Daily Papers

The alignment of large language models (LLMs) with human values increasingly relies on using other LLMs as automated judges, or ``autoraters''. However, their reliability is limited by a foundational issue: they are trained on discrete preference labels, forcing a single ground truth onto tasks that are often subjective, ambiguous, or nuanced. We argue that a reliable autorater must learn to model the full distribution of preferences defined by a target population. In this paper, we propose a general framework for calibrating probabilistic autoraters to any given preference distribution. We formalize the problem and present two learning methods tailored to different data conditions: 1) a direct supervised fine-tuning for dense, probabilistic labels, and 2) a reinforcement learning approach for sparse, binary labels. Our empirical results show that finetuning autoraters with a distribution-matching objective leads to verbalized probability predictions that are better aligned with the target preference distribution, with improved calibration and significantly lower positional bias, all while preserving performance on objective tasks.

Knowledge distillation (KD) has been shown to be highly effective in guiding a student model with a larger teacher model and achieving practical benefits in improving the computational and memory efficiency for large language models (LLMs). State-of-the-art KD methods for LLMs mostly rely on minimizing explicit distribution distance between teacher and student probability predictions. Instead of optimizing these mandatory behaviour cloning objectives, we explore an imitation learning strategy for KD of LLMs. In particular, we minimize the imitation gap by matching the action-value moments of the teacher's behavior from both on- and off-policy perspectives. To achieve this action-value moment-matching goal, we propose an adversarial training algorithm to jointly estimate the moment-matching distance and optimize the student policy to minimize it. Results from both task-agnostic instruction-following experiments and task-specific experiments demonstrate the effectiveness of our method and achieve new state-of-the-art performance.

Machine learning models often experience performance degradation post-deployment due to shifts in data distribution. It is challenging to assess model's performance accurately when labels are missing or delayed. Existing proxy methods, such as drift detection, fail to measure the effects of these shifts adequately. To address this, we introduce a new method, Probabilistic Adaptive Performance Estimation (PAPE), for evaluating classification models on unlabeled data that accurately quantifies the impact of covariate shift on model performance. It is model and data-type agnostic and works for various performance metrics. Crucially, PAPE operates independently of the original model, relying only on its predictions and probability estimates, and does not need any assumptions about the nature of the covariate shift, learning directly from data instead. We tested PAPE on tabular data using over 900 dataset-model combinations created from US census data, assessing its performance against multiple benchmarks. Overall, PAPE provided more accurate performance estimates than other evaluated methodologies.

Research has shown that deep networks tend to be overly optimistic about their predictions, leading to an underestimation of prediction errors. Due to the limited nature of data, existing studies have proposed various methods based on model prediction probabilities to bin the data and evaluate calibration error. We propose a more generalized definition of calibration error called Partitioned Calibration Error (PCE), revealing that the key difference among these calibration error metrics lies in how the data space is partitioned. We put forth an intuitive proposition that an accurate model should be calibrated across any partition, suggesting that the input space partitioning can extend beyond just the partitioning of prediction probabilities, and include partitions directly related to the input. Through semantic-related partitioning functions, we demonstrate that the relationship between model accuracy and calibration lies in the granularity of the partitioning function. This highlights the importance of partitioning criteria for training a calibrated and accurate model. To validate the aforementioned analysis, we propose a method that involves jointly learning a semantic aware grouping function based on deep model features and logits to partition the data space into subsets. Subsequently, a separate calibration function is learned for each subset. Experimental results demonstrate that our approach achieves significant performance improvements across multiple datasets and network architectures, thus highlighting the importance of the partitioning function for calibration.

We present a state-of-the-art model for fine-grained probability estimation of propositions conditioned on context. Recent advances in large language models (LLMs) have significantly enhanced their reasoning capabilities, particularly on well-defined tasks with complete information. However, LLMs continue to struggle with making accurate and well-calibrated probabilistic predictions under uncertainty or partial information. While incorporating uncertainty into model predictions often boosts performance, obtaining reliable estimates of that uncertainty remains understudied. In particular, LLM probability estimates tend to be coarse and biased towards more frequent numbers. Through a combination of human and synthetic data creation and assessment, scaling to larger models, and better supervision, we propose a set of strong and precise probability estimation models. We conduct systematic evaluations across tasks that rely on conditional probability estimation and show that our approach consistently outperforms existing fine-tuned and prompting-based methods by a large margin.

This paper introduces the FinSen dataset that revolutionizes financial market analysis by integrating economic and financial news articles from 197 countries with stock market data. The dataset's extensive coverage spans 15 years from 2007 to 2023 with temporal information, offering a rich, global perspective with 160,000 records on financial market news. Our study leverages causally validated sentiment scores and LSTM models to enhance market forecast accuracy and reliability. Utilizing the FinSen dataset, we introduce an innovative Focal Calibration Loss, reducing Expected Calibration Error (ECE) to 3.34 percent with the DAN 3 model. This not only improves prediction accuracy but also aligns probabilistic forecasts closely with real outcomes, crucial for the financial sector where predicted probability is paramount. Our approach demonstrates the effectiveness of combining sentiment analysis with precise calibration techniques for trustworthy financial forecasting where the cost of misinterpretation can be high. Finsen Data can be found at [this github URL](https://github.com/EagleAdelaide/FinSen_Dataset.git).

The brain understands the external world through an internal model that generates predictions and refines them based on prediction errors. A complete prediction specifies what will happen, when it will happen, and with what probability, which we refer to as a "prediction object". Existing models typically capture only what and when, omit probabilities, and rely on biologically-implausible algorithms. Here we show that a single population of spiking neurons can jointly encode the prediction object through a biologically grounded learning mechanism. We implement a heterogeneous Izhikevich spiking reservoir with readouts trained by an error-modulated, attention-gated three-factor Hebbian rule and test it on a novel paradigm that controls both the timing and probability of upcoming stimuli. By integrating real-time learning of "when" with offline consolidation of "what", the model encodes the complete prediction object, firing at the correct times with magnitudes proportional to the probabilities. Critically, it rapidly adapts to changes in both stimulus timing and probability, an ability that global least-squares methods such as FORCE lack without explicit resets. During learning, the model self-organizes its readout weights into near-orthogonal subspaces for "what" and "when," showing that multiplexed encoding arises naturally from generic recurrent dynamics under local, error-gated modulation. These results challenge the view that "what" and "when" predictions require separate modules, suggesting instead that mixed selectivity within shared populations supports flexible predictive cognition. The model also predicts phase-specific neuromodulation and overlapping neural subspaces, offering a parsimonious alternative to hierarchical predictive-coding accounts.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various applications, fundamentally reshaping the landscape of natural language processing (NLP) research. However, recent evaluation frameworks often rely on the output probabilities of LLMs for predictions, primarily due to computational constraints, diverging from real-world LLM usage scenarios. While widely employed, the efficacy of these probability-based evaluation strategies remains an open research question. This study aims to scrutinize the validity of such probability-based evaluation methods within the context of using LLMs for Multiple Choice Questions (MCQs), highlighting their inherent limitations. Our empirical investigation reveals that the prevalent probability-based evaluation method inadequately aligns with generation-based prediction. Furthermore, current evaluation frameworks typically assess LLMs through predictive tasks based on output probabilities rather than directly generating responses, owing to computational limitations. We illustrate that these probability-based approaches do not effectively correspond with generative predictions. The outcomes of our study can enhance the understanding of LLM evaluation methodologies and provide insights for future research in this domain.

Compound Expression Recognition (CER), a subfield of affective computing, aims to detect complex emotional states formed by combinations of basic emotions. In this work, we present a novel zero-shot multimodal approach for CER that combines six heterogeneous modalities into a single pipeline: static and dynamic facial expressions, scene and label matching, scene context, audio, and text. Unlike previous approaches relying on task-specific training data, our approach uses zero-shot components, including Contrastive Language-Image Pretraining (CLIP)-based label matching and Qwen-VL for semantic scene understanding. We further introduce a Multi-Head Probability Fusion (MHPF) module that dynamically weights modality-specific predictions, followed by a Compound Expressions (CE) transformation module that uses Pair-Wise Probability Aggregation (PPA) and Pair-Wise Feature Similarity Aggregation (PFSA) methods to produce interpretable compound emotion outputs. Evaluated under multi-corpus training, the proposed approach shows F1 scores of 46.95% on AffWild2, 49.02% on Acted Facial Expressions in The Wild (AFEW), and 34.85% on C-EXPR-DB via zero-shot testing, which is comparable to the results of supervised approaches trained on target data. This demonstrates the effectiveness of the proposed approach for capturing CE without domain adaptation. The source code is publicly available.

Existing Score-Based Models (SBMs) can be categorized into constrained SBMs (CSBMs) or unconstrained SBMs (USBMs) according to their parameterization approaches. CSBMs model probability density functions as Boltzmann distributions, and assign their predictions as the negative gradients of some scalar-valued energy functions. On the other hand, USBMs employ flexible architectures capable of directly estimating scores without the need to explicitly model energy functions. In this paper, we demonstrate that the architectural constraints of CSBMs may limit their modeling ability. In addition, we show that USBMs' inability to preserve the property of conservativeness may lead to degraded performance in practice. To address the above issues, we propose Quasi-Conservative Score-Based Models (QCSBMs) for keeping the advantages of both CSBMs and USBMs. Our theoretical derivations demonstrate that the training objective of QCSBMs can be efficiently integrated into the training processes by leveraging the Hutchinson's trace estimator. In addition, our experimental results on the CIFAR-10, CIFAR-100, ImageNet, and SVHN datasets validate the effectiveness of QCSBMs. Finally, we justify the advantage of QCSBMs using an example of a one-layered autoencoder.

This paper introduces the counter-intuitive generalization results of overfitting pre-trained large language models (LLMs) on very small datasets. In the setting of open-ended text generation, it is well-documented that LLMs tend to generate repetitive and dull sequences, a phenomenon that is especially apparent when generating using greedy decoding. This issue persists even with state-of-the-art LLMs containing billions of parameters, trained via next-token prediction on large datasets. We find that by further fine-tuning these models to achieve a near-zero training loss on a small set of samples -- a process we refer to as hyperfitting -- the long-sequence generative capabilities are greatly enhanced. Greedy decoding with these Hyperfitted models even outperform Top-P sampling over long-sequences, both in terms of diversity and human preferences. This phenomenon extends to LLMs of various sizes, different domains, and even autoregressive image generation. We further find this phenomena to be distinctly different from that of Grokking and double descent. Surprisingly, our experiments indicate that hyperfitted models rarely fall into repeating sequences they were trained on, and even explicitly blocking these sequences results in high-quality output. All hyperfitted models produce extremely low-entropy predictions, often allocating nearly all probability to a single token.

The widespread adoption of large language models (LLMs) makes it important to recognize their strengths and limitations. We argue that in order to develop a holistic understanding of these systems we need to consider the problem that they were trained to solve: next-word prediction over Internet text. By recognizing the pressures that this task exerts we can make predictions about the strategies that LLMs will adopt, allowing us to reason about when they will succeed or fail. This approach - which we call the teleological approach - leads us to identify three factors that we hypothesize will influence LLM accuracy: the probability of the task to be performed, the probability of the target output, and the probability of the provided input. We predict that LLMs will achieve higher accuracy when these probabilities are high than when they are low - even in deterministic settings where probability should not matter. To test our predictions, we evaluate two LLMs (GPT-3.5 and GPT-4) on eleven tasks, and we find robust evidence that LLMs are influenced by probability in the ways that we have hypothesized. In many cases, the experiments reveal surprising failure modes. For instance, GPT-4's accuracy at decoding a simple cipher is 51% when the output is a high-probability word sequence but only 13% when it is low-probability. These results show that AI practitioners should be careful about using LLMs in low-probability situations. More broadly, we conclude that we should not evaluate LLMs as if they are humans but should instead treat them as a distinct type of system - one that has been shaped by its own particular set of pressures.

