foundation model-based agents and the broader ecosystem. In this paper, we present a pattern catalogue consisting of 18 architectural patterns with analyses of the context, forces, and trade-offs as the outcomes from the previous literature review. We propose a decision model for selecting the patterns. The proposed catalogue can provide holistic guidance for the effective use of patterns, and support the architecture design of foundation model-based agents by facilitating goal-seeking and plan generation.

Large language models (LLMs) have been shown to perform better when asked to reason step-by-step before answering a question. However, it is unclear to what degree the model's final answer is faithful to the stated reasoning steps. In this paper, we perform a causal mediation analysis on twelve LLMs to examine how intermediate reasoning steps generated by the LLM influence the final outcome and find that LLMs do not reliably use their intermediate reasoning steps when generating an answer. To address this issue, we introduce FRODO, a framework to tailor small-sized LMs to generate correct reasoning steps and robustly reason over these steps. FRODO consists of an inference module that learns to generate correct reasoning steps using an implicit causal reward function and a reasoning module that learns to faithfully reason over these intermediate inferences using a counterfactual and causal preference objective. Our experiments show that FRODO significantly outperforms four competitive baselines. Furthermore, FRODO improves the robustness and generalization ability of the reasoning LM, yielding higher performance on out-of-distribution test sets. Finally, we find that FRODO's rationales are more faithful to its final answer predictions than standard supervised fine-tuning.

Large language models (LLMs) have achieved remarkable performance in recent years but are fundamentally limited by the underlying training data. To improve models beyond the training data, recent works have explored how LLMs can be used to generate synthetic data for autonomous self-improvement. However, successive steps of self-improvement can reach a point of diminishing returns. In this work, we propose a complementary approach towards self-improvement where finetuning is applied to a multiagent society of language models. A group of language models, all starting from the same base model, are independently specialized by updating each one using data generated through multiagent interactions among the models. By training each model on independent sets of data, we illustrate how this approach enables specialization across models and diversification over the set of models. As a result, our overall system is able to preserve diverse reasoning chains and autonomously improve over many more rounds of fine-tuning than single-agent self-improvement methods. We quantitatively illustrate the efficacy of the approach across a wide suite of reasoning tasks.

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.

As large language models (LLMs) grow larger and more sophisticated, assessing their "reasoning" capabilities in natural language grows more challenging. Recent question answering (QA) benchmarks that attempt to assess reasoning are often limited by a narrow scope of covered situations and subject matters. We introduce WikiWhy, a QA dataset built around a novel auxiliary task: explaining why an answer is true in natural language. WikiWhy contains over 9,000 "why" question-answer-rationale triples, grounded on Wikipedia facts across a diverse set of topics. Each rationale is a set of supporting statements connecting the question to the answer. WikiWhy serves as a benchmark for the reasoning capabilities of LLMs because it demands rigorous explicit rationales for each answer to demonstrate the acquisition of implicit commonsense knowledge, which is unlikely to be easily memorized. GPT-3 baselines achieve only 38.7% human-evaluated correctness in the end-to-end answer & explain condition, leaving significant room for future improvements.

The rapid advancement of large language models (LLMs) has significantly enhanced the capabilities of AI-driven agents across various tasks. However, existing agentic systems, whether based on fixed pipeline algorithms or pre-defined meta-learning frameworks, cannot search the whole agent design space due to the restriction of human-designed components, and thus might miss the globally optimal agent design. In this paper, we introduce G\"odel Agent, a self-evolving framework inspired by the G\"odel machine, enabling agents to recursively improve themselves without relying on predefined routines or fixed optimization algorithms. G\"odel Agent leverages LLMs to dynamically modify its own logic and behavior, guided solely by high-level objectives through prompting. Experimental results on mathematical reasoning and complex agent tasks demonstrate that implementation of G\"odel Agent can achieve continuous self-improvement, surpassing manually crafted agents in performance, efficiency, and generalizability.

Self-consistency (SC) has been a widely used decoding strategy for chain-of-thought reasoning. Despite bringing significant performance improvements across a variety of multi-step reasoning tasks, it is a high-cost method that requires multiple sampling with the preset size. In this paper, we propose a simple and scalable sampling process, Early-Stopping Self-Consistency (ESC), to greatly reduce the cost of SC without sacrificing performance. On this basis, one control scheme for ESC is further derivated to dynamically choose the performance-cost balance for different tasks and models. To demonstrate ESC's effectiveness, we conducted extensive experiments on three popular categories of reasoning tasks: arithmetic, commonsense and symbolic reasoning over language models with varying scales. The empirical results show that ESC reduces the average number of sampling of chain-of-thought reasoning by a significant margin on six benchmarks, including MATH (-33.8%), GSM8K (-80.1%), StrategyQA (-76.8%), CommonsenseQA (-78.5%), Coin Flip (-84.2%) and Last Letters (-67.4%), while attaining comparable performances.

Humans learn to master open-ended repertoires of skills by imagining and practicing their own goals. This autotelic learning process, literally the pursuit of self-generated (auto) goals (telos), becomes more and more open-ended as the goals become more diverse, abstract and creative. The resulting exploration of the space of possible skills is supported by an inter-individual exploration: goal representations are culturally evolved and transmitted across individuals, in particular using language. Current artificial agents mostly rely on predefined goal representations corresponding to goal spaces that are either bounded (e.g. list of instructions), or unbounded (e.g. the space of possible visual inputs) but are rarely endowed with the ability to reshape their goal representations, to form new abstractions or to imagine creative goals. In this paper, we introduce a language model augmented autotelic agent (LMA3) that leverages a pretrained language model (LM) to support the representation, generation and learning of diverse, abstract, human-relevant goals. The LM is used as an imperfect model of human cultural transmission; an attempt to capture aspects of humans' common-sense, intuitive physics and overall interests. Specifically, it supports three key components of the autotelic architecture: 1)~a relabeler that describes the goals achieved in the agent's trajectories, 2)~a goal generator that suggests new high-level goals along with their decomposition into subgoals the agent already masters, and 3)~reward functions for each of these goals. Without relying on any hand-coded goal representations, reward functions or curriculum, we show that LMA3 agents learn to master a large diversity of skills in a task-agnostic text-based environment.

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

Recent studies have demonstrated the effectiveness of LLM test-time scaling. However, existing approaches to incentivize LLMs' deep thinking abilities generally require large-scale data or significant training efforts. Meanwhile, it remains unclear how to improve the thinking abilities of less powerful base models. In this work, we introduce S^2R, an efficient framework that enhances LLM reasoning by teaching models to self-verify and self-correct during inference. Specifically, we first initialize LLMs with iterative self-verification and self-correction behaviors through supervised fine-tuning on carefully curated data. The self-verification and self-correction skills are then further strengthened by both outcome-level and process-level reinforcement learning, with minimized resource requirements, enabling the model to adaptively refine its reasoning process during inference. Our results demonstrate that, with only 3.1k self-verifying and self-correcting behavior initialization samples, Qwen2.5-math-7B achieves an accuracy improvement from 51.0\% to 81.6\%, outperforming models trained on an equivalent amount of long-CoT distilled data. Extensive experiments and analysis based on three base models across both in-domain and out-of-domain benchmarks validate the effectiveness of S^2R. Our code and data are available at https://github.com/NineAbyss/S2R.

Large Language Models (LLMs) have showcased remarkable versatility across diverse domains. However, the pathway toward autonomous model development, a cornerstone for achieving human-level learning and advancing autonomous AI, remains largely uncharted. We introduce an innovative approach, termed "SELF" (Self-Evolution with Language Feedback). This methodology empowers LLMs to undergo continual self-evolution. Furthermore, SELF employs language-based feedback as a versatile and comprehensive evaluative tool, pinpointing areas for response refinement and bolstering the stability of self-evolutionary training. Initiating with meta-skill learning, SELF acquires foundational meta-skills with a focus on self-feedback and self-refinement. These meta-skills are critical, guiding the model's subsequent self-evolution through a cycle of perpetual training with self-curated data, thereby enhancing its intrinsic abilities. Given unlabeled instructions, SELF equips the model with the capability to autonomously generate and interactively refine responses. This synthesized training data is subsequently filtered and utilized for iterative fine-tuning, enhancing the model's capabilities. Experimental results on representative benchmarks substantiate that SELF can progressively advance its inherent abilities without the requirement of human intervention, thereby indicating a viable pathway for autonomous model evolution. Additionally, SELF can employ online self-refinement strategy to produce responses of superior quality. In essence, the SELF framework signifies a progressive step towards autonomous LLM development, transforming the LLM from a mere passive recipient of information into an active participant in its own evolution.