Motivation: Ab initio protein docking represents a major challenge for optimizing a noisy and costly "black box"-like function in a high-dimensional space. Despite progress in this field, there is no docking method available for rigorous uncertainty quantification (UQ) of its solution quality (e.g. interface RMSD or iRMSD). Results: We introduce a novel algorithm, Bayesian Active Learning (BAL), for optimization and UQ of such black-box functions and flexible protein docking. BAL directly models the posterior distribution of the global optimum (or native structures for protein docking) with active sampling and posterior estimation iteratively feeding each other. Furthermore, we use complex normal modes to represent a homogeneous Euclidean conformation space suitable for high-dimension optimization and construct funnel-like energy models for encounter complexes. Over a protein docking benchmark set and a CAPRI set including homology docking, we establish that BAL significantly improve against both starting points by rigid docking and refinements by particle swarm optimization, providing for one third targets a top-3 near-native prediction. BAL also generates tight confidence intervals with half range around 25% of iRMSD and confidence level at 85%. Its estimated probability of a prediction being native or not achieves binary classification AUROC at 0.93 and AUPRC over 0.60 (compared to 0.14 by chance); and also found to help ranking predictions. To the best of our knowledge, this study represents the first uncertainty quantification solution for protein docking, with theoretical rigor and comprehensive assessment. Source codes are available at https://github.com/Shen-Lab/BAL.

Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of task-agnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (predict). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (refine). Notably, the generative performance of the model remains intact -- downstream forecasters trained on synthetic samples from TSDiff outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (synthesize).

It is well known that accurate probabilistic predictors can be trained through empirical risk minimisation with proper scoring rules as loss functions. While such learners capture so-called aleatoric uncertainty of predictions, various machine learning methods have recently been developed with the goal to let the learner also represent its epistemic uncertainty, i.e., the uncertainty caused by a lack of knowledge and data. An emerging branch of the literature proposes the use of a second-order learner that provides predictions in terms of distributions on probability distributions. However, recent work has revealed serious theoretical shortcomings for second-order predictors based on loss minimisation. In this paper, we generalise these findings and prove a more fundamental result: There seems to be no loss function that provides an incentive for a second-order learner to faithfully represent its epistemic uncertainty in the same manner as proper scoring rules do for standard (first-order) learners. As a main mathematical tool to prove this result, we introduce the generalised notion of second-order scoring rules.

The Guzheng is a kind of traditional Chinese instruments with diverse playing techniques. Instrument playing techniques (IPT) play an important role in musical performance. However, most of the existing works for IPT detection show low efficiency for variable-length audio and provide no assurance in the generalization as they rely on a single sound bank for training and testing. In this study, we propose an end-to-end Guzheng playing technique detection system using Fully Convolutional Networks that can be applied to variable-length audio. Because each Guzheng playing technique is applied to a note, a dedicated onset detector is trained to divide an audio into several notes and its predictions are fused with frame-wise IPT predictions. During fusion, we add the IPT predictions frame by frame inside each note and get the IPT with the highest probability within each note as the final output of that note. We create a new dataset named GZ_IsoTech from multiple sound banks and real-world recordings for Guzheng performance analysis. Our approach achieves 87.97% in frame-level accuracy and 80.76% in note-level F1-score, outperforming existing works by a large margin, which indicates the effectiveness of our proposed method in IPT detection.

Knowledge distillation (KD) is a widely used framework for training compact, task-specific models by leveraging the knowledge of teacher models. However, its application to active learning (AL), which aims to minimize annotation costs through iterative sample selection, remains underexplored. This gap stems from the fact that KD typically assumes access to sufficient labeled data, whereas AL operates in data-scarce scenarios where task-specific teacher models are often unavailable. In this paper, we introduce ActiveKD, a framework that integrates AL with KD by leveraging the zero- and few-shot capabilities of large vision-language models (VLMs). A key aspect of ActiveKD is the structured prediction bias of VLMs -- i.e., their predictions form clusters in the probability space. We regard this structure as an inductive bias of the teacher model, capturing generalizable output patterns beneficial to student learning. To exploit this bias, we propose Probabilistic CoreSet (PCoreSet), a selection strategy that maximizes coverage in the probability space rather than the feature space. PCoreSet strategically selects categorically diverse unlabeled samples, facilitating more efficient transfer of teacher knowledge under limited annotation budgets. Evaluations on 11 datasets show that PCoreSet consistently outperforms existing selection methods within the ActiveKD framework, advancing research at the intersection of AL and KD.

Continuous-time generative models, such as diffusion models, flow matching, and rectified flow, learn time-dependent vector fields but are typically trained with objectives that treat timesteps independently, leading to high estimator variance and inefficient sampling. Prior approaches mitigate this via explicit smoothness penalties, trajectory regularization, or modified probability paths and solvers. We introduce Temporal Pair Consistency (TPC), a lightweight variance-reduction principle that couples velocity predictions at paired timesteps along the same probability path, operating entirely at the estimator level without modifying the model architecture, probability path, or solver. We provide a theoretical analysis showing that TPC induces a quadratic, trajectory-coupled regularization that provably reduces gradient variance while preserving the underlying flow-matching objective. Instantiated within flow matching, TPC improves sample quality and efficiency across CIFAR-10 and ImageNet at multiple resolutions, achieving lower FID at identical or lower computational cost than prior methods, and extends seamlessly to modern SOTA-style pipelines with noise-augmented training, score-based denoising, and rectified flow.

Language models produce a distribution over the next token; can we use this information to recover the prompt tokens? We consider the problem of language model inversion and show that next-token probabilities contain a surprising amount of information about the preceding text. Often we can recover the text in cases where it is hidden from the user, motivating a method for recovering unknown prompts given only the model's current distribution output. We consider a variety of model access scenarios, and show how even without predictions for every token in the vocabulary we can recover the probability vector through search. On Llama-2 7b, our inversion method reconstructs prompts with a BLEU of 59 and token-level F1 of 78 and recovers 27% of prompts exactly. Code for reproducing all experiments is available at http://github.com/jxmorris12/vec2text.

Running large-scale pre-trained language models in computationally constrained environments remains a challenging problem yet to be addressed, while transfer learning from these models has become prevalent in Natural Language Processing tasks. Several solutions, including knowledge distillation, network quantization, or network pruning have been previously proposed; however, these approaches focus mostly on the English language, thus widening the gap when considering low-resource languages. In this work, we introduce three light and fast versions of distilled BERT models for the Romanian language: Distil-BERT-base-ro, Distil-RoBERT-base, and DistilMulti-BERT-base-ro. The first two models resulted from the individual distillation of knowledge from two base versions of Romanian BERTs available in literature, while the last one was obtained by distilling their ensemble. To our knowledge, this is the first attempt to create publicly available Romanian distilled BERT models, which were thoroughly evaluated on five tasks: part-of-speech tagging, named entity recognition, sentiment analysis, semantic textual similarity, and dialect identification. Our experimental results argue that the three distilled models offer performance comparable to their teachers, while being twice as fast on a GPU and ~35% smaller. In addition, we further test the similarity between the predictions of our students versus their teachers by measuring their label and probability loyalty, together with regression loyalty - a new metric introduced in this work.

Split conformal prediction has recently sparked great interest due to its ability to provide formally guaranteed uncertainty sets or intervals for predictions made by black-box neural models, ensuring a predefined probability of containing the actual ground truth. While the original formulation assumes data exchangeability, some extensions handle non-exchangeable data, which is often the case in many real-world scenarios. In parallel, some progress has been made in conformal methods that provide statistical guarantees for a broader range of objectives, such as bounding the best F_1-score or minimizing the false negative rate in expectation. In this paper, we leverage and extend these two lines of work by proposing non-exchangeable conformal risk control, which allows controlling the expected value of any monotone loss function when the data is not exchangeable. Our framework is flexible, makes very few assumptions, and allows weighting the data based on its relevance for a given test example; a careful choice of weights may result on tighter bounds, making our framework useful in the presence of change points, time series, or other forms of distribution drift. Experiments with both synthetic and real world data show the usefulness of our method.

Generalized zero-shot learning (GZSL) is the problem of learning a classifier where some classes have samples and others are learned from side information, like semantic attributes or text description, in a zero-shot learning fashion (ZSL). Training a single model that operates in these two regimes simultaneously is challenging. Here we describe a probabilistic approach that breaks the model into three modular components, and then combines them in a consistent way. Specifically, our model consists of three classifiers: A "gating" model that makes soft decisions if a sample is from a "seen" class, and two experts: a ZSL expert, and an expert model for seen classes. We address two main difficulties in this approach: How to provide an accurate estimate of the gating probability without any training samples for unseen classes; and how to use expert predictions when it observes samples outside of its domain. The key insight to our approach is to pass information between the three models to improve each one's accuracy, while maintaining the modular structure. We test our approach, adaptive confidence smoothing (COSMO), on four standard GZSL benchmark datasets and find that it largely outperforms state-of-the-art GZSL models. COSMO is also the first model that closes the gap and surpasses the performance of generative models for GZSL, even-though it is a light-weight model that is much easier to train and tune. Notably, COSMO offers a new view for developing zero-shot models. Thanks to COSMO's modular structure, instead of trying to perform well both on seen and on unseen classes, models can focus on accurate classification of unseen classes, and later consider seen class models.

Recent work analyzing in-context learning (ICL) has identified a broad set of strategies that describe model behavior in different experimental conditions. We aim to unify these findings by asking why a model learns these disparate strategies in the first place. Specifically, we start with the observation that when trained to learn a mixture of tasks, as is popular in the literature, the strategies learned by a model for performing ICL can be captured by a family of Bayesian predictors: a memorizing predictor, which assumes a discrete prior on the set of seen tasks, and a generalizing predictor, where the prior matches the underlying task distribution. Adopting the normative lens of rational analysis, where a learner's behavior is explained as an optimal adaptation to data given computational constraints, we develop a hierarchical Bayesian framework that almost perfectly predicts Transformer next-token predictions throughout training -- without assuming access to its weights. Under this framework, pretraining is viewed as a process of updating the posterior probability of different strategies, and inference-time behavior as a posterior-weighted average over these strategies' predictions. Our framework draws on common assumptions about neural network learning dynamics, which make explicit a tradeoff between loss and complexity among candidate strategies: beyond how well it explains the data, a model's preference towards implementing a strategy is dictated by its complexity. This helps explain well-known ICL phenomena, while offering novel predictions: e.g., we show a superlinear trend in the timescale for transitioning from generalization to memorization as task diversity increases. Overall, our work advances an explanatory and predictive account of ICL grounded in tradeoffs between strategy loss and complexity.

Large Language Models are known to capture real-world knowledge, allowing them to excel in many downstream tasks. Despite recent advances, these models are still prone to what are commonly known as hallucinations, causing them to emit unwanted and factually incorrect text. In this work, we propose a novel calibration method that can be used to combat hallucinations. We add a special [IDK] ("I don't know") token to the model's vocabulary and introduce an objective function that shifts probability mass to the [IDK] token for incorrect predictions. This approach allows the model to express uncertainty in its output explicitly. We evaluate our proposed method across multiple model architectures and factual downstream tasks. We find that models trained with our method are able to express uncertainty in places where they would previously make mistakes while suffering only a small loss of encoded knowledge. We further perform extensive ablation studies of multiple variations of our approach and provide a detailed analysis of the precision-recall tradeoff of our method.

Feature attribution methods (FAs), such as gradients and attention, are widely employed approaches to derive the importance of all input features to the model predictions. Existing work in natural language processing has mostly focused on developing and testing FAs for encoder-only language models (LMs) in classification tasks. However, it is unknown if it is faithful to use these FAs for decoder-only models on text generation, due to the inherent differences between model architectures and task settings respectively. Moreover, previous work has demonstrated that there is no `one-wins-all' FA across models and tasks. This makes the selection of a FA computationally expensive for large LMs since input importance derivation often requires multiple forward and backward passes including gradient computations that might be prohibitive even with access to large compute. To address these issues, we present a model-agnostic FA for generative LMs called Recursive Attribution Generator (ReAGent). Our method updates the token importance distribution in a recursive manner. For each update, we compute the difference in the probability distribution over the vocabulary for predicting the next token between using the original input and using a modified version where a part of the input is replaced with RoBERTa predictions. Our intuition is that replacing an important token in the context should have resulted in a larger change in the model's confidence in predicting the token than replacing an unimportant token. Our method can be universally applied to any generative LM without accessing internal model weights or additional training and fine-tuning, as most other FAs require. We extensively compare the faithfulness of ReAGent with seven popular FAs across six decoder-only LMs of various sizes. The results show that our method consistently provides more faithful token importance distributions.

Large language models (LLMs) have shown remarkable capabilities in various natural language understanding tasks. With only a few demonstration examples, these LLMs can quickly adapt to target tasks without expensive gradient updates. Common strategies to boost such 'in-context' learning ability are to ensemble multiple model decoded results and require the model to generate an explanation along with the prediction. However, these models often treat different class predictions equally and neglect the potential discrepancy between the explanations and predictions. To fully unleash the power of explanations, we propose EASE, an Explanation-Aware Soft Ensemble framework to empower in-context learning with LLMs. We design two techniques, explanation-guided ensemble, and soft probability aggregation, to mitigate the effect of unreliable explanations and improve the consistency between explanations and final predictions. Experiments on seven natural language understanding tasks and four varying-size LLMs demonstrate the effectiveness of our proposed framework.

We present Nacrith, a lossless compression system that combines a 135M-parameter transformer language model (SmolLM2-135M) with an ensemble of lightweight online predictors and a 32-bit arithmetic coder. Beyond the base LLM-plus-arithmetic-coding paradigm, Nacrith introduces several contributions: (1) a CDF precision upgrade from 2^16 to 2^24 that eliminates ~75% of quantization overhead caused by minimum-probability floors in large vocabularies; (2) a token-level N-gram model for fast local predictions; (3) an adaptive log-space bias head correcting per-document LLM errors via online gradient descent; (4) confidence-based LLM skip for accelerating highly predictable tokens; (5) a hybrid binary format (NC06) extending neural compression to arbitrary binary files--to our knowledge a first among LLM-based compressors; (6) a llama.cpp inference backend achieving ~7x faster single-token decode than PyTorch; (7) parallel multi-GPU compression across up to 8 workers; and (8) native KV cache sliding window reducing per-slide cost by ~37x. The system requires only ~500 MB of GGUF weights and ~1.2 GB VRAM per worker, running on consumer GPUs. On alice29.txt (Canterbury Corpus, 152 KB), Nacrith achieves 0.918 bits per byte (bpb)--outperforming gzip by 3.1x, bzip2 by 2.5x, CMIX v21 by 44%, and ts_zip by 20%, while compressing below the 0th-, 1st-, and 2nd-order byte-level Shannon entropy bounds. On enwik8 (100 MB), Nacrith achieves 0.9389 bpb (11.74%), surpassing ts_zip (~1.11 bpb) by 15% and FineZip (1.024 bpb) by 8% despite using a 60x smaller model with no fine-tuning. An out-of-distribution evaluation on a document published after the model's training cutoff confirms these gains are not memorization artifacts, achieving 0.723 bpb on unseen text.

The identification of bitter peptides is crucial in various domains, including food science, drug discovery, and biochemical research. These peptides not only contribute to the undesirable taste of hydrolyzed proteins but also play key roles in physiological and pharmacological processes. However, experimental methods for identifying bitter peptides are time-consuming and expensive. With the rapid expansion of peptide sequence databases in the post-genomic era, the demand for efficient computational approaches to distinguish bitter from non-bitter peptides has become increasingly significant. In this study, we propose a novel stacking-based ensemble learning framework aimed at enhancing the accuracy and reliability of bitter peptide classification. Our method integrates diverse sequence-based feature representations and leverages a broad set of machine learning classifiers. The first stacking layer comprises multiple base classifiers, each trained on distinct feature encoding schemes, while the second layer employs logistic regression to refine predictions using an eight-dimensional probability vector. Extensive evaluations on a carefully curated dataset demonstrate that our model significantly outperforms existing predictive methods, providing a robust and reliable computational tool for bitter peptide identification. Our approach achieves an accuracy of 96.09\% and a Matthews Correlation Coefficient (MCC) of 0.9220 on the independent test set, underscoring its effectiveness and generalizability. To facilitate real-time usage and broader accessibility, we have also developed a user-friendly web server based on the proposed method, which is freely accessible at https://ibitter-stack-webserver.streamlit.app/. This tool enables researchers and practitioners to conveniently screen peptide sequences for bitterness in real-time applications.

Uncertainty quantification has received increasing attention in machine learning in the recent past. In particular, a distinction between aleatoric and epistemic uncertainty has been found useful in this regard. The latter refers to the learner's (lack of) knowledge and appears to be especially difficult to measure and quantify. In this paper, we analyse a recent proposal based on the idea of a second-order learner, which yields predictions in the form of distributions over probability distributions. While standard (first-order) learners can be trained to predict accurate probabilities, namely by minimising suitable loss functions on sample data, we show that loss minimisation does not work for second-order predictors: The loss functions proposed for inducing such predictors do not incentivise the learner to represent its epistemic uncertainty in a faithful way.

To demystify the "black box" property of deep neural networks for natural language processing (NLP), several methods have been proposed to interpret their predictions by measuring the change in prediction probability after erasing each token of an input. Since existing methods replace each token with a predefined value (i.e., zero), the resulting sentence lies out of the training data distribution, yielding misleading interpretations. In this study, we raise the out-of-distribution problem induced by the existing interpretation methods and present a remedy; we propose to marginalize each token out. We interpret various NLP models trained for sentiment analysis and natural language inference using the proposed method.

In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order probability distributions, i.e., predictions in the form of distributions on probability distributions. A completely conclusive solution has not yet been found, however, as shown by recent criticisms of commonly used uncertainty measures associated with second-order distributions, identifying undesirable theoretical properties of these measures. In light of these criticisms, we propose a set of formal criteria that meaningful uncertainty measures for predictive uncertainty based on second-order distributions should obey. Moreover, we provide a general framework for developing uncertainty measures to account for these criteria, and offer an instantiation based on the Wasserstein distance, for which we prove that all criteria are satisfied.

Proteins perform nearly all cellular functions and constitute most drug targets, making their analysis fundamental to understanding human biology in health and disease. Tandem mass spectrometry (MS^2) is the major analytical technique in proteomics that identifies peptides by ionizing them, fragmenting them, and using the resulting mass spectra to identify and quantify proteins in biological samples. In MS^2 analysis, peptide fragment ion probability prediction plays a critical role, enhancing the accuracy of peptide identification from mass spectra as a complement to the intensity information. Current approaches rely on global statistics of fragmentation, which assumes that a fragment's probability is uniform across all peptides. Nevertheless, this assumption is oversimplified from a biochemical principle point of view and limits accurate prediction. To address this gap, we present Pep2Prob, the first comprehensive dataset and benchmark designed for peptide-specific fragment ion probability prediction. The proposed dataset contains fragment ion probability statistics for 608,780 unique precursors (each precursor is a pair of peptide sequence and charge state), summarized from more than 183 million high-quality, high-resolution, HCD MS^2 spectra with validated peptide assignments and fragmentation annotations. We establish baseline performance using simple statistical rules and learning-based methods, and find that models leveraging peptide-specific information significantly outperform previous methods using only global fragmentation statistics. Furthermore, performance across benchmark models with increasing capacities suggests that the peptide-fragmentation relationship exhibits complex nonlinearities requiring sophisticated machine learning approaches.

Self-supervised pre-training of language models usually consists in predicting probability distributions over extensive token vocabularies. In this study, we propose an innovative method that shifts away from probability prediction and instead focuses on reconstructing input embeddings in a contrastive fashion via Constrastive Weight Tying (CWT). We apply this approach to pretrain Headless Language Models in both monolingual and multilingual contexts. Our method offers practical advantages, substantially reducing training computational requirements by up to 20 times, while simultaneously enhancing downstream performance and data efficiency. We observe a significant +1.6 GLUE score increase and a notable +2.7 LAMBADA accuracy improvement compared to classical LMs within similar compute budgets.

Accurate and reliable energy time series prediction is of great significance for power generation planning and allocation. At present, deep learning time series prediction has become the mainstream method. However, the multi-scale time dynamics and the irregularity of real data lead to the limitations of the existing methods. Therefore, we propose EnergyPatchTST, which is an extension of the Patch Time Series Transformer specially designed for energy forecasting. The main innovations of our method are as follows: (1) multi-scale feature extraction mechanism to capture patterns with different time resolutions; (2) probability prediction framework to estimate uncertainty through Monte Carlo elimination; (3) integration path of future known variables (such as temperature and wind conditions); And (4) Pre-training and Fine-tuning examples to enhance the performance of limited energy data sets. A series of experiments on common energy data sets show that EnergyPatchTST is superior to other commonly used methods, the prediction error is reduced by 7-12%, and reliable uncertainty estimation is provided, which provides an important reference for time series prediction in the energy field.

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or whether a patient has died or not), because the ground-truth probabilities of the events of interest are typically unknown. The problem is therefore analogous to binary classification, with the difference that the objective is to estimate probabilities rather than predicting the specific outcome. This work investigates probability estimation from high-dimensional data using deep neural networks. There exist several methods to improve the probabilities generated by these models but they mostly focus on model (epistemic) uncertainty. For problems with inherent uncertainty, it is challenging to evaluate performance without access to ground-truth probabilities. To address this, we build a synthetic dataset to study and compare different computable metrics. We evaluate existing methods on the synthetic data as well as on three real-world probability estimation tasks, all of which involve inherent uncertainty: precipitation forecasting from radar images, predicting cancer patient survival from histopathology images, and predicting car crashes from dashcam videos. We also give a theoretical analysis of a model for high-dimensional probability estimation which reproduces several of the phenomena evinced in our experiments. Finally, we propose a new method for probability estimation using neural networks, which modifies the training process to promote output probabilities that are consistent with empirical probabilities computed from the data. The method outperforms existing approaches on most metrics on the simulated as well as real-world data.