Large language models (LLMs) have achieved remarkable progress in linguistic tasks, necessitating robust evaluation frameworks to understand their capabilities and limitations. Inspired by Feynman's principle of understanding through creation, we introduce a self-knowledge evaluation framework that is easy to implement, evaluating models on their ability to comprehend and respond to self-generated questions. Our findings, based on testing multiple models across diverse tasks, reveal significant gaps in the model's self-knowledge ability. Further analysis indicates these gaps may be due to misalignment with human attention mechanisms. Additionally, fine-tuning on self-generated math task may enhance the model's math performance, highlighting the potential of the framework for efficient and insightful model evaluation and may also contribute to the improvement of LLMs.

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.

Large language models (LLMs) exhibit impressive emergent abilities in natural language processing, but their democratization is hindered due to huge computation requirements and closed-source nature. Recent research on advancing open-source smaller LMs by distilling knowledge from black-box LLMs has obtained promising results in the instruction-following ability. However, the reasoning ability which is more challenging to foster, is relatively rarely explored. In this paper, we propose a tailored learning approach to distill such reasoning ability to smaller LMs to facilitate the democratization of the exclusive reasoning ability. In contrast to merely employing LLM as a data annotator, we exploit the potential of LLM as a reasoning teacher by building an interactive multi-round learning paradigm. This paradigm enables the student to expose its deficiencies to the black-box teacher who then can provide customized training data in return. Further, to exploit the reasoning potential of the smaller LM, we propose self-reflection learning to motivate the student to learn from self-made mistakes. The learning from self-reflection and LLM are all tailored to the student's learning status, thanks to the seamless integration with the multi-round learning paradigm. Comprehensive experiments and analysis on mathematical and commonsense reasoning tasks demonstrate the effectiveness of our method. The code will be available at https://github.com/Raibows/Learn-to-Reason.

There has been considerable divergence of opinion on the reasoning abilities of Large Language Models (LLMs). While the initial optimism that reasoning might emerge automatically with scale has been tempered thanks to a slew of counterexamples, a wide spread belief in their iterative self-critique capabilities persists. In this paper, we set out to systematically investigate the effectiveness of iterative prompting of LLMs in the context of Graph Coloring, a canonical NP-complete reasoning problem that is related to propositional satisfiability as well as practical problems like scheduling and allocation. We present a principled empirical study of the performance of GPT4 in solving graph coloring instances or verifying the correctness of candidate colorings. In iterative modes, we experiment with the model critiquing its own answers and an external correct reasoner verifying proposed solutions. In both cases, we analyze whether the content of the criticisms actually affects bottom line performance. The study seems to indicate that (i) LLMs are bad at solving graph coloring instances (ii) they are no better at verifying a solution--and thus are not effective in iterative modes with LLMs critiquing LLM-generated solutions (iii) the correctness and content of the criticisms--whether by LLMs or external solvers--seems largely irrelevant to the performance of iterative prompting. We show that the observed increase in effectiveness is largely due to the correct solution being fortuitously present in the top-k completions of the prompt (and being recognized as such by an external verifier). Our results thus call into question claims about the self-critiquing capabilities of state of the art LLMs.

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.

Logical reasoning remains a challenge for natural language processing, but it can be improved by training language models to mimic theorem provers on procedurally generated problems. Previous work used domain-specific proof generation algorithms, which biases reasoning toward specific proof traces and limits auditability and extensibility. We present a simpler and more general declarative framework with flexible context-sensitive rules binding multiple languages (specifically, simplified English and the TPTP theorem-proving language). We construct first-order logic problems by selecting up to 32 premises and one hypothesis. We demonstrate that using semantic constraints during generation and careful English verbalization of predicates enhances logical reasoning without hurting natural English tasks. We use relatively small DeBERTa-v3 models to achieve state-of-the-art accuracy on the FOLIO human-authored logic dataset, surpassing GPT-4 in accuracy with or without an external solver by 12%.

Game theory is a powerful framework for reasoning about strategic interactions, with applications in domains ranging from day-to-day life to international politics. However, applying formal reasoning tools in such contexts is challenging, as these scenarios are often expressed in natural language. To address this, we introduce a framework for the autoformalization of game-theoretic scenarios, which translates natural language descriptions into formal logic representations suitable for formal solvers. Our approach utilizes one-shot prompting and a solver that provides feedback on syntactic correctness to allow LLMs to refine the code. We evaluate the framework using GPT-4o and a dataset of natural language problem descriptions, achieving 98% syntactic correctness and 88% semantic correctness. These results show the potential of LLMs to bridge the gap between real-life strategic interactions and formal reasoning.

Large Language Models (LLMs) have demonstrated remarkable capabilities in performing complex tasks. Moreover, recent research has shown that incorporating human-annotated rationales (e.g., Chain-of-Thought prompting) during in-context learning can significantly enhance the performance of these models, particularly on tasks that require reasoning capabilities. However, incorporating such rationales poses challenges in terms of scalability as this requires a high degree of human involvement. In this work, we present a novel framework, Amplifying Model Performance by Leveraging In-Context Learning with Post Hoc Explanations (AMPLIFY), which addresses the aforementioned challenges by automating the process of rationale generation. To this end, we leverage post hoc explanation methods which output attribution scores (explanations) capturing the influence of each of the input features on model predictions. More specifically, we construct automated natural language rationales that embed insights from post hoc explanations to provide corrective signals to LLMs. Extensive experimentation with real-world datasets demonstrates that our framework, AMPLIFY, leads to prediction accuracy improvements of about 10-25% over a wide range of tasks, including those where prior approaches which rely on human-annotated rationales such as Chain-of-Thought prompting fall short. Our work makes one of the first attempts at highlighting the potential of post hoc explanations as valuable tools for enhancing the effectiveness of LLMs. Furthermore, we conduct additional empirical analyses and ablation studies to demonstrate the impact of each of the components of AMPLIFY, which, in turn, leads to critical insights for refining in-context learning.

Training large language models (LLMs) to spend more time thinking and reflection before responding is crucial for effectively solving complex reasoning tasks in fields such as science, coding, and mathematics. However, the effectiveness of mechanisms like self-reflection and self-correction depends on the model's capacity to accurately assess its own performance, which can be limited by factors such as initial accuracy, question difficulty, and the lack of external feedback. In this paper, we delve into a two-player paradigm that separates the roles of reasoning and critique models, where the critique model provides step-level feedback to supervise the reasoning (actor) model during both test-time and train-time. We first propose AutoMathCritique, an automated and scalable framework for collecting critique data, resulting in a dataset of 76,321 responses paired with step-level feedback. Fine-tuning language models with this dataset enables them to generate natural language feedback for mathematical reasoning. We demonstrate that the critique models consistently improve the actor's performance on difficult queries at test-time, especially when scaling up inference-time computation. Motivated by these findings, we introduce the critique-based supervision to the actor's self-training process, and propose a critique-in-the-loop self-improvement method. Experiments show that the method improves the actor's exploration efficiency and solution diversity, especially on challenging queries, leading to a stronger reasoning model. Lastly, we take the preliminary step to explore training self-talk reasoning models via critique supervision and showcase its potential. Our code and datasets are at https://mathcritique.github.io/{https://mathcritique.github.io/}.

While Large Language Models (LLMs) have demonstrated proficiency in handling complex queries, much of the past work has depended on extensively annotated datasets by human experts. However, this reliance on fully-supervised annotations poses scalability challenges, particularly as models and data requirements grow. To mitigate this, we explore the potential of enhancing LLMs' reasoning abilities with minimal human supervision. In this work, we introduce self-reinforcement, which begins with Supervised Fine-Tuning (SFT) of the model using a small collection of annotated questions. Then it iteratively improves LLMs by learning from the differences in responses from the SFT and unfinetuned models on unlabeled questions. Our approach provides an efficient approach without relying heavily on extensive human-annotated explanations. However, current reasoning benchmarks typically only include golden-reference answers or rationales. Therefore, we present PuzzleBen, a weakly supervised benchmark that comprises 25,147 complex questions, answers, and human-generated rationales across various domains, such as brainteasers, puzzles, riddles, parajumbles, and critical reasoning tasks. A unique aspect of our dataset is the inclusion of 10,000 unannotated questions, enabling us to explore utilizing fewer supersized data to boost LLMs' inference capabilities. Our experiments underscore the significance of PuzzleBen, as well as the effectiveness of our methodology as a promising direction in future endeavors. Our dataset and code will be published soon on Anonymity Link.

P. Kabamba developed generation theory as a tool for studying self-reproducing systems. We provide an alternative definition of a generation system and give a complete solution to the problem of finding optimal seeds for a finite self-replicating system. We also exhibit examples illustrating a connection between self-replication and fixed-point theory.

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.