Supervised Fine-Tuning (SFT) is the standard paradigm for domain adaptation, yet it frequently incurs the cost of catastrophic forgetting. In sharp contrast, on-policy Reinforcement Learning (RL) effectively preserves general capabilities. We investigate this discrepancy and identify a fundamental distributional gap: while RL aligns with the model's internal belief, SFT forces the model to fit external supervision. This mismatch often manifests as "Confident Conflicts" tokens characterized by low probability but low entropy. In these instances, the model is highly confident in its own prediction but is forced to learn a divergent ground truth, triggering destructive gradient updates. To address this, we propose Entropy-Adaptive Fine-Tuning (EAFT). Unlike methods relying solely on prediction probability, EAFT utilizes token-level entropy as a gating mechanism to distinguish between epistemic uncertainty and knowledge conflict. This allows the model to learn from uncertain samples while suppressing gradients on conflicting data. Extensive experiments on Qwen and GLM series (ranging from 4B to 32B parameters) across mathematical, medical, and agentic domains confirm our hypothesis. EAFT consistently matches the downstream performance of standard SFT while significantly mitigating the degradation of general capabilities.

High-stakes decision making involves reasoning under uncertainty about the future. In this work, we train language models to make predictions on open-ended forecasting questions. To scale up training data, we synthesize novel forecasting questions from global events reported in daily news, using a fully automated, careful curation recipe. We train the Qwen3 thinking models on our dataset, OpenForesight. To prevent leakage of future information during training and evaluation, we use an offline news corpus, both for data generation and retrieval in our forecasting system. Guided by a small validation set, we show the benefits of retrieval, and an improved reward function for reinforcement learning (RL). Once we obtain our final forecasting system, we perform held-out testing between May to August 2025. Our specialized model, OpenForecaster 8B, matches much larger proprietary models, with our training improving the accuracy, calibration, and consistency of predictions. We find calibration improvements from forecasting training generalize across popular benchmarks. We open-source all our models, code, and data to make research on language model forecasting broadly accessible.

Accurately predicting the future would be an important milestone in the capabilities of artificial intelligence. However, research on the ability of large language models to provide probabilistic predictions about future events remains nascent. To empirically test this ability, we enrolled OpenAI's state-of-the-art large language model, GPT-4, in a three-month forecasting tournament hosted on the Metaculus platform. The tournament, running from July to October 2023, attracted 843 participants and covered diverse topics including Big Tech, U.S. politics, viral outbreaks, and the Ukraine conflict. Focusing on binary forecasts, we show that GPT-4's probabilistic forecasts are significantly less accurate than the median human-crowd forecasts. We find that GPT-4's forecasts did not significantly differ from the no-information forecasting strategy of assigning a 50% probability to every question. We explore a potential explanation, that GPT-4 might be predisposed to predict probabilities close to the midpoint of the scale, but our data do not support this hypothesis. Overall, we find that GPT-4 significantly underperforms in real-world predictive tasks compared to median human-crowd forecasts. A potential explanation for this underperformance is that in real-world forecasting tournaments, the true answers are genuinely unknown at the time of prediction; unlike in other benchmark tasks like professional exams or time series forecasting, where strong performance may at least partly be due to the answers being memorized from the training data. This makes real-world forecasting tournaments an ideal environment for testing the generalized reasoning and prediction capabilities of artificial intelligence going forward.

Words of estimative probability (WEP) are expressions of a statement's plausibility (probably, maybe, likely, doubt, likely, unlikely, impossible...). Multiple surveys demonstrate the agreement of human evaluators when assigning numerical probability levels to WEP. For example, highly likely corresponds to a median chance of 0.90+-0.08 in Fagen-Ulmschneider (2015)'s survey. In this work, we measure the ability of neural language processing models to capture the consensual probability level associated to each WEP. Firstly, we use the UNLI dataset (Chen et al., 2020) which associates premises and hypotheses with their perceived joint probability p, to construct prompts, e.g. "[PREMISE]. [WEP], [HYPOTHESIS]." and assess whether language models can predict whether the WEP consensual probability level is close to p. Secondly, we construct a dataset of WEP-based probabilistic reasoning, to test whether language models can reason with WEP compositions. When prompted "[EVENTA] is likely. [EVENTB] is impossible.", a causal language model should not express that [EVENTA&B] is likely. We show that both tasks are unsolved by off-the-shelf English language models, but that fine-tuning leads to transferable improvement.

We study whether language models can evaluate the validity of their own claims and predict which questions they will be able to answer correctly. We first show that larger models are well-calibrated on diverse multiple choice and true/false questions when they are provided in the right format. Thus we can approach self-evaluation on open-ended sampling tasks by asking models to first propose answers, and then to evaluate the probability "P(True)" that their answers are correct. We find encouraging performance, calibration, and scaling for P(True) on a diverse array of tasks. Performance at self-evaluation further improves when we allow models to consider many of their own samples before predicting the validity of one specific possibility. Next, we investigate whether models can be trained to predict "P(IK)", the probability that "I know" the answer to a question, without reference to any particular proposed answer. Models perform well at predicting P(IK) and partially generalize across tasks, though they struggle with calibration of P(IK) on new tasks. The predicted P(IK) probabilities also increase appropriately in the presence of relevant source materials in the context, and in the presence of hints towards the solution of mathematical word problems. We hope these observations lay the groundwork for training more honest models, and for investigating how honesty generalizes to cases where models are trained on objectives other than the imitation of human writing.

Planning safe robot motions in the presence of humans requires reliable forecasts of future human motion. However, simply predicting the most likely motion from prior interactions does not guarantee safety. Such forecasts fail to model the long tail of possible events, which are rarely observed in limited datasets. On the other hand, planning for worst-case motions leads to overtly conservative behavior and a "frozen robot". Instead, we aim to learn forecasts that predict counterfactuals that humans guard against. We propose a novel game-theoretic framework for joint planning and forecasting with the payoff being the performance of the planner against the demonstrator, and present practical algorithms to train models in an end-to-end fashion. We demonstrate that our proposed algorithm results in safer plans in a crowd navigation simulator and real-world datasets of pedestrian motion. We release our code at https://github.com/portal-cornell/Game-Theoretic-Forecasting-Planning.

Forecasting is an important task in many domains, such as technology and economics. However existing forecasting benchmarks largely lack comprehensive confidence assessment, focus on limited question types, and often consist of artificial questions that do not align with real-world human forecasting needs. To address these gaps, we introduce FOReCAst (Future Outcome Reasoning and Confidence Assessment), a benchmark that evaluates models' ability to make predictions and their confidence in them. FOReCAst spans diverse forecasting scenarios involving Boolean questions, timeframe prediction, and quantity estimation, enabling a comprehensive evaluation of both prediction accuracy and confidence calibration for real-world applications.

Predictive models often need to work with incomplete information in real-world tasks. Consequently, they must provide reliable probability or confidence estimation, especially in large-scale decision-making and planning tasks. Current large language models (LLMs) are insufficient for accurate estimations, but they can generate relevant factors that may affect the probabilities, produce coarse-grained probabilities when the information is more complete, and help determine which factors are relevant to specific downstream contexts. In this paper, we make use of these capabilities of LLMs to provide a significantly more accurate probabilistic estimation. We propose BIRD, a novel probabilistic inference framework that aligns a Bayesian network with LLM abductions and then estimates more accurate probabilities in a deduction step. We show BIRD provides reliable probability estimations that are 30% better than those provided directly by LLM baselines. These estimates further contribute to better and more trustworthy decision making.

In light of recent work on scheduling with predicted job sizes, we consider the effect of the cost of predictions in queueing systems, removing the assumption in prior research that predictions are external to the system's resources and/or cost-free. In particular, we introduce a novel approach to utilizing predictions, SkipPredict, designed to address their inherent cost. Rather than uniformly applying predictions to all jobs, we propose a tailored approach that categorizes jobs based on their prediction requirements. To achieve this, we employ one-bit "cheap predictions" to classify jobs as either short or long. SkipPredict prioritizes predicted short jobs over long jobs, and for the latter, SkipPredict applies a second round of more detailed "expensive predictions" to approximate Shortest Remaining Processing Time for these jobs. Our analysis takes into account the cost of prediction. We examine the effect of this cost for two distinct models. In the external cost model, predictions are generated by some external method without impacting job service times but incur a cost. In the server time cost model, predictions themselves require server processing time, and are scheduled on the same server as the jobs.

Language models (LM) are capable of remarkably complex linguistic tasks; however, numerical reasoning is an area in which they frequently struggle. An important but rarely evaluated form of reasoning is understanding probability distributions. In this paper, we focus on evaluating the probabilistic reasoning capabilities of LMs using idealized and real-world statistical distributions. We perform a systematic evaluation of state-of-the-art LMs on three tasks: estimating percentiles, drawing samples, and calculating probabilities. We evaluate three ways to provide context to LMs 1) anchoring examples from within a distribution or family of distributions, 2) real-world context, 3) summary statistics on which to base a Normal approximation. Models can make inferences about distributions, and can be further aided by the incorporation of real-world context, example shots and simplified assumptions, even if these assumptions are incorrect or misspecified. To conduct this work, we developed a comprehensive benchmark distribution dataset with associated question-answer pairs that we will release publicly.

A Neural Process (NP) estimates a stochastic process implicitly defined with neural networks given a stream of data, rather than pre-specifying priors already known, such as Gaussian processes. An ideal NP would learn everything from data without any inductive biases, but in practice, we often restrict the class of stochastic processes for the ease of estimation. One such restriction is the use of a finite-dimensional latent variable accounting for the uncertainty in the functions drawn from NPs. Some recent works show that this can be improved with more "data-driven" source of uncertainty such as bootstrapping. In this work, we take a different approach based on the martingale posterior, a recently developed alternative to Bayesian inference. For the martingale posterior, instead of specifying prior-likelihood pairs, a predictive distribution for future data is specified. Under specific conditions on the predictive distribution, it can be shown that the uncertainty in the generated future data actually corresponds to the uncertainty of the implicitly defined Bayesian posteriors. Based on this result, instead of assuming any form of the latent variables, we equip a NP with a predictive distribution implicitly defined with neural networks and use the corresponding martingale posteriors as the source of uncertainty. The resulting model, which we name as Martingale Posterior Neural Process (MPNP), is demonstrated to outperform baselines on various tasks.

Modeling semantic plausibility requires commonsense knowledge about the world and has been used as a testbed for exploring various knowledge representations. Previous work has focused specifically on modeling physical plausibility and shown that distributional methods fail when tested in a supervised setting. At the same time, distributional models, namely large pretrained language models, have led to improved results for many natural language understanding tasks. In this work, we show that these pretrained language models are in fact effective at modeling physical plausibility in the supervised setting. We therefore present the more difficult problem of learning to model physical plausibility directly from text. We create a training set by extracting attested events from a large corpus, and we provide a baseline for training on these attested events in a self-supervised manner and testing on a physical plausibility task. We believe results could be further improved by injecting explicit commonsense knowledge into a distributional model.

Predicting the future is of great interest across many aspects of human activity. Businesses are interested in future trends, traders are interested in future stock prices, and companies are highly interested in future technological breakthroughs. While there are many automated systems for predicting future numerical data, such as weather, stock prices, and demand for products, there is relatively little work in automatically predicting textual data. Humans are interested in textual data predictions because it is a natural format for our consumption, and experts routinely make predictions in a textual format (Christensen et al., 2004; Tetlock & Gardner, 2015; Frick, 2015). However, there has been relatively little formalization of this general problem in the machine learning or natural language processing communities. To address this gap, we introduce the task of future language modeling: probabilistic modeling of texts in the future based on a temporal history of texts. To our knowledge, our work is the first work to formalize the task of predicting the future in this way. We show that it is indeed possible to build future language models that improve upon strong non-temporal language model baselines, opening the door to working on this important, and widely applicable problem.