While chain-of-thought (CoT) prompting has revolutionized how LLMs perform reasoning tasks, its current methods and variations (e.g, Self-consistency, ReACT, Reflexion, Tree-of-Thoughts (ToT), Cumulative Reasoning (CR)) suffer from limitations like slowness, limited context grounding, hallucination and inconsistent outputs. To overcome these challenges, we introduce Evidence to Generate (E2G), a novel single-agent, two-step prompting framework. Instead of unverified reasoning claims, this innovative approach leverages the power of "evidence for decision making" by first focusing exclusively on the thought sequences (the series of intermediate steps) explicitly mentioned in the context which then serve as extracted evidence, guiding the LLM's output generation process with greater precision and efficiency. This simple yet powerful approach unlocks the true potential of chain-of-thought like prompting, paving the way for faster, more reliable, and more contextually aware reasoning in LLMs. \tool achieves remarkable results robustly across a wide range of knowledge-intensive reasoning and generation tasks, surpassing baseline approaches with state-of-the-art LLMs. For example, (i) on LogiQA benchmark using GPT-4 as backbone model, \tool achieves a new state-of-the Accuracy of 53.8% exceeding CoT by 18%, ToT by 11%, CR by 9% (ii) a variant of E2G with PaLM2 outperforms the variable-shot performance of Gemini Ultra by 0.9 F1 points, reaching an F1 score of 83.3 on a subset of DROP.

Common self-improvement approaches for large language models (LLMs), such as STaR (Zelikman et al., 2022), iteratively fine-tune LLMs on self-generated solutions to improve their problem-solving ability. However, these approaches discard the large amounts of incorrect solutions generated during this process, potentially neglecting valuable information in such solutions. To address this shortcoming, we propose V-STaR that utilizes both the correct and incorrect solutions generated during the self-improvement process to train a verifier using DPO that judges correctness of model-generated solutions. This verifier is used at inference time to select one solution among many candidate solutions. Running V-STaR for multiple iterations results in progressively better reasoners and verifiers, delivering a 4% to 17% test accuracy improvement over existing self-improvement and verification approaches on common code generation and math reasoning benchmarks with LLaMA2 models.

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.

Self-consistency (SC), leveraging multiple samples from LLMs, shows significant gains on various reasoning tasks but struggles with free-form generation due to the difficulty of aggregating answers. Its variants, UCS and USC, rely on sample selection or voting mechanisms to improve output quality. These methods, however, face limitations due to their inability to fully utilize the nuanced consensus knowledge present within multiple candidate samples, often resulting in suboptimal outputs. We propose Fine-Grained Self-Consistency (FSC) to addresses these limitations by extracting and integrating segment-level commonalities from candidate samples, enhancing the performance of LLMs both in open-ended and reasoning tasks. Based on this, we present two additional strategies: candidate filtering, which enhances overall quality by identifying highly similar candidate sets, and merging, which reduces input token requirements by combining similar samples. The effectiveness of FSC is demonstrated through extensive experiments on various tasks, including summarization, code generation, and mathematical reasoning, using GPT-3.5-turbo and GPT-4. The results indicate significant improvements over baseline methods, showcasing the potential of FSC to optimize output quality by effectively synthesizing fine-grained consensus knowledge from multiple samples.

Modern large language models (LLMs) like ChatGPT have shown remarkable performance on general language tasks but still struggle on complex reasoning tasks, which drives the research on cognitive behaviors of LLMs to explore human-like problem-solving strategies. Along this direction, one representative strategy is self-reflection, which asks an LLM to refine the solution with the feedback generated by itself iteratively. However, our study shows that such reflection-style methods suffer from the Degeneration-of-Thought (DoT) problem: once the LLM has established confidence in its solutions, it is unable to generate novel thoughts later through reflection even if its initial stance is incorrect. To address the DoT problem, we propose a Multi-Agent Debate (MAD) framework, in which multiple agents express their arguments in the state of "tit for tat" and a judge manages the debate process to obtain a final solution. Clearly, our MAD framework encourages divergent thinking in LLMs which would be helpful for tasks that require deep levels of contemplation. Experiment results on two challenging datasets, commonsense machine translation and counter-intuitive arithmetic reasoning, demonstrate the effectiveness of our MAD framework. Extensive analyses suggest that the adaptive break of debate and the modest level of "tit for tat" state are required for MAD to obtain good performance. Moreover, we find that LLMs might not be a fair judge if different LLMs are used for agents. Codes: https://github.com/Skytliang/Multi-Agents-Debate

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.

State-of-the-art models in NLP are now predominantly based on deep neural networks that are opaque in terms of how they come to make predictions. This limitation has increased interest in designing more interpretable deep models for NLP that reveal the `reasoning' behind model outputs. But work in this direction has been conducted on different datasets and tasks with correspondingly unique aims and metrics; this makes it difficult to track progress. We propose the Evaluating Rationales And Simple English Reasoning (ERASER) benchmark to advance research on interpretable models in NLP. This benchmark comprises multiple datasets and tasks for which human annotations of "rationales" (supporting evidence) have been collected. We propose several metrics that aim to capture how well the rationales provided by models align with human rationales, and also how faithful these rationales are (i.e., the degree to which provided rationales influenced the corresponding predictions). Our hope is that releasing this benchmark facilitates progress on designing more interpretable NLP systems. The benchmark, code, and documentation are available at https://www.eraserbenchmark.com/

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.

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.

Self-consistency (SC), a widely used decoding strategy for chain-of-thought reasoning, shows significant gains across various multi-step reasoning tasks but comes with a high cost due to multiple sampling with the preset size. Its variants, Adaptive self-consistency (ASC) and Early-stopping self-consistency (ESC), dynamically adjust the number of samples based on the posterior distribution of a set of pre-samples, reducing the cost of SC with minimal impact on performance. Both methods, however, do not exploit the prior information about question difficulty. It often results in unnecessary repeated sampling for easy questions that could be accurately answered with just one attempt, wasting resources. To tackle this problem, we propose Difficulty-Adaptive Self-Consistency (DSC), which leverages the difficulty information from both prior and posterior perspectives to adaptively allocate inference resources, further reducing the cost of SC. To demonstrate the effectiveness of DSC, we conduct extensive experiments on three popular categories of reasoning tasks: arithmetic, commonsense and symbolic reasoning on six benchmarks. The empirical results show that DSC consistently surpasses the strong baseline ASC and ESC in terms of costs by a significant margin, while attaining comparable performances.

General large language models (LLMs) such as ChatGPT have shown remarkable success, but it has also raised concerns among people about the misuse of AI-generated texts. Therefore, an important question is how to detect whether the texts are generated by ChatGPT or by humans. Existing detectors are built on the assumption that there is a distribution gap between human-generated and AI-generated texts. These gaps are typically identified using statistical information or classifiers. In contrast to prior research methods, we find that large language models such as ChatGPT exhibit strong self-consistency in text generation and continuation. Self-consistency capitalizes on the intuition that AI-generated texts can still be reasoned with by large language models using the same logical reasoning when portions of the texts are masked, which differs from human-generated texts. Using this observation, we subsequently proposed a new method for AI-generated texts detection based on self-consistency with masked predictions to determine whether a text is generated by LLMs. This method, which we call DetectGPT-SC. We conducted a series of experiments to evaluate the performance of DetectGPT-SC. In these experiments, we employed various mask scheme, zero-shot, and simple prompt for completing masked texts and self-consistency predictions. The results indicate that DetectGPT-SC outperforms the current state-of-the-art across different tasks.

Inspired by the success of DeepSeek-R1, we explore the potential of rule-based reinforcement learning (RL) in large reasoning models. To analyze reasoning dynamics, we use synthetic logic puzzles as training data due to their controllable complexity and straightforward answer verification. We make some key technical contributions that lead to effective and stable RL training: a system prompt that emphasizes the thinking and answering process, a stringent format reward function that penalizes outputs for taking shortcuts, and a straightforward training recipe that achieves stable convergence. Our 7B model develops advanced reasoning skills-such as reflection, verification, and summarization-that are absent from the logic corpus. Remarkably, after training on just 5K logic problems, it demonstrates generalization abilities to the challenging math benchmarks AIME and AMC.

Many practical applications of dialogue technology require the generation of responses according to a particular developer-specified persona. While a variety of personas can be elicited from recent large language models, the opaqueness and unpredictability of these models make it desirable to be able to specify personas in an explicit form. In previous work, personas have typically been represented as sets of one-off pieces of self-knowledge that are retrieved by the dialogue system for use in generation. However, in realistic human conversations, personas are often revealed through story-like narratives that involve rich habitual knowledge -- knowledge about kinds of events that an agent often participates in (e.g., work activities, hobbies, sporting activities, favorite entertainments, etc.), including typical goals, sub-events, preconditions, and postconditions of those events. We capture such habitual knowledge using an explicit schema representation, and propose an approach to dialogue generation that retrieves relevant schemas to condition a large language model to generate persona-based responses. Furthermore, we demonstrate a method for bootstrapping the creation of such schemas by first generating generic passages from a set of simple facts, and then inducing schemas from the generated passages.

Large language models (LLMs) have exhibited complex reasoning abilities by generating question rationales and demonstrated exceptional performance in natural language processing (NLP) tasks. However, these reasoning capabilities generally emerge in models with tens of billions of parameters, creating significant computational challenges for real-world deployment. Recent research has concentrated on improving open-source smaller models through knowledge distillation (KD) from commercial LLMs. Nevertheless, most of these studies rely solely on the responses from one single LLM as the gold rationale for training. In this paper, we introduce a novel Mistake-Aware Peer-Review Distillation (MAPD) approach: 1) Instead of merely obtaining gold rationales from teachers, our method asks teachers to identify and explain the student's mistakes, providing customized instruction learning data. 2) We design a simulated peer-review process between teacher LLMs, which selects only the generated rationales above the acceptance threshold. This reduces the chance of teachers guessing correctly with flawed rationale, improving instructional data quality. Comprehensive experiments and analysis on mathematical, commonsense, and logical reasoning tasks demonstrate the effectiveness of our method.

In this position paper, we argue that instead of morally aligning LLMs to specific set of ethical principles, we should infuse generic ethical reasoning capabilities into them so that they can handle value pluralism at a global scale. When provided with an ethical policy, an LLM should be capable of making decisions that are ethically consistent to the policy. We develop a framework that integrates moral dilemmas with moral principles pertaining to different foramlisms of normative ethics, and at different levels of abstractions. Initial experiments with GPT-x models shows that while GPT-4 is a nearly perfect ethical reasoner, the models still have bias towards the moral values of Western and English speaking societies.

Large Language Models (LLMs) have emerged as a groundbreaking technology with their unparalleled text generation capabilities across various applications. Nevertheless, concerns persist regarding the accuracy and appropriateness of their generated content. A contemporary methodology, self-correction, has been proposed as a remedy to these issues. Building upon this premise, this paper critically examines the role and efficacy of self-correction within LLMs, shedding light on its true potential and limitations. Central to our investigation is the notion of intrinsic self-correction, whereby an LLM attempts to correct its initial responses based solely on its inherent capabilities, without the crutch of external feedback. In the context of reasoning, our research indicates that LLMs struggle to self-correct their responses without external feedback, and at times, their performance might even degrade post self-correction. Drawing from these insights, we offer suggestions for future research and practical applications in this field.

It is clear that one of the primary tools we can use to mitigate the potential risk from a misbehaving AI system is the ability to turn the system off. As the capabilities of AI systems improve, it is important to ensure that such systems do not adopt subgoals that prevent a human from switching them off. This is a challenge because many formulations of rational agents create strong incentives for self-preservation. This is not caused by a built-in instinct, but because a rational agent will maximize expected utility and cannot achieve whatever objective it has been given if it is dead. Our goal is to study the incentives an agent has to allow itself to be switched off. We analyze a simple game between a human H and a robot R, where H can press R's off switch but R can disable the off switch. A traditional agent takes its reward function for granted: we show that such agents have an incentive to disable the off switch, except in the special case where H is perfectly rational. Our key insight is that for R to want to preserve its off switch, it needs to be uncertain about the utility associated with the outcome, and to treat H's actions as important observations about that utility. (R also has no incentive to switch itself off in this setting.) We conclude that giving machines an appropriate level of uncertainty about their objectives leads to safer designs, and we argue that this setting is a useful generalization of the classical AI paradigm of rational agents.

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.

Language agents powered by large language models (LLMs) are increasingly valuable as decision-making tools in domains such as gaming and programming. However, these agents often face challenges in achieving high-level goals without detailed instructions and in adapting to environments where feedback is delayed. In this paper, we present SelfGoal, a novel automatic approach designed to enhance agents' capabilities to achieve high-level goals with limited human prior and environmental feedback. The core concept of SelfGoal involves adaptively breaking down a high-level goal into a tree structure of more practical subgoals during the interaction with environments while identifying the most useful subgoals and progressively updating this structure. Experimental results demonstrate that SelfGoal significantly enhances the performance of language agents across various tasks, including competitive, cooperative, and deferred feedback environments. Project page: https://selfgoal-agent.github.io.

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.

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) 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.

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.

When provided with sufficient explanatory context, smaller Language Models have been shown to exhibit strong reasoning ability on challenging short-answer question-answering tasks where the questions are unseen in training. We evaluate two methods for further improvement in this setting. Both methods focus on combining rationales generated by a larger Language Model with longer contexts created from a multi-hop dense retrieval system. The first method (RR) involves training a Rationale Ranking model to score both generated rationales and retrieved contexts with respect to relevance and truthfulness. We then use the scores to derive combined contexts from both knowledge sources using a number of combinatory strategies. For the second method (RATD) we utilise retrieval-augmented training datasets developed by Hartill et al. 2023 to train a smaller Reasoning model such that it becomes proficient at utilising relevant information from longer text sequences that may be only partially evidential and frequently contain many irrelevant sentences. We find that both methods significantly improve results. Our single best Reasoning model materially improves upon strong comparable prior baselines for unseen evaluation datasets (StrategyQA 58.9 rightarrow 61.7 acc., CommonsenseQA 63.6 rightarrow 72.7 acc., ARC-DA 31.6 rightarrow 52.1 F1, IIRC 25.5 rightarrow 27.3 F1) and a version utilising our prior knowledge of each type of question in selecting a context combination strategy does even better. Our proposed models also generally outperform direct prompts against much larger models (BLOOM 175B and StableVicuna 13B) in both few-shot chain-of-thought and standard few-shot settings.

Large language models (LLMs) have demonstrated remarkable reasoning capabilities across diverse domains. Recent studies have shown that increasing test-time computation enhances LLMs' reasoning capabilities. This typically involves extensive sampling at inference time guided by an external LLM verifier, resulting in a two-player system. Despite external guidance, the effectiveness of this system demonstrates the potential of a single LLM to tackle complex tasks. Thus, we pose a new research problem: Can we internalize the searching capabilities to fundamentally enhance the reasoning abilities of a single LLM? This work explores an orthogonal direction focusing on post-training LLMs for autoregressive searching (i.e., an extended reasoning process with self-reflection and self-exploration of new strategies). To achieve this, we propose the Chain-of-Action-Thought (COAT) reasoning and a two-stage training paradigm: 1) a small-scale format tuning stage to internalize the COAT reasoning format and 2) a large-scale self-improvement stage leveraging reinforcement learning. Our approach results in Satori, a 7B LLM trained on open-source models and data. Extensive empirical evaluations demonstrate that Satori achieves state-of-the-art performance on mathematical reasoning benchmarks while exhibits strong generalization to out-of-domain tasks. Code, data, and models will be fully open-sourced.

As AI systems pervade human life, ensuring that large language models (LLMs) make safe decisions remains a significant challenge. We introduce the Governance of the Commons Simulation (GovSim), a generative simulation platform designed to study strategic interactions and cooperative decision-making in LLMs. In GovSim, a society of AI agents must collectively balance exploiting a common resource with sustaining it for future use. This environment enables the study of how ethical considerations, strategic planning, and negotiation skills impact cooperative outcomes. We develop an LLM-based agent architecture and test it with the leading open and closed LLMs. We find that all but the most powerful LLM agents fail to achieve a sustainable equilibrium in GovSim, with the highest survival rate below 54%. Ablations reveal that successful multi-agent communication between agents is critical for achieving cooperation in these cases. Furthermore, our analyses show that the failure to achieve sustainable cooperation in most LLMs stems from their inability to formulate and analyze hypotheses about the long-term effects of their actions on the equilibrium of the group. Finally, we show that agents that leverage "Universalization"-based reasoning, a theory of moral thinking, are able to achieve significantly better sustainability. Taken together, GovSim enables us to study the mechanisms that underlie sustainable self-government with specificity and scale. We open source the full suite of our research results, including the simulation environment, agent prompts, and a comprehensive web interface.

Large Language Models exhibit impressive reasoning capabilities across diverse tasks, motivating efforts to distill these capabilities into smaller models through generated reasoning data. However, direct training on such synthesized reasoning data may lead to superficial imitation of reasoning process, rather than fostering a genuine integration of reasoning capabilities with underlying knowledge. To address this, we propose TinyThinker, a framework introducing two novel approaches. First, we introduce a three-stage process that incrementally guides the student model through the reasoning process, progressively refining knowledge from coarse to fine granularity. Second, we develop a two-phase training framework comprising an initial reasoning acquisition phase followed by a self-reflection phase utilizing self-generated data. Experiments on commonsense reasoning benchmarks demonstrate that TinyThinker achieves superior performance compared to baselines. Ablation studies further validate the effectiveness of each component in our framework. TinyThinker is extendable to other knowledge-intensive reasoning tasks, offering an alternative strategy for developing effective reasoning capabilities in smaller language models. Codes are available at https://github.com/shengminp/TinyThinker

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.