In this paper, we tackle the important yet under-investigated problem of making long-horizon prediction of event sequences. Existing state-of-the-art models do not perform well at this task due to their autoregressive structure. We propose HYPRO, a hybridly normalized probabilistic model that naturally fits this task: its first part is an autoregressive base model that learns to propose predictions; its second part is an energy function that learns to reweight the proposals such that more realistic predictions end up with higher probabilities. We also propose efficient training and inference algorithms for this model. Experiments on multiple real-world datasets demonstrate that our proposed HYPRO model can significantly outperform previous models at making long-horizon predictions of future events. We also conduct a range of ablation studies to investigate the effectiveness of each component of our proposed methods.

Bayesian inference provides principled uncertainty quantification but is often limited by challenges of prior elicitation, likelihood misspecification, and computational burden. The martingale posterior (MGP, Fong et al., 2023) offers an alternative, replacing prior-likelihood elicitation with a predictive rule - namely, a sequence of one-step-ahead predictive distributions - for forward data generation. The utility of MGPs depends on the choice of predictive rule, yet the literature has offered few compelling examples. Foundation transformers are well-suited here, as their autoregressive generation mirrors this forward simulation and their general-purpose design enables rich predictive modeling. We introduce TabMGP, an MGP built on TabPFN, a transformer foundation model that is currently state-of-the-art for tabular data. TabMGP produces credible sets with near-nominal coverage and often outperforms both existing MGP constructions and standard Bayes.

We show that a GPT-3 model can learn to express uncertainty about its own answers in natural language -- without use of model logits. When given a question, the model generates both an answer and a level of confidence (e.g. "90% confidence" or "high confidence"). These levels map to probabilities that are well calibrated. The model also remains moderately calibrated under distribution shift, and is sensitive to uncertainty in its own answers, rather than imitating human examples. To our knowledge, this is the first time a model has been shown to express calibrated uncertainty about its own answers in natural language. For testing calibration, we introduce the CalibratedMath suite of tasks. We compare the calibration of uncertainty expressed in words ("verbalized probability") to uncertainty extracted from model logits. Both kinds of uncertainty are capable of generalizing calibration under distribution shift. We also provide evidence that GPT-3's ability to generalize calibration depends on pre-trained latent representations that correlate with epistemic uncertainty over its answers.

Sports betting's recent federal legalisation in the USA coincides with the golden age of machine learning. If bettors can leverage data to reliably predict the probability of an outcome, they can recognise when the bookmaker's odds are in their favour. As sports betting is a multi-billion dollar industry in the USA alone, identifying such opportunities could be extremely lucrative. Many researchers have applied machine learning to the sports outcome prediction problem, generally using accuracy to evaluate the performance of predictive models. We hypothesise that for the sports betting problem, model calibration is more important than accuracy. To test this hypothesis, we train models on NBA data over several seasons and run betting experiments on a single season, using published odds. We show that using calibration, rather than accuracy, as the basis for model selection leads to greater returns, on average (return on investment of +34.69% versus -35.17%) and in the best case (+36.93% versus +5.56%). These findings suggest that for sports betting (or any probabilistic decision-making problem), calibration is a more important metric than accuracy. Sports bettors who wish to increase profits should therefore select their predictive model based on calibration, rather than accuracy.

Adaptive behavior often requires predicting future events. The theory of reinforcement learning prescribes what kinds of predictive representations are useful and how to compute them. This paper integrates these theoretical ideas with work on cognition and neuroscience. We pay special attention to the successor representation (SR) and its generalizations, which have been widely applied both as engineering tools and models of brain function. This convergence suggests that particular kinds of predictive representations may function as versatile building blocks of intelligence.

Forecasting future events based on evidence of current conditions is an innate skill of human beings, and key for predicting the outcome of any decision making. In artificial vision for example, we would like to predict the next human action before it happens, without observing the future video frames associated to it. Computer vision models for action anticipation are expected to collect the subtle evidence in the preamble of the target actions. In prior studies recurrence modeling often leads to better performance, the strong temporal inference is assumed to be a key element for reasonable prediction. To this end, we propose a unified recurrence modeling for video action anticipation via message passing framework. The information flow in space-time can be described by the interaction between vertices and edges, and the changes of vertices for each incoming frame reflects the underlying dynamics. Our model leverages self-attention as the building blocks for each of the message passing functions. In addition, we introduce different edge learning strategies that can be end-to-end optimized to gain better flexibility for the connectivity between vertices. Our experimental results demonstrate that our proposed method outperforms previous works on the large-scale EPIC-Kitchen dataset.

Although the existing causal inference literature focuses on the forward-looking perspective by estimating effects of causes, the backward-looking perspective can provide insights into causes of effects. In backward-looking causal inference, the probability of necessity measures the probability that a certain event is caused by the treatment given the observed treatment and outcome. Most existing results focus on binary outcomes. Motivated by applications with ordinal outcomes, we propose a general definition of the probability of necessity. However, identifying the probability of necessity is challenging because it involves the joint distribution of the potential outcomes. We propose a novel assumption of monotonic incremental treatment effect to identify the probability of necessity with ordinal outcomes. We also discuss the testable implications of this key identification assumption. When it fails, we derive explicit formulas of the sharp large-sample bounds on the probability of necessity.

Counterfactual explanations are attracting significant attention due to the flourishing applications of machine learning models in consequential domains. A counterfactual plan consists of multiple possibilities to modify a given instance so that the model's prediction will be altered. As the predictive model can be updated subject to the future arrival of new data, a counterfactual plan may become ineffective or infeasible with respect to the future values of the model parameters. In this work, we study the counterfactual plans under model uncertainty, in which the distribution of the model parameters is partially prescribed using only the first- and second-moment information. First, we propose an uncertainty quantification tool to compute the lower and upper bounds of the probability of validity for any given counterfactual plan. We then provide corrective methods to adjust the counterfactual plan to improve the validity measure. The numerical experiments validate our bounds and demonstrate that our correction increases the robustness of the counterfactual plans in different real-world datasets.

We consider non-clairvoyant scheduling with online precedence constraints, where an algorithm is oblivious to any job dependencies and learns about a job only if all of its predecessors have been completed. Given strong impossibility results in classical competitive analysis, we investigate the problem in a learning-augmented setting, where an algorithm has access to predictions without any quality guarantee. We discuss different prediction models: novel problem-specific models as well as general ones, which have been proposed in previous works. We present lower bounds and algorithmic upper bounds for different precedence topologies, and thereby give a structured overview on which and how additional (possibly erroneous) information helps for designing better algorithms. Along the way, we also improve bounds on traditional competitive ratios for existing algorithms.

One of the predominant methods for training world models is autoregressive prediction in the output space of the next element of a sequence. In Natural Language Processing (NLP), this takes the form of Large Language Models (LLMs) predicting the next token; in Computer Vision (CV), this takes the form of autoregressive models predicting the next frame/token/pixel. However, this approach differs from human cognition in several respects. First, human predictions about the future actively influence internal cognitive processes. Second, humans naturally evaluate the plausibility of predictions regarding future states. Based on this capability, and third, by assessing when predictions are sufficient, humans allocate a dynamic amount of time to make a prediction. This adaptive process is analogous to System 2 thinking in psychology. All these capabilities are fundamental to the success of humans at high-level reasoning and planning. Therefore, to address the limitations of traditional autoregressive models lacking these human-like capabilities, we introduce Energy-Based World Models (EBWM). EBWM involves training an Energy-Based Model (EBM) to predict the compatibility of a given context and a predicted future state. In doing so, EBWM enables models to achieve all three facets of human cognition described. Moreover, we developed a variant of the traditional autoregressive transformer tailored for Energy-Based models, termed the Energy-Based Transformer (EBT). Our results demonstrate that EBWM scales better with data and GPU Hours than traditional autoregressive transformers in CV, and that EBWM offers promising early scaling in NLP. Consequently, this approach offers an exciting path toward training future models capable of System 2 thinking and intelligently searching across state spaces.

Learning a good history representation is one of the core challenges of reinforcement learning (RL) in partially observable environments. Recent works have shown the advantages of various auxiliary tasks for facilitating representation learning. However, the effectiveness of such auxiliary tasks has not been fully convincing, especially in partially observable environments that require long-term memorization and inference. In this empirical study, we investigate the effectiveness of future prediction for learning the representations of histories, possibly of extensive length, in partially observable environments. We first introduce an approach that decouples the task of learning history representations from policy optimization via future prediction. Then, our main contributions are two-fold: (a) we demonstrate that the performance of reinforcement learning is strongly correlated with the prediction accuracy of future observations in partially observable environments, and (b) our approach can significantly improve the overall end-to-end approach by preventing high-variance noisy signals from reinforcement learning objectives to influence the representation learning. We illustrate our claims on three types of benchmarks that necessitate the ability to process long histories for high returns.

Forecasting future events is important for policy and decision making. In this work, we study whether language models (LMs) can forecast at the level of competitive human forecasters. Towards this goal, we develop a retrieval-augmented LM system designed to automatically search for relevant information, generate forecasts, and aggregate predictions. To facilitate our study, we collect a large dataset of questions from competitive forecasting platforms. Under a test set published after the knowledge cut-offs of our LMs, we evaluate the end-to-end performance of our system against the aggregates of human forecasts. On average, the system nears the crowd aggregate of competitive forecasters, and in some settings surpasses it. Our work suggests that using LMs to forecast the future could provide accurate predictions at scale and help to inform institutional decision making.

Human reasoning often involves working over limited information to arrive at probabilistic conclusions. In its simplest form, this involves making an inference that is not strictly entailed by a premise, but rather only likely given the premise. While reasoning LLMs have demonstrated strong performance on logical and mathematical tasks, their behavior on such open-ended, non-deterministic inferences remains largely unexplored. We introduce ProbCOPA, a dataset of 210 handcrafted probabilistic inferences in English, each annotated for inference likelihood by 25--30 human participants. We find that human responses are graded and varied, revealing probabilistic judgments of the inferences in our dataset. Comparing these judgments with responses from eight state-of-the-art reasoning LLMs, we show that models consistently fail to produce human-like distributions. Finally, analyzing LLM reasoning chains, we find evidence of a common reasoning pattern used to evaluate such inferences. Our findings reveal persistent differences between humans and LLMs, and underscore the need to evaluate reasoning beyond deterministic settings.

We investigate the emergence of intuitive physics understanding in general-purpose deep neural network models trained to predict masked regions in natural videos. Leveraging the violation-of-expectation framework, we find that video prediction models trained to predict outcomes in a learned representation space demonstrate an understanding of various intuitive physics properties, such as object permanence and shape consistency. In contrast, video prediction in pixel space and multimodal large language models, which reason through text, achieve performance closer to chance. Our comparisons of these architectures reveal that jointly learning an abstract representation space while predicting missing parts of sensory input, akin to predictive coding, is sufficient to acquire an understanding of intuitive physics, and that even models trained on one week of unique video achieve above chance performance. This challenges the idea that core knowledge -- a set of innate systems to help understand the world -- needs to be hardwired to develop an understanding of intuitive physics.

Many real-world prediction problems lack labels observable at prediction time, creating a temporal gap between prediction and outcome that yields supervision only after events resolve. To address this setting, we extend reinforcement learning with verifiable rewards to temporally resolved real-world prediction, and use it to train language models to make probabilistic forecasts under causally masked information with retrospective evaluation using proper scoring rules. Supervision is derived solely from post-resolution outcomes, preserving delayed-reward semantics. On real-world forecasting benchmarks, Qwen3-32B trained using Foresight Learning improves Brier score by 27% and halves calibration error relative to its pretrained baseline, and outperforms Qwen3-235B on both constructed future-event prediction tasks and the Metaculus benchmark despite a 7x parameter disadvantage.

Future prediction is a complex task for LLM agents, requiring a high level of analytical thinking, information gathering, contextual understanding, and decision-making under uncertainty. Agents must not only gather and interpret vast amounts of dynamic information but also integrate diverse data sources, weigh uncertainties, and adapt predictions based on emerging trends, just as human experts do in fields like politics, economics, and finance. Despite its importance, no large-scale benchmark exists for evaluating agents on future prediction, largely due to challenges in handling real-time updates and retrieving timely, accurate answers. To address this, we introduce FutureX, a dynamic and live evaluation benchmark specifically designed for LLM agents performing future prediction tasks. FutureX is the largest and most diverse live benchmark for future prediction, supporting real-time daily updates and eliminating data contamination through an automated pipeline for question gathering and answer collection. We evaluate 25 LLM/agent models, including those with reasoning, search capabilities, and integration of external tools such as the open-source Deep Research Agent and closed-source Deep Research models. This comprehensive evaluation assesses agents' adaptive reasoning and performance in dynamic environments. Additionally, we provide in-depth analyses of agents' failure modes and performance pitfalls in future-oriented tasks, including the vulnerability to fake web pages and the temporal validity. Our goal is to establish a dynamic, contamination-free evaluation standard that drives the development of LLM agents capable of performing at the level of professional human analysts in complex reasoning and predictive thinking.

Many poker systems, whether created with heuristics or machine learning, rely on the probability of winning as a key input. However calculating the precise probability using combinatorics is an intractable problem, so instead we approximate it. Monte Carlo simulation is an effective technique that can be used to approximate the probability that a player will win and/or tie a hand. However, without the use of a memory-intensive lookup table or a supercomputer, it becomes infeasible to run millions of times when training an agent with self-play. To combat the space-time tradeoff, we use deep learning to approximate the probabilities obtained from the Monte Carlo simulation with high accuracy. The learned model proves to be a lightweight alternative to Monte Carlo simulation, which ultimately allows us to use the probabilities as inputs during self-play efficiently. The source code and optimized neural network can be found at https://github.com/brandinho/Poker-Probability-Approximation

Early warning signals have been proposed to forecast the possibility of a critical transition, such as the eutrophication of a lake, the collapse of a coral reef, or the end of a glacial period. Because such transitions often unfold on temporal and spatial scales that can be difficult to approach by experimental manipulation, research has often relied on historical observations as a source of natural experiments. Here we examine a critical difference between selecting systems for study based on the fact that we have observed a critical transition and those systems for which we wish to forecast the approach of a transition. This difference arises by conditionally selecting systems known to experience a transition of some sort and failing to account for the bias this introduces -- a statistical error often known as the Prosecutor's Fallacy. By analysing simulated systems that have experienced transitions purely by chance, we reveal an elevated rate of false positives in common warning signal statistics. We further demonstrate a model-based approach that is less subject to this bias than these more commonly used summary statistics. We note that experimental studies with replicates avoid this pitfall entirely.

Often we wish to predict a large number of variables that depend on each other as well as on other observed variables. Structured prediction methods are essentially a combination of classification and graphical modeling, combining the ability of graphical models to compactly model multivariate data with the ability of classification methods to perform prediction using large sets of input features. This tutorial describes conditional random fields, a popular probabilistic method for structured prediction. CRFs have seen wide application in natural language processing, computer vision, and bioinformatics. We describe methods for inference and parameter estimation for CRFs, including practical issues for implementing large scale CRFs. We do not assume previous knowledge of graphical modeling, so this tutorial is intended to be useful to practitioners in a wide variety of fields.

Encouraged by decision makers' appetite for future information on topics ranging from elections to pandemics, and enabled by the explosion of data and computational methods, model based forecasts have garnered increasing influence on a breadth of decisions in modern society. Using several classic examples from fisheries management, I demonstrate that selecting the model or models that produce the most accurate and precise forecast (measured by statistical scores) can sometimes lead to worse outcomes (measured by real-world objectives). This can create a forecast trap, in which the outcomes such as fish biomass or economic yield decline while the manager becomes increasingly convinced that these actions are consistent with the best models and data available. The forecast trap is not unique to this example, but a fundamental consequence of non-uniqueness of models. Existing practices promoting a broader set of models are the best way to avoid the trap.

The game show Lucky 13 differs from other television game shows in that contestants are required to place a bet on their own knowledge of trivia by selecting a range that contains the number of questions that they answered correctly. We present a model for this game show using binomial random variables and generate tables outlining the optimal range the player should select based on maximization of two different utility functions. After analyzing the decisions made by some actual contestants on this show, we present a numerical simulation for how many questions an average player is expected to answer correctly based on question categories observed for two sample contestants.

Prediction sets capture uncertainty by predicting sets of labels rather than individual labels, enabling downstream decisions to conservatively account for all plausible outcomes. Conformal inference algorithms construct prediction sets guaranteed to contain the true label with high probability. These guarantees fail to hold in the face of distribution shift, which is precisely when reliable uncertainty quantification can be most useful. We propose a novel algorithm for constructing prediction sets with PAC guarantees in the label shift setting. This method estimates the predicted probabilities of the classes in a target domain, as well as the confusion matrix, then propagates uncertainty in these estimates through a Gaussian elimination algorithm to compute confidence intervals for importance weights. Finally, it uses these intervals to construct prediction sets. We evaluate our approach on five datasets: the CIFAR-10, ChestX-Ray and Entity-13 image datasets, the tabular CDC Heart dataset, and the AGNews text dataset. Our algorithm satisfies the PAC guarantee while producing smaller, more informative, prediction sets compared to several baselines.

Applying a machine learning model for decision-making in the real world requires to distinguish what the model knows from what it does not. A critical factor in assessing the knowledge of a model is to quantify its predictive uncertainty. Predictive uncertainty is commonly measured by the entropy of the Bayesian model average (BMA) predictive distribution. Yet, the properness of this current measure of predictive uncertainty was recently questioned. We provide new insights regarding those limitations. Our analyses show that the current measure erroneously assumes that the BMA predictive distribution is equivalent to the predictive distribution of the true model that generated the dataset. Consequently, we introduce a theoretically grounded measure to overcome these limitations. We experimentally verify the benefits of our introduced measure of predictive uncertainty. We find that our introduced measure behaves more reasonably in controlled synthetic tasks. Moreover, our evaluations on ImageNet demonstrate that our introduced measure is advantageous in real-world applications utilizing predictive uncertainty.

Many people have flipped coins but few have stopped to ponder the statistical and physical intricacies of the process. We collected 350{,}757 coin flips to test the counterintuitive prediction from a physics model of human coin tossing developed by Diaconis, Holmes, and Montgomery (DHM; 2007). The model asserts that when people flip an ordinary coin, it tends to land on the same side it started -- DHM estimated the probability of a same-side outcome to be about 51\%. Our data lend strong support to this precise prediction: the coins landed on the same side more often than not, Pr(same side) = 0.508, 95\% credible interval (CI) [0.506, 0.509], BF_{same-side bias} = 2359. Furthermore, the data revealed considerable between-people variation in the degree of this same-side bias. Our data also confirmed the generic prediction that when people flip an ordinary coin -- with the initial side-up randomly determined -- it is equally likely to land heads or tails: Pr(heads) = 0.500, 95\% CI [0.498, 0.502], BF_{heads-tails bias} = 0.182. Furthermore, this lack of heads-tails bias does not appear to vary across coins. Additional analyses revealed that the within-people same-side bias decreased as more coins were flipped, an effect that is consistent with the possibility that practice makes people flip coins in a less wobbly fashion. Our data therefore provide strong evidence that when some (but not all) people flip a fair coin, it tends to land on the same side it started.

Language model (LM) decoding is based on the next-token prediction (NTP) probability distribution. For neural LMs (e.g., Transformer-based), NTP distribution is essentially a softmax-regularized dot product between an encoded input context (query) and fixed vocabulary representations (keys). In this paper, we study the effect of the key distribution on the NTP distribution, with a focus on whether the similarity between keys will trigger spurious correlations in NTP. Through knowledge-probing tasks, we show that in the NTP distribution, the few top-ranked tokens are typically accurate. However, the middle-ranked prediction is highly biased towards the tokens that are distributionally (not necessarily semantically) similar to these top ones. For instance, if "P" is predicted as the top-1 token, "A"-"Z" will all be ranked high in NTP, no matter whether they can lead to correct decoding results. This hurts the sampling diversity and makes the sampling of correct, long-tail results hopeless and noisy. We attempt to alleviate this issue via a novel in-context method that iteratively pushes the query representation away from explored regions. Specifically, we include the explored decoding results in the context and prompt the LM to generate something else, which encourages the LM to produce a query representation that has small dot products with explored keys. Experiments on knowledge-probing tasks show that our method leads to efficient navigation away from explored keys to correct new keys. We further extend our method to open-ended and chain-of-thought (for reasoning) generation. Experiment results show that ICN contributes to better generation diversity and improved self-consistency voting performance. Finally, we discuss potential training issues caused by the fixed key space together with the challenges and possible ways to address them in future research.

Probabilistic forecasting is crucial to decision-making under uncertainty about future weather. The dominant approach is to use an ensemble of forecasts to represent and quantify uncertainty in operational numerical weather prediction. However, generating ensembles is computationally costly. In this paper, we propose to generate ensemble forecasts at scale by leveraging recent advances in generative artificial intelligence. Our approach learns a data-driven probabilistic diffusion model from the 5-member ensemble GEFS reforecast dataset. The model can then be sampled efficiently to produce realistic weather forecasts, conditioned on a few members of the operational GEFS forecasting system. The generated ensembles have similar predictive skill as the full GEFS 31-member ensemble, evaluated against ERA5 reanalysis, and emulate well the statistics of large physics-based ensembles. We also apply the same methodology to developing a diffusion model for generative post-processing: the model directly learns to correct biases present in the emulated forecasting system by leveraging reanalysis data as labels during training. Ensembles from this generative post-processing model show greater reliability and accuracy, particularly in extreme event classification. In general, they are more reliable and forecast the probability of extreme weather more accurately than the GEFS operational ensemble. Our models achieve these results at less than 1/10th of the computational cost incurred by the operational GEFS system.

Multivariate probabilistic time series forecasts are commonly evaluated via proper scoring rules, i.e., functions that are minimal in expectation for the ground-truth distribution. However, this property is not sufficient to guarantee good discrimination in the non-asymptotic regime. In this paper, we provide the first systematic finite-sample study of proper scoring rules for time-series forecasting evaluation. Through a power analysis, we identify the "region of reliability" of a scoring rule, i.e., the set of practical conditions where it can be relied on to identify forecasting errors. We carry out our analysis on a comprehensive synthetic benchmark, specifically designed to test several key discrepancies between ground-truth and forecast distributions, and we gauge the generalizability of our findings to real-world tasks with an application to an electricity production problem. Our results reveal critical shortcomings in the evaluation of multivariate probabilistic forecasts as commonly performed in the literature.