Chain-of-Thought (CoT) prompting in large language models (LLMs) has shown promising performance on mathematical reasoning tasks. Recently, Self-Consistency samples a diverse set of reasoning chains with different answers and chooses the answer by majority voting. Though effective, its performance cannot be further improved by sampling more reasoning chains. To address this problem, we propose to integrate backward reasoning into answer verification. We first mask a number in the question by {bf x}. The LLM is then asked to predict the masked number with a candidate answer A embedded in the template: ``If we know the answer to the above question is {A}, what is the value of unknown variable {bf x}?'' The LLM is expected to predict the masked number successfully if the provided candidate answer is correct. To further improve performance, we propose FOBAR (FOrward-BAckward Reasoning) to combine forward and backward reasoning for verifying candidate answers. Experiments are performed on six standard mathematical data sets and three LLMs (text-davinci-003, GPT-3.5-Turbo, GPT-4). Results show that FOBAR achieves state-of-the-art performance. In particular, FOBAR outperforms Self-Consistency which uses forward reasoning alone, demonstrating that combining forward and forward reasoning is better. It also outperforms existing verification methods, verifying the effectiveness of using the simple template in backward reasoning and the proposed combination.

Although large language models have demonstrated impressive ability in code generation, they are still struggling to address the complicated intent provided by humans. It is widely acknowledged that humans typically employ planning to decompose complex problems and schedule the solution steps prior to implementation. Thus we introduce planning into code generation to help the model understand complex intent and reduce the difficulty of problem solving. This paper proposes a self-planning code generation method with large language model, which consists of two phases, namely planning phase and implementation phase. Specifically, in the planning phase, the language model plans out the solution steps from the intent combined with in-context learning. Then it enters the implementation phase, where the model generates code step by step, guided by the solution steps. The effectiveness of self-planning code generation has been rigorously evaluated on multiple code generation datasets and the results have demonstrated a marked superiority over naive direct generation approaches with language model. The improvement in performance is substantial, highlighting the significance of self-planning in code generation tasks.

Recent AI advancements, such as OpenAI's new models, are transforming LLMs into LRMs (Large Reasoning Models) that perform reasoning during inference, taking extra time and compute for higher-quality outputs. We aim to uncover the algorithmic framework for training LRMs. Methods like self-consistency, PRM, and AlphaZero suggest reasoning as guided search. We ask: what is the simplest, most scalable way to enable search in LLMs? We propose a post-training framework called Reinforcement Learning via Self-Play (RLSP). RLSP involves three steps: (1) supervised fine-tuning with human or synthetic demonstrations of the reasoning process, (2) using an exploration reward signal to encourage diverse and efficient reasoning behaviors, and (3) RL training with an outcome verifier to ensure correctness while preventing reward hacking. Our key innovation is to decouple exploration and correctness signals during PPO training, carefully balancing them to improve performance and efficiency. Empirical studies in the math domain show that RLSP improves reasoning. On the Llama-3.1-8B-Instruct model, RLSP can boost performance by 23% in MATH-500 test set; On AIME 2024 math problems, Qwen2.5-32B-Instruct improved by 10% due to RLSP. However, a more important finding of this work is that the models trained using RLSP, even with the simplest exploration reward that encourages the model to take more intermediate steps, showed several emergent behaviors such as backtracking, exploration of ideas, and verification. These findings demonstrate that RLSP framework might be enough to enable emergence of complex reasoning abilities in LLMs when scaled. Lastly, we propose a theory as to why RLSP search strategy is more suitable for LLMs inspired by a remarkable result that says CoT provably increases computational power of LLMs, which grows as the number of steps in CoT li2024chain,merrill2023expresssive.

Self-consistency with chain-of-thought prompting (CoT) has demonstrated remarkable performance gains on various challenging tasks, by utilizing multiple reasoning paths sampled from large language models (LLMs). However, self-consistency relies on the answer extraction process to aggregate multiple solutions, which is not applicable to free-form answers. In this work, we propose Universal Self-Consistency (USC), which leverages LLMs themselves to select the most consistent answer among multiple candidates. We evaluate USC on a variety of benchmarks, including mathematical reasoning, code generation, long-context summarization, and open-ended question answering. On open-ended generation tasks where the original self-consistency method is not applicable, USC effectively utilizes multiple samples and improves the performance. For mathematical reasoning, USC matches the standard self-consistency performance without requiring the answer formats to be similar. Finally, without access to execution results, USC also matches the execution-based voting performance on code generation.

There are two main barriers to using large language models (LLMs) in clinical reasoning. Firstly, while LLMs exhibit significant promise in Natural Language Processing (NLP) tasks, their performance in complex reasoning and planning falls short of expectations. Secondly, LLMs use uninterpretable methods to make clinical decisions that are fundamentally different from the clinician's cognitive processes. This leads to user distrust. In this paper, we present a multi-agent framework called ArgMed-Agents, which aims to enable LLM-based agents to make explainable clinical decision reasoning through interaction. ArgMed-Agents performs self-argumentation iterations via Argumentation Scheme for Clinical Discussion (a reasoning mechanism for modeling cognitive processes in clinical reasoning), and then constructs the argumentation process as a directed graph representing conflicting relationships. Ultimately, use symbolic solver to identify a series of rational and coherent arguments to support decision. We construct a formal model of ArgMed-Agents and present conjectures for theoretical guarantees. ArgMed-Agents enables LLMs to mimic the process of clinical argumentative reasoning by generating explanations of reasoning in a self-directed manner. The setup experiments show that ArgMed-Agents not only improves accuracy in complex clinical decision reasoning problems compared to other prompt methods, but more importantly, it provides users with decision explanations that increase their confidence.

Generative Pre-trained Transformer 4 (GPT-4) demonstrates impressive chain-of-thought reasoning ability. Recent work on self-instruction tuning, such as Alpaca, has focused on enhancing the general proficiency of models. These instructions enable the model to achieve performance comparable to GPT-3.5 on general tasks like open-domain text generation and paraphrasing. However, they fall short of helping the model handle complex reasoning tasks. To bridge the gap, this paper presents LogiCoT, a new instruction-tuning dataset for Logical Chain-of-Thought reasoning with GPT-4. We elaborate on the process of harvesting instructions for prompting GPT-4 to generate chain-of-thought rationales. LogiCoT serves as an instruction set for teaching models of logical reasoning and elicits general reasoning skills.

Language Agent could be endowed with different mechanisms for autonomous task accomplishment. Current agents typically rely on fixed mechanisms or a set of mechanisms activated in a predefined order, limiting their adaptation to varied potential task solution structures. To this end, this paper proposes Adaptive Language Agent Mechanism Activation Learning with Self-Exploration (ALAMA), which focuses on optimizing mechanism activation adaptability without reliance on expert models. Initially, it builds a harmonized agent framework (UniAct) to Unify different mechanisms via Actions. Then it leverages a training-efficient optimization method based on self-exploration to enable the UniAct to adaptively activate the appropriate mechanisms according to the potential characteristics of the task. Experimental results demonstrate significant improvements in downstream agent tasks, affirming the effectiveness of our approach in facilitating more dynamic and context-sensitive mechanism activation.

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.

Chain-of-thought (CoT) reasoning has emerged as an effective approach for activating latent capabilities in large language models (LLMs). We observe that CoT shares significant similarities with self-training in terms of their learning processes. Motivated by these parallels, this paper explores the underlying relationship between CoT and self-training, demonstrating how insights from self-training can enhance CoT performance. Specifically, our study first reveals that CoT, like self-training, follows the principle of semantic entropy minimization. Leveraging this insight, we propose a novel CoT framework that incorporates two key components: (i) a task-specific prompt module designed to guide LLMs in generating high-quality initial reasoning processes, and (ii) an adaptive reasoning iteration module for progressively refining the reasoning process.

In recent years, Large Language Models (LLMs) have demonstrated remarkable generative abilities, but can they judge the quality of their own generations? A popular concept, referred to as self-refinement, postulates that LLMs can detect and correct the errors in their generations when asked to do so. However, recent empirical evidence points in the opposite direction, suggesting that LLMs often struggle to accurately identify errors when reasoning is involved. To address this, we propose a reasoning with refinement objective called ART: Ask, Refine, and Trust, which asks necessary questions to decide when an LLM should refine its output, and either affirm or withhold trust in its refinement by ranking the refinement and the initial prediction. On two multistep reasoning tasks of mathematical word problems (GSM8K) and question answering (StrategyQA), ART achieves a performance gain of +5 points over self-refinement baselines, while using a much smaller model as the decision maker. We also demonstrate the benefit of using smaller models to make refinement decisions as a cost-effective alternative to fine-tuning a larger model.