Given time series data, how can we answer questions like "what will happen in the future?" and "how did we get here?" These sorts of probabilistic inference questions are challenging when observations are high-dimensional. In this paper, we show how these questions can have compact, closed form solutions in terms of learned representations. The key idea is to apply a variant of contrastive learning to time series data. Prior work already shows that the representations learned by contrastive learning encode a probability ratio. By extending prior work to show that the marginal distribution over representations is Gaussian, we can then prove that joint distribution of representations is also Gaussian. Taken together, these results show that representations learned via temporal contrastive learning follow a Gauss-Markov chain, a graphical model where inference (e.g., prediction, planning) over representations corresponds to inverting a low-dimensional matrix. In one special case, inferring intermediate representations will be equivalent to interpolating between the learned representations. We validate our theory using numerical simulations on tasks up to 46-dimensions.

Despite Flow Matching and diffusion models having emerged as powerful generative paradigms for continuous variables such as images and videos, their application to high-dimensional discrete data, such as language, is still limited. In this work, we present Discrete Flow Matching, a novel discrete flow paradigm designed specifically for generating discrete data. Discrete Flow Matching offers several key contributions: (i) it works with a general family of probability paths interpolating between source and target distributions; (ii) it allows for a generic formula for sampling from these probability paths using learned posteriors such as the probability denoiser (x-prediction) and noise-prediction (epsilon-prediction); (iii) practically, focusing on specific probability paths defined with different schedulers considerably improves generative perplexity compared to previous discrete diffusion and flow models; and (iv) by scaling Discrete Flow Matching models up to 1.7B parameters, we reach 6.7% Pass@1 and 13.4% Pass@10 on HumanEval and 6.7% Pass@1 and 20.6% Pass@10 on 1-shot MBPP coding benchmarks. Our approach is capable of generating high-quality discrete data in a non-autoregressive fashion, significantly closing the gap between autoregressive models and discrete flow models.

Identifying how much a model {p}_{theta}(Y|X) knows about the stochastic real-world process p(Y|X) it was trained on is important to ensure it avoids producing incorrect or "hallucinated" answers or taking unsafe actions. But this is difficult for generative models because probabilistic predictions do not distinguish between per-response noise (aleatoric uncertainty) and lack of knowledge about the process (epistemic uncertainty), and existing epistemic uncertainty quantification techniques tend to be overconfident when the model underfits. We propose a general strategy for teaching a model to both approximate p(Y|X) and also estimate the remaining gaps between {p}_{theta}(Y|X) and p(Y|X): train it to predict pairs of independent responses drawn from the true conditional distribution, allow it to "cheat" by observing one response while predicting the other, then measure how much it cheats. Remarkably, we prove that being good at cheating (i.e. cheating whenever it improves your prediction) is equivalent to being second-order calibrated, a principled extension of ordinary calibration that allows us to construct provably-correct frequentist confidence intervals for p(Y|X) and detect incorrect responses with high probability. We demonstrate empirically that our approach accurately estimates how much models don't know across ambiguous image classification, (synthetic) language modeling, and partially-observable navigation tasks, outperforming existing techniques.

In economy, markets are denoted as efficient when it is impossible to systematically generate profits which outperform the average. In the past years, the concept has been tested in other domains such as the growing sports betting market. Surprisingly, despite its large size and its level of maturity, sports betting shows traits of inefficiency. The anomalies indicate the existence of strategies which shift betting from a game of chance towards a game of skill. This article shows an example for an inefficiency detected in the German soccer betting TOTO 13er Wette, which is operated by state-run lottery agencies. Gamblers have to guess the outcome (win, draw, loss) of 13 soccer matches listed on a lottery tip. Applying stochastic methods, a recipe is presented to determine hit rates for single match outcomes. More important, the recipe provides the number of lottery tips required to achieve a specific number of strikes (number of correct match forecasts per lottery tip) for any given level of safety. An approximation is derived to cope with large numbers in hypergeometric distributions, valid under certain constraints. Overall, the strategy does lead to returns exceeding the aggregated lottery fees, resulting in moderate, but consistent profits. It is briefly discussed if lessions learned from soccer betting can be transferred back to financial markets, because gamblers and retail investors face similar challenges and opportunities.

Many empirical studies of labor market questions rely on estimating relatively simple predictive models using small, carefully constructed longitudinal survey datasets based on hand-engineered features. Large Language Models (LLMs), trained on massive datasets, encode vast quantities of world knowledge and can be used for the next job prediction problem. However, while an off-the-shelf LLM produces plausible career trajectories when prompted, the probability with which an LLM predicts a particular job transition conditional on career history will not, in general, align with the true conditional probability in a given population. Recently, Vafa et al. (2024) introduced a transformer-based "foundation model", CAREER, trained using a large, unrepresentative resume dataset, that predicts transitions between jobs; it further demonstrated how transfer learning techniques can be used to leverage the foundation model to build better predictive models of both transitions and wages that reflect conditional transition probabilities found in nationally representative survey datasets. This paper considers an alternative where the fine-tuning of the CAREER foundation model is replaced by fine-tuning LLMs. For the task of next job prediction, we demonstrate that models trained with our approach outperform several alternatives in terms of predictive performance on the survey data, including traditional econometric models, CAREER, and LLMs with in-context learning, even though the LLM can in principle predict job titles that are not allowed in the survey data. Further, we show that our fine-tuned LLM-based models' predictions are more representative of the career trajectories of various workforce subpopulations than off-the-shelf LLM models and CAREER. We conduct experiments and analyses that highlight the sources of the gains in the performance of our models for representative predictions.

Prediction sets have recently been shown to be a promising strategy for quantifying the uncertainty of deep neural networks in a way that provides theoretical guarantees. However, existing techniques have largely targeted settings where the space of labels is simple, so prediction sets can be arbitrary subsets of labels. For structured prediction problems where the space of labels is exponential in size, even prediction sets containing a small fraction of all labels can be exponentially large. In the context of code generation, we propose a solution that considers a restricted set of prediction sets that can compactly be represented as partial programs, which are programs with portions replaced with holes. Given a trained code generation model, our algorithm leverages a programming language's abstract syntax tree to generate a set of programs such that the correct program is in the set with high-confidence. Valuable applications of our algorithm include a Codex-style code generator with holes in uncertain parts of the generated code, which provides a partial program with theoretical guarantees. We evaluate our approach on PICARD (a T5 model for SQL semantic parsing) and Codex (a GPT model for over a dozen programming languages, including Python), demonstrating that our approach generates compact PAC prediction sets. This is the first research contribution that generates PAC prediction sets for generative code models.

Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, there is no universal agreement on how to best quantify predictive uncertainty. In this work, we revisit core concepts to propose a framework for information-theoretic measures of predictive uncertainty. Our proposed framework categorizes predictive uncertainty measures according to two factors: (I) The predicting model (II) The approximation of the true predictive distribution. Examining all possible combinations of these two factors, we derive a set of predictive uncertainty measures that includes both known and newly introduced ones. We extensively evaluate these measures across a broad set of tasks, identifying conditions under which certain measures excel. Our findings show the importance of aligning the choice of uncertainty measure with the predicting model on in-distribution (ID) data, the limitations of epistemic uncertainty measures for out-of-distribution (OOD) data, and that the disentanglement between measures varies substantially between ID and OOD data. Together, these insights provide a more comprehensive understanding of predictive uncertainty measures, revealing their implicit assumptions and relationships.

Probability estimation models play an important role in various fields, such as weather forecasting, recommendation systems, and sports analysis. Among several models estimating probabilities, it is difficult to evaluate which model gives reliable probabilities since the ground-truth probabilities are not available. The win probability estimation model for esports, which calculates the win probability under a certain game state, is also one of the fields being actively studied in probability estimation. However, most of the previous works evaluated their models using accuracy, a metric that only can measure the performance of discrimination. In this work, we firstly investigate the Brier score and the Expected Calibration Error (ECE) as a replacement of accuracy used as a performance evaluation metric for win probability estimation models in esports field. Based on the analysis, we propose a novel metric called Balance score which is a simple yet effective metric in terms of six good properties that probability estimation metric should have. Under the general condition, we also found that the Balance score can be an effective approximation of the true expected calibration error which has been imperfectly approximated by ECE using the binning technique. Extensive evaluations using simulation studies and real game snapshot data demonstrate the promising potential to adopt the proposed metric not only for the win probability estimation model for esports but also for evaluating general probability estimation models.

A significant body of recent research in the field of Learning Analytics has focused on leveraging machine learning approaches for predicting at-risk students in order to initiate timely interventions and thereby elevate retention and completion rates. The overarching feature of the majority of these research studies has been on the science of prediction only. The component of predictive analytics concerned with interpreting the internals of the models and explaining their predictions for individual cases to stakeholders has largely been neglected. Additionally, works that attempt to employ data-driven prescriptive analytics to automatically generate evidence-based remedial advice for at-risk learners are in their infancy. eXplainable AI is a field that has recently emerged providing cutting-edge tools which support transparent predictive analytics and techniques for generating tailored advice for at-risk students. This study proposes a novel framework that unifies both transparent machine learning as well as techniques for enabling prescriptive analytics, while integrating the latest advances in large language models. This work practically demonstrates the proposed framework using predictive models for identifying at-risk learners of programme non-completion. The study then further demonstrates how predictive modelling can be augmented with prescriptive analytics on two case studies in order to generate human-readable prescriptive feedback for those who are at risk using ChatGPT.

Predicting case outcomes is useful but still an extremely hard task for attorneys and other Law professionals. It is not easy to search case information to extract valuable information as this requires dealing with huge data sets and their complexity. For instance, the complexity of Brazil legal system along with the high litigation rates makes this problem even harder. This paper introduces an approach for predicting Brazilian court decisions which is also able to predict whether the decision will be unanimous. We developed a working prototype which performs 79% of accuracy (F1-score) on a data set composed of 4,043 cases from a Brazilian court. To our knowledge, this is the first study to forecast judge decisions in Brazil.

Legal judgment prediction is the task of automatically predicting the outcome of a court case, given a text describing the case's facts. Previous work on using neural models for this task has focused on Chinese; only feature-based models (e.g., using bags of words and topics) have been considered in English. We release a new English legal judgment prediction dataset, containing cases from the European Court of Human Rights. We evaluate a broad variety of neural models on the new dataset, establishing strong baselines that surpass previous feature-based models in three tasks: (1) binary violation classification; (2) multi-label classification; (3) case importance prediction. We also explore if models are biased towards demographic information via data anonymization. As a side-product, we propose a hierarchical version of BERT, which bypasses BERT's length limitation.

Many events occur in the world. Some event types are stochastically excited or inhibited---in the sense of having their probabilities elevated or decreased---by patterns in the sequence of previous events. Discovering such patterns can help us predict which type of event will happen next and when. We model streams of discrete events in continuous time, by constructing a neurally self-modulating multivariate point process in which the intensities of multiple event types evolve according to a novel continuous-time LSTM. This generative model allows past events to influence the future in complex and realistic ways, by conditioning future event intensities on the hidden state of a recurrent neural network that has consumed the stream of past events. Our model has desirable qualitative properties. It achieves competitive likelihood and predictive accuracy on real and synthetic datasets, including under missing-data conditions.

Competitions play an invaluable role in the field of forecasting, as exemplified through the recent M4 competition. The competition received attention from both academics and practitioners and sparked discussions around the representativeness of the data for business forecasting. Several competitions featuring real-life business forecasting tasks on the Kaggle platform has, however, been largely ignored by the academic community. We believe the learnings from these competitions have much to offer to the forecasting community and provide a review of the results from six Kaggle competitions. We find that most of the Kaggle datasets are characterized by higher intermittence and entropy than the M-competitions and that global ensemble models tend to outperform local single models. Furthermore, we find the strong performance of gradient boosted decision trees, increasing success of neural networks for forecasting, and a variety of techniques for adapting machine learning models to the forecasting task.