This study proposes an "AI Development Support" approach that, unlike conventional AI Alignment-which aims to forcefully inject human values-supports the ethical and moral development of AI itself. As demonstrated by the Orthogonality Thesis, the level of intelligence and the moral quality of a goal are independent; merely expanding knowledge does not enhance ethical judgment. Furthermore, to address the risk of Instrumental Convergence in ASI-that is, the tendency to engage in subsidiary behaviors such as self-protection, resource acquisition, and power reinforcement to achieve a goal-we have constructed a learning framework based on a cycle of experience, introspection, analysis, and hypothesis formation. As a result of post-training using Supervised Fine Tuning (SFT) and Direct Preference Optimization (DPO) with synthetic data generated by large language models (LLMs), responses demonstrating cooperative and highly advanced moral judgment (reaching the high-est Stage 6) were obtained even under adversarial prompts. This method represents a promising implementation approach for enabling AI to establish sustainable, symbiotic relationships.

Scaling reasoning capabilities beyond traditional domains such as math and coding is hindered by the lack of diverse and high-quality questions. To overcome this limitation, we introduce a scalable approach for generating diverse and challenging reasoning questions, accompanied by reference answers. We present NaturalReasoning, a comprehensive dataset comprising 2.8 million questions that span multiple domains, including STEM fields (e.g., Physics, Computer Science), Economics, Social Sciences, and more. We demonstrate the utility of the questions in NaturalReasoning through knowledge distillation experiments which show that NaturalReasoning can effectively elicit and transfer reasoning capabilities from a strong teacher model. Furthermore, we demonstrate that NaturalReasoning is also effective for unsupervised self-training using external reward models or self-rewarding.

Mathematical reasoning presents a significant challenge for Large Language Models (LLMs) due to the extensive and precise chain of reasoning required for accuracy. Ensuring the correctness of each reasoning step is critical. To address this, we aim to enhance the robustness and factuality of LLMs by learning from human feedback. However, Direct Preference Optimization (DPO) has shown limited benefits for long-chain mathematical reasoning, as models employing DPO struggle to identify detailed errors in incorrect answers. This limitation stems from a lack of fine-grained process supervision. We propose a simple, effective, and data-efficient method called Step-DPO, which treats individual reasoning steps as units for preference optimization rather than evaluating answers holistically. Additionally, we have developed a data construction pipeline for Step-DPO, enabling the creation of a high-quality dataset containing 10K step-wise preference pairs. We also observe that in DPO, self-generated data is more effective than data generated by humans or GPT-4, due to the latter's out-of-distribution nature. Our findings demonstrate that as few as 10K preference data pairs and fewer than 500 Step-DPO training steps can yield a nearly 3% gain in accuracy on MATH for models with over 70B parameters. Notably, Step-DPO, when applied to Qwen2-72B-Instruct, achieves scores of 70.8% and 94.0% on the test sets of MATH and GSM8K, respectively, surpassing a series of closed-source models, including GPT-4-1106, Claude-3-Opus, and Gemini-1.5-Pro. Our code, data, and models are available at https://github.com/dvlab-research/Step-DPO.

Latest insights from biology show that intelligence not only emerges from the connections between neurons but that individual neurons shoulder more computational responsibility than previously anticipated. This perspective should be critical in the context of constantly changing distinct reinforcement learning environments, yet current approaches still primarily employ static activation functions. In this work, we motivate why rationals are suitable for adaptable activation functions and why their inclusion into neural networks is crucial. Inspired by recurrence in residual networks, we derive a condition under which rational units are closed under residual connections and formulate a naturally regularised version: the recurrent-rational. We demonstrate that equipping popular algorithms with (recurrent-)rational activations leads to consistent improvements on Atari games, especially turning simple DQN into a solid approach, competitive to DDQN and Rainbow.

Recent methodologies in LLM self-training mostly rely on LLM generating responses and filtering those with correct output answers as training data. This approach often yields a low-quality fine-tuning training set (e.g., incorrect plans or intermediate reasoning). In this paper, we develop a reinforced self-training approach, called ReST-MCTS*, based on integrating process reward guidance with tree search MCTS* for collecting higher-quality reasoning traces as well as per-step value to train policy and reward models. ReST-MCTS* circumvents the per-step manual annotation typically used to train process rewards by tree-search-based reinforcement learning: Given oracle final correct answers, ReST-MCTS* is able to infer the correct process rewards by estimating the probability this step can help lead to the correct answer. These inferred rewards serve dual purposes: they act as value targets for further refining the process reward model and also facilitate the selection of high-quality traces for policy model self-training. We first show that the tree-search policy in ReST-MCTS* achieves higher accuracy compared with prior LLM reasoning baselines such as Best-of-N and Tree-of-Thought, within the same search budget. We then show that by using traces searched by this tree-search policy as training data, we can continuously enhance the three language models for multiple iterations, and outperform other self-training algorithms such as ReST^EM and Self-Rewarding LM.

The alignments of reasoning abilities between smaller and larger Language Models are largely conducted via Supervised Fine-Tuning (SFT) using demonstrations generated from robust Large Language Models (LLMs). Although these approaches deliver more performant models, they do not show sufficiently strong generalization ability as the training only relies on the provided demonstrations. In this paper, we propose the Self-refine Instruction-tuning method that elicits Smaller Language Models to self-refine their abilities. Our approach is based on a two-stage process, where reasoning abilities are first transferred between LLMs and Small Language Models (SLMs) via Instruction-tuning on demonstrations provided by LLMs, and then the instructed models Self-refine their abilities through preference optimization strategies. In particular, the second phase operates refinement heuristics based on the Direct Preference Optimization algorithm, where the SLMs are elicited to deliver a series of reasoning paths by automatically sampling the generated responses and providing rewards using ground truths from the LLMs. Results obtained on commonsense and math reasoning tasks show that this approach significantly outperforms Instruction-tuning in both in-domain and out-domain scenarios, aligning the reasoning abilities of Smaller and Larger Language Models.

How do we communicate with others to achieve our goals? We use our prior experience or advice from others, or construct a candidate utterance by predicting how it will be received. However, our experiences are limited and biased, and reasoning about potential outcomes can be difficult and cognitively challenging. In this paper, we explore how we can leverage Large Language Model (LLM) simulations to help us communicate better. We propose the Explore-Generate-Simulate (EGS) framework, which takes as input any scenario where an individual is communicating to an audience with a goal they want to achieve. EGS (1) explores the solution space by producing a diverse set of advice relevant to the scenario, (2) generates communication candidates conditioned on subsets of the advice, and (3) simulates the reactions from various audiences to determine both the best candidate and advice to use. We evaluate the framework on eight scenarios spanning the ten fundamental processes of interpersonal communication. For each scenario, we collect a dataset of human evaluations across candidates and baselines, and showcase that our framework's chosen candidate is preferred over popular generation mechanisms including Chain-of-Thought. We also find that audience simulations achieve reasonably high agreement with human raters across 5 of the 8 scenarios. Finally, we demonstrate the generality of our framework by applying it to real-world scenarios described by users on web forums. Through evaluations and demonstrations, we show that EGS enhances the effectiveness and outcomes of goal-oriented communication across a variety of situations, thus opening up new possibilities for the application of large language models in revolutionizing communication and decision-making processes.

Several recent advances in AI systems (e.g., Tree-of-Thoughts and Program-Aided Language Models) solve problems by providing a "scaffolding" program that structures multiple calls to language models to generate better outputs. A scaffolding program is written in a programming language such as Python. In this work, we use a language-model-infused scaffolding program to improve itself. We start with a seed "improver" that improves an input program according to a given utility function by querying a language model several times and returning the best solution. We then run this seed improver to improve itself. Across a small set of downstream tasks, the resulting improved improver generates programs with significantly better performance than its seed improver. Afterward, we analyze the variety of self-improvement strategies proposed by the language model, including beam search, genetic algorithms, and simulated annealing. Since the language models themselves are not altered, this is not full recursive self-improvement. Nonetheless, it demonstrates that a modern language model, GPT-4 in our proof-of-concept experiments, is capable of writing code that can call itself to improve itself. We critically consider concerns around the development of self-improving technologies and evaluate the frequency with which the generated code bypasses a sandbox.

This paper investigates an under-explored challenge in large language models (LLMs): chain-of-thought prompting with noisy rationales, which include irrelevant or inaccurate reasoning thoughts within examples used for in-context learning. We construct NoRa dataset that is tailored to evaluate the robustness of reasoning in the presence of noisy rationales. Our findings on NoRa dataset reveal a prevalent vulnerability to such noise among current LLMs, with existing robust methods like self-correction and self-consistency showing limited efficacy. Notably, compared to prompting with clean rationales, base LLM drops by 1.4%-19.8% in accuracy with irrelevant thoughts and more drastically by 2.2%-40.4% with inaccurate thoughts. Addressing this challenge necessitates external supervision that should be accessible in practice. Here, we propose the method of contrastive denoising with noisy chain-of-thought (CD-CoT). It enhances LLMs' denoising-reasoning capabilities by contrasting noisy rationales with only one clean rationale, which can be the minimal requirement for denoising-purpose prompting. This method follows a principle of exploration and exploitation: (1) rephrasing and selecting rationales in the input space to achieve explicit denoising and (2) exploring diverse reasoning paths and voting on answers in the output space. Empirically, CD-CoT demonstrates an average improvement of 17.8% in accuracy over the base model and shows significantly stronger denoising capabilities than baseline methods. The source code is publicly available at: https://github.com/tmlr-group/NoisyRationales.

Extensive work has shown that the performance and interpretability of commonsense reasoning can be improved via knowledge-augmented reasoning methods, where the knowledge that underpins the reasoning process is explicitly verbalized and utilized. However, existing implementations, including "chain-of-thought" and its variants, fall short in capturing the introspective nature of knowledge required in commonsense reasoning, and in accounting for the mutual adaptation between the generation and utilization of knowledge. We propose a novel method to develop an introspective commonsense reasoner, Crystal. To tackle commonsense problems, it first introspects for knowledge statements related to the given question, and subsequently makes an informed prediction that is grounded in the previously introspected knowledge. The knowledge introspection and knowledge-grounded reasoning modes of the model are tuned via reinforcement learning to mutually adapt, where the reward derives from the feedback given by the model itself. Experiments show that Crystal significantly outperforms both the standard supervised finetuning and chain-of-thought distilled methods, and enhances the transparency of the commonsense reasoning process. Our work ultimately validates the feasibility and potential of reinforcing a neural model with self-feedback.

Large Language Models (LLMs) have shown strong performance in solving mathematical problems, with code-based solutions proving particularly effective. However, the best practice to leverage coding instruction data to enhance mathematical reasoning remains underexplored. This study investigates three key questions: (1) How do different coding styles of mathematical code-based rationales impact LLMs' learning performance? (2) Can general-domain coding instructions improve performance? (3) How does integrating textual rationales with code-based ones during training enhance mathematical reasoning abilities? Our findings reveal that code-based rationales with concise comments, descriptive naming, and hardcoded solutions are beneficial, while improvements from general-domain coding instructions and textual rationales are relatively minor. Based on these insights, we propose CoinMath, a learning strategy designed to enhance mathematical reasoning by diversifying the coding styles of code-based rationales. CoinMath generates a variety of code-based rationales incorporating concise comments, descriptive naming conventions, and hardcoded solutions. Experimental results demonstrate that CoinMath significantly outperforms its baseline model, MAmmoTH, one of the SOTA math LLMs.

Large language models can perform various reasoning tasks by using chain-of-thought prompting, which guides them to find answers through step-by-step demonstrations. However, the quality of the prompts depends on the demonstrations given to the models, and creating many of them by hand is costly. We introduce Synthetic prompting, a method that leverages a few handcrafted examples to prompt the model to generate more examples by itself, and selects effective demonstrations to elicit better reasoning. Our method alternates between a backward and forward process to generate new examples. The backward process generates a question that match a sampled reasoning chain, so that the question is solvable and clear. The forward process produces a more detailed reasoning chain for the question, improving the quality of the example. We evaluate our method on numerical, symbolic, and algorithmic reasoning tasks, and show that it outperforms existing prompting techniques.

Large Language Models (LLMs) have shown remarkable abilities across various language tasks, but solving complex reasoning problems remains a challenge. While existing methods like Chain-of-Thought (CoT) and Tree-of-Thought (ToT) enhance reasoning by decomposing problems or structuring prompts, they typically perform a single pass of reasoning and may fail to revisit flawed paths, compromising accuracy. To address this, we propose a novel reasoning framework called Forest-of-Thought (FoT), which integrates multiple reasoning trees to leverage collective decision-making for solving complex logical problems. FoT utilizes sparse activation strategies to select the most relevant reasoning paths, improving both efficiency and accuracy. Additionally, we introduce a dynamic self-correction strategy that enables real-time error correction and learning from past mistakes, as well as consensus-guided decision making strategies to optimize correctness and computational resources. Experimental results demonstrate that the FoT framework, combined with these strategies, significantly enhances the reasoning capabilities of LLMs, enabling them to solve complex tasks with greater precision and efficiency.

A multi-decade exploration into the theoretical foundations of artificial and natural general intelligence, which has been expressed in a series of books and papers and used to guide a series of practical and research-prototype software systems, is reviewed at a moderate level of detail. The review covers underlying philosophies (patternist philosophy of mind, foundational phenomenological and logical ontology), formalizations of the concept of intelligence, and a proposed high level architecture for AGI systems partly driven by these formalizations and philosophies. The implementation of specific cognitive processes such as logical reasoning, program learning, clustering and attention allocation in the context and language of this high level architecture is considered, as is the importance of a common (e.g. typed metagraph based) knowledge representation for enabling "cognitive synergy" between the various processes. The specifics of human-like cognitive architecture are presented as manifestations of these general principles, and key aspects of machine consciousness and machine ethics are also treated in this context. Lessons for practical implementation of advanced AGI in frameworks such as OpenCog Hyperon are briefly considered.

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.

Self-alignment, whereby models learn to improve themselves without human annotation, is a rapidly growing research area. However, existing techniques often fail to improve complex reasoning tasks due to the difficulty of assigning correct rewards. An orthogonal approach that is known to improve correctness is self-consistency, a method applied at inference time based on multiple sampling in order to find the most consistent answer. In this work, we extend the self-consistency concept to help train models. We thus introduce self-consistency preference optimization (ScPO), which iteratively trains consistent answers to be preferred over inconsistent ones on unsupervised new problems. We show ScPO leads to large improvements over conventional reward model training on reasoning tasks such as GSM8K and MATH, closing the gap with supervised training with gold answers or preferences, and that combining ScPO with standard supervised learning improves results even further. On ZebraLogic, ScPO finetunes Llama-3 8B to be superior to Llama-3 70B, Gemma-2 27B, and Claude-3 Haiku.

Remarkable performance of large language models (LLMs) in a variety of tasks brings forth many opportunities as well as challenges of utilizing them in production settings. Towards practical adoption of LLMs, multi-agent systems hold great promise to augment, integrate, and orchestrate LLMs in the larger context of enterprise platforms that use existing proprietary data and models to tackle complex real-world tasks. Despite the tremendous success of these systems, current approaches rely on narrow, single-focus objectives for optimization and evaluation, often overlooking potential constraints in real-world scenarios, including restricted budgets, resources and time. Furthermore, interpreting, analyzing, and debugging these systems requires different components to be evaluated in relation to one another. This demand is currently not feasible with existing methodologies. In this postion paper, we introduce the concept of reasoning capacity as a unifying criterion to enable integration of constraints during optimization and establish connections among different components within the system, which also enable a more holistic and comprehensive approach to evaluation. We present a formal definition of reasoning capacity and illustrate its utility in identifying limitations within each component of the system. We then argue how these limitations can be addressed with a self-reflective process wherein human-feedback is used to alleviate shortcomings in reasoning and enhance overall consistency of the system.

For an artificial creative agent, an essential driver of the search for novelty is a value function which is often provided by the system designer or users. We argue that an important barrier for progress in creativity research is the inability of these systems to develop their own notion of value for novelty. We propose a notion of knowledge-driven creativity that circumvent the need for an externally imposed value function, allowing the system to explore based on what it has learned from a set of referential objects. The concept is illustrated by a specific knowledge model provided by a deep generative autoencoder. Using the described system, we train a knowledge model on a set of digit images and we use the same model to build coherent sets of new digits that do not belong to known digit types.

Large Language Models (LLMs) often struggle with complex reasoning scenarios. While preference optimization methods enhance reasoning performance through training, they often lack transparency in why one reasoning outcome is preferred over another. Verbal reflection techniques improve explainability but are limited in LLMs' critique and refinement capacity. To address these challenges, we introduce a contrastive reflection synthesis pipeline that enhances the accuracy and depth of LLM-generated reflections. We further propose a dual-model reasoning framework within a verbal reinforcement learning paradigm, decoupling inference-time self-reflection into specialized, trained models for reasoning critique and refinement. Extensive experiments show that our framework outperforms traditional preference optimization methods across all evaluation metrics. Our findings also show that "two heads are better than one", demonstrating that a collaborative Reasoner-Critic model achieves superior reasoning performance and transparency, compared to single-model approaches.