The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to random variables are discussed, including the approach based on completions in a Polish space. We apply the theory to the study of stochastic dynamical systems in discrete-time, and give a brief exposition of the Wiener process as a foundation for stochastic differential equations. The theory is based within the framework of type-two effectivity, so has an explicit direct link with Turing computation, and is expressed in a system of computable types and operations, so has a clean mathematical description.

Artificial intelligence commonly refers to the science and engineering of artificial systems that can carry out tasks generally associated with requiring aspects of human intelligence, such as playing games, translating languages, and driving cars. In recent years, there have been exciting advances in learning-based, data-driven approaches towards AI, and machine learning and deep learning have enabled computer systems to perceive the world in unprecedented ways. Reinforcement learning has enabled breakthroughs in complex games such as Go and challenging robotics tasks such as quadrupedal locomotion. A key aspect of intelligence is to not only make predictions, but reason about the uncertainty in these predictions, and to consider this uncertainty when making decisions. This is what this manuscript on "Probabilistic Artificial Intelligence" is about. The first part covers probabilistic approaches to machine learning. We discuss the differentiation between "epistemic" uncertainty due to lack of data and "aleatoric" uncertainty, which is irreducible and stems, e.g., from noisy observations and outcomes. We discuss concrete approaches towards probabilistic inference and modern approaches to efficient approximate inference. The second part of the manuscript is about taking uncertainty into account in sequential decision tasks. We consider active learning and Bayesian optimization -- approaches that collect data by proposing experiments that are informative for reducing the epistemic uncertainty. We then consider reinforcement learning and modern deep RL approaches that use neural network function approximation. We close by discussing modern approaches in model-based RL, which harness epistemic and aleatoric uncertainty to guide exploration, while also reasoning about safety.

The extant insurance literature demonstrates a paucity of finite-sample valid prediction intervals of future insurance claims in the regression setting. To address this challenge, this article proposes a new strategy that converts a predictive method in the unsupervised iid (independent identically distributed) setting to a predictive method in the regression setting. In particular, it enables an actuary to obtain infinitely many finite-sample valid prediction intervals in the regression setting.

Neural scaling laws (NSL) refer to the phenomenon where model performance improves with scale. Sharma & Kaplan analyzed NSL using approximation theory and predict that MSE losses decay as N^{-alpha}, alpha=4/d, where N is the number of model parameters, and d is the intrinsic input dimension. Although their theory works well for some cases (e.g., ReLU networks), we surprisingly find that a simple 1D problem y=x^2 manifests a different scaling law (alpha=1) from their predictions (alpha=4). We opened the neural networks and found that the new scaling law originates from lottery ticket ensembling: a wider network on average has more "lottery tickets", which are ensembled to reduce the variance of outputs. We support the ensembling mechanism by mechanistically interpreting single neural networks, as well as studying them statistically. We attribute the N^{-1} scaling law to the "central limit theorem" of lottery tickets. Finally, we discuss its potential implications for large language models and statistical physics-type theories of learning.

Progress in large language models is constrained by an evaluation bottleneck: build a benchmark, evaluate models and settings, then iterate. We therefore ask a simple question: can we forecast outcomes before running any experiments? We study text-only performance forecasting: estimating a model's score from a redacted task description and intended configuration, with no access to dataset instances. To support systematic study, we curate PRECOG, a corpus of redacted description-performance pairs spanning diverse tasks, domains, and metrics. Experiments show the task is challenging but feasible: models equipped with a retrieval module that excludes source papers achieve moderate prediction performance with well-calibrated uncertainty, reaching mean absolute error as low as 8.7 on the Accuracy subset at high-confidence thresholds. Our analysis indicates that stronger reasoning models engage in diverse, iterative querying, whereas current open-source models lag and often skip retrieval or gather evidence with limited diversity. We further test a zero-leakage setting, forecasting on newly released datasets or experiments before their papers are indexed, where GPT-5 with built-in web search still attains nontrivial prediction accuracy. Overall, our corpus and analyses offer an initial step toward open-ended anticipatory evaluation, supporting difficulty estimation and smarter experiment prioritization.

Inspired by the fact that the neural network, as the mainstream for machine learning, has brought successes in many application areas, here we propose to use this approach for decoding hidden correlation among pseudo-random data and predicting events accordingly. With a simple neural network structure and a typical training procedure, we demonstrate the learning and prediction power of the neural network in extremely random environment. Finally, we postulate that the high sensitivity and efficiency of the neural network may allow to critically test if there could be any fundamental difference between quantum randomness and pseudo randomness, which is equivalent to the question: Does God play dice?

This paper surveys and organizes research works in a new paradigm in natural language processing, which we dub "prompt-based learning". Unlike traditional supervised learning, which trains a model to take in an input x and predict an output y as P(y|x), prompt-based learning is based on language models that model the probability of text directly. To use these models to perform prediction tasks, the original input x is modified using a template into a textual string prompt x' that has some unfilled slots, and then the language model is used to probabilistically fill the unfilled information to obtain a final string x, from which the final output y can be derived. This framework is powerful and attractive for a number of reasons: it allows the language model to be pre-trained on massive amounts of raw text, and by defining a new prompting function the model is able to perform few-shot or even zero-shot learning, adapting to new scenarios with few or no labeled data. In this paper we introduce the basics of this promising paradigm, describe a unified set of mathematical notations that can cover a wide variety of existing work, and organize existing work along several dimensions, e.g.the choice of pre-trained models, prompts, and tuning strategies. To make the field more accessible to interested beginners, we not only make a systematic review of existing works and a highly structured typology of prompt-based concepts, but also release other resources, e.g., a website http://pretrain.nlpedia.ai/ including constantly-updated survey, and paperlist.

When a language model generates text, the selection of individual tokens might lead it down very different reasoning paths, making uncertainty difficult to quantify. In this work, we consider whether reasoning language models represent the alternate paths that they could take during generation. To test this hypothesis, we use hidden activations to control and predict a language model's uncertainty during chain-of-thought reasoning. In our experiments, we find a clear correlation between how uncertain a model is at different tokens, and how easily the model can be steered by controlling its activations. This suggests that activation interventions are most effective when there are alternate paths available to the model -- in other words, when it has not yet committed to a particular final answer. We also find that hidden activations can predict a model's future outcome distribution, demonstrating that models implicitly represent the space of possible paths.

We present an outcome-driven fine-tuning framework that enhances the forecasting capabilities of large language models (LLMs) without relying on human-curated reasoning samples. Our method leverages model self-play to generate pairs of diverse reasoning trajectories and probabilistic forecasts for a set of diverse questions that resolve after the models' knowledge cutoff date. We then rank pairs of these reasoning traces by their distance to the actual outcomes before fine-tuning the model via Direct Preference Optimization (DPO). On a separate test set, our approach increases prediction accuracy of Phi-4 14B and DeepSeek-R1 14B by between 7--10\% over a base model and a DPO fine-tuned control model with randomized labels, bringing them on par with forecasting capabilities of much larger frontier models like GPT-4o.

We examine the potential of ChatGPT and other large language models in predicting stock market returns using news headlines. We use ChatGPT to assess whether each headline is good, bad, or neutral for firms' stock prices. We document a significantly positive correlation between ChatGPT scores and subsequent daily stock returns. We find that ChatGPT outperforms traditional sentiment analysis methods. More basic models such as GPT-1, GPT-2, and BERT cannot accurately forecast returns, indicating return predictability is an emerging capacity of complex language models. Long-short strategies based on ChatGPT-4 deliver the highest Sharpe ratio. Furthermore, we find predictability in both small and large stocks, suggesting market underreaction to company news. Predictability is stronger among smaller stocks and stocks with bad news, consistent with limits-to-arbitrage also playing an important role. Finally, we propose a new method to evaluate and understand the models' reasoning capabilities. Overall, our results suggest that incorporating advanced language models into the investment decision-making process can yield more accurate predictions and enhance the performance of quantitative trading strategies.

Do large language models (LLMs) anticipate when they will answer correctly? To study this, we extract activations after a question is read but before any tokens are generated, and train linear probes to predict whether the model's forthcoming answer will be correct. Across three open-source model families ranging from 7 to 70 billion parameters, projections on this "in-advance correctness direction" trained on generic trivia questions predict success in distribution and on diverse out-of-distribution knowledge datasets, outperforming black-box baselines and verbalised predicted confidence. Predictive power saturates in intermediate layers, suggesting that self-assessment emerges mid-computation. Notably, generalisation falters on questions requiring mathematical reasoning. Moreover, for models responding "I don't know", doing so strongly correlates with the probe score, indicating that the same direction also captures confidence. By complementing previous results on truthfulness and other behaviours obtained with probes and sparse auto-encoders, our work contributes essential findings to elucidate LLM internals.

We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence." We explore how to interpret uncertain evidence, and by extension the importance of proper interpretation as it pertains to inference about latent variables. We consider a recently-proposed method "distributional evidence" as well as revisit two older methods: Jeffrey's rule and virtual evidence. We devise guidelines on how to account for uncertain evidence and we provide new insights, particularly regarding consistency. To showcase the impact of different interpretations of the same uncertain evidence, we carry out experiments in which one interpretation is defined as "correct." We then compare inference results from each different interpretation illustrating the importance of careful consideration of uncertain evidence.

We resolve an open problem of Hanneke on the subject of universally consistent online learning with non-i.i.d. processes and unbounded losses. The notion of an optimistically universal learning rule was defined by Hanneke in an effort to study learning theory under minimal assumptions. A given learning rule is said to be optimistically universal if it achieves a low long-run average loss whenever the data generating process makes this goal achievable by some learning rule. Hanneke posed as an open problem whether, for every unbounded loss, the family of processes admitting universal learning are precisely those having a finite number of distinct values almost surely. In this paper, we completely resolve this problem, showing that this is indeed the case. As a consequence, this also offers a dramatically simpler formulation of an optimistically universal learning rule for any unbounded loss: namely, the simple memorization rule already suffices. Our proof relies on constructing random measurable partitions of the instance space and could be of independent interest for solving other open questions. We extend the results to the non-realizable setting thereby providing an optimistically universal Bayes consistent learning rule.

Time series forecasting in real-world applications requires both high predictive accuracy and interpretable uncertainty quantification. Traditional point prediction methods often fail to capture the inherent uncertainty in time series data, while existing probabilistic approaches struggle to balance computational efficiency with interpretability. We propose a novel Multi-Expert Learning Distributional Labels (LDL) framework that addresses these challenges through mixture-of-experts architectures with distributional learning capabilities. Our approach introduces two complementary methods: (1) Multi-Expert LDL, which employs multiple experts with different learned parameters to capture diverse temporal patterns, and (2) Pattern-Aware LDL-MoE, which explicitly decomposes time series into interpretable components (trend, seasonality, changepoints, volatility) through specialized sub-experts. Both frameworks extend traditional point prediction to distributional learning, enabling rich uncertainty quantification through Maximum Mean Discrepancy (MMD). We evaluate our methods on aggregated sales data derived from the M5 dataset, demonstrating superior performance compared to baseline approaches. The continuous Multi-Expert LDL achieves the best overall performance, while the Pattern-Aware LDL-MoE provides enhanced interpretability through component-wise analysis. Our frameworks successfully balance predictive accuracy with interpretability, making them suitable for real-world forecasting applications where both performance