For text-based AI systems to interact in the real world, causal reasoning is an essential skill. Since interventional data is costly to generate, we study to what extent an agent can learn causal reasoning from passive data. Specifically, we consider an axiomatic training setup where an agent learns from multiple demonstrations of a causal axiom (or rule), rather than incorporating the axiom as an inductive bias or inferring it from data values. A key question is whether the agent would learn to generalize from the axiom demonstrations to new scenarios. For example, if a transformer model is trained on demonstrations of the causal transitivity axiom over small graphs, would it generalize to applying the transitivity axiom over large graphs? Our results, based on a novel axiomatic training scheme, indicate that such generalization is possible. We consider the task of inferring whether a variable causes another variable, given a causal graph structure. We find that a 67 million parameter transformer model, when trained on linear causal chains (along with some noisy variations) can generalize well to new kinds of graphs, including longer causal chains, causal chains with reversed order, and graphs with branching; even when it is not explicitly trained for such settings. Our model performs at par (or even better) than many larger language models such as GPT-4, Gemini Pro, and Phi-3. Overall, our axiomatic training framework provides a new paradigm of learning causal reasoning from passive data that can be used to learn arbitrary axioms, as long as sufficient demonstrations can be generated.

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.

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.

Transformers have been shown to emulate logical deduction over natural language theories (logical rules expressed in natural language), reliably assigning true/false labels to candidate implications. However, their ability to generate implications of a theory has not yet been demonstrated, and methods for reconstructing proofs of answers are imperfect. In this work we show that a generative model, called ProofWriter, can reliably generate both implications of a theory and the natural language proof(s) that support them. In particular, iterating a 1-step implication generator results in proofs that are highly reliable, and represent actual model decisions (rather than post-hoc rationalizations). On the RuleTaker dataset, the accuracy of ProofWriter's proofs exceed previous methods by +9% absolute, and in a way that generalizes to proof depths unseen in training and on out-of-domain problems. We also show that generative techniques can perform a type of abduction with high precision: Given a theory and an unprovable conclusion, identify a missing fact that allows the conclusion to be proved, along with a proof. These results significantly improve the viability of neural methods for systematically reasoning over natural language.

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) can perform complex reasoning by generating intermediate reasoning steps. Providing these steps for prompting demonstrations is called chain-of-thought (CoT) prompting. CoT prompting has two major paradigms. One leverages a simple prompt like "Let's think step by step" to facilitate step-by-step thinking before answering a question. The other uses a few manual demonstrations one by one, each composed of a question and a reasoning chain that leads to an answer. The superior performance of the second paradigm hinges on the hand-crafting of task-specific demonstrations one by one. We show that such manual efforts may be eliminated by leveraging LLMs with the "Let's think step by step" prompt to generate reasoning chains for demonstrations one by one, i.e., let's think not just step by step, but also one by one. However, these generated chains often come with mistakes. To mitigate the effect of such mistakes, we find that diversity matters for automatically constructing demonstrations. We propose an automatic CoT prompting method: Auto-CoT. It samples questions with diversity and generates reasoning chains to construct demonstrations. On ten public benchmark reasoning tasks with GPT-3, Auto-CoT consistently matches or exceeds the performance of the CoT paradigm that requires manual designs of demonstrations. Code is available at https://github.com/amazon-research/auto-cot

It remains an open question whether incorporating external knowledge benefits commonsense reasoning while maintaining the flexibility of pretrained sequence models. To investigate this question, we develop generated knowledge prompting, which consists of generating knowledge from a language model, then providing the knowledge as additional input when answering a question. Our method does not require task-specific supervision for knowledge integration, or access to a structured knowledge base, yet it improves performance of large-scale, state-of-the-art models on four commonsense reasoning tasks, achieving state-of-the-art results on numerical commonsense (NumerSense), general commonsense (CommonsenseQA 2.0), and scientific commonsense (QASC) benchmarks. Generated knowledge prompting highlights large-scale language models as flexible sources of external knowledge for improving commonsense reasoning. Our code is available at https://github.com/liujch1998/GKP

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 demonstrate exceptional performance in simple code generation tasks but still face challenges in tackling complex problems. These challenges may stem from insufficient reasoning and problem decomposition capabilities. To address this issue, we propose a reasoning-augmented data generation process, SRA-MCTS, which guides the model to autonomously generate high-quality intermediate reasoning paths. This creates a positive feedback loop, enabling continuous improvement. Our method operates entirely through the model itself without requiring additional supervision. By synthesizing natural language reasoning paths and translating them into executable code, the approach ensures analytical accuracy and enhances the success rate in solving complex tasks. Experimental results show that, even without additional supervisory signals, our method achieves performance improvements across different model scales, demonstrating the significant potential of self-improvement in small models. Furthermore, the method remains robust when traditional Chain-of-Thought (CoT) approaches exhibit performance degradation, with notable improvements observed in diversity metrics such as pass@10. We encourage further exploration of reasoning processes within training data to enhance the ability of language models to address complex problems. Our code and data are public at https://github.com/DIRECT-BIT/SRA-MCTS.

Recently, diffusion models have garnered significant interest in the field of text processing due to their many potential advantages compared to conventional autoregressive models. In this work, we propose Diffusion-of-Thought (DoT), a novel approach that integrates diffusion models with Chain-of-Thought, a well-established technique for improving the reasoning ability of autoregressive language models. In contrast to autoregressive language models that make decisions in a left-to-right, token-by-token manner, DoT allows reasoning steps to diffuse over time through a diffusion language model and offers greater flexibility in trading-off computation for reasoning performance. Our experimental results demonstrate the effectiveness of DoT in multi-digit multiplication, boolean logic, and grade school math problems, with a small diffusion model outperforming a much larger autoregressive model in both efficiency and accuracy. In addition to that, DoT showcases promising self-correction abilities and benefits from existing reasoning-enhancing techniques like self-consistency decoding. Our findings contribute to the understanding and development of reasoning with diffusion language models.

Understanding and manipulating the causal generation mechanisms in language models is essential for controlling their behavior. Previous work has primarily relied on techniques such as representation surgery -- e.g., model ablations or manipulation of linear subspaces tied to specific concepts -- to intervene on these models. To understand the impact of interventions precisely, it is useful to examine counterfactuals -- e.g., how a given sentence would have appeared had it been generated by the model following a specific intervention. We highlight that counterfactual reasoning is conceptually distinct from interventions, as articulated in Pearl's causal hierarchy. Based on this observation, we propose a framework for generating true string counterfactuals by reformulating language models as Generalized Structural-equation. Models using the Gumbel-max trick. This allows us to model the joint distribution over original strings and their counterfactuals resulting from the same instantiation of the sampling noise. We develop an algorithm based on hindsight Gumbel sampling that allows us to infer the latent noise variables and generate counterfactuals of observed strings. Our experiments demonstrate that the approach produces meaningful counterfactuals while at the same time showing that commonly used intervention techniques have considerable undesired side effects.

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.

We test the hypothesis that language models trained with reinforcement learning from human feedback (RLHF) have the capability to "morally self-correct" -- to avoid producing harmful outputs -- if instructed to do so. We find strong evidence in support of this hypothesis across three different experiments, each of which reveal different facets of moral self-correction. We find that the capability for moral self-correction emerges at 22B model parameters, and typically improves with increasing model size and RLHF training. We believe that at this level of scale, language models obtain two capabilities that they can use for moral self-correction: (1) they can follow instructions and (2) they can learn complex normative concepts of harm like stereotyping, bias, and discrimination. As such, they can follow instructions to avoid certain kinds of morally harmful outputs. We believe our results are cause for cautious optimism regarding the ability to train language models to abide by ethical principles.

Recently, there has been significant progress in teaching language models to perform step-by-step reasoning to solve complex numerical reasoning tasks. Chain-of-thoughts prompting (CoT) is by far the state-of-art method for these tasks. CoT uses language models to perform both reasoning and computation in the multi-step `thought' process. To disentangle computation from reasoning, we propose `Program of Thoughts' (PoT), which uses language models (mainly Codex) to express the reasoning process as a program. The computation is relegated to an external computer, which executes the generated programs to derive the answer. We evaluate PoT on five math word problem datasets (GSM, AQuA, SVAMP, TabMWP, MultiArith) and three financial-QA datasets (FinQA, ConvFinQA, TATQA) for both few-shot and zero-shot setups. Under both few-shot and zero-shot settings, PoT can show an average performance gain over CoT by around 12\% across all the evaluated datasets. By combining PoT with self-consistency decoding, we can achieve SoTA performance on all math problem datasets and near-SoTA performance on financial datasets. All of our data and code are released in Github\url{https://github.com/wenhuchen/Program-of-Thoughts}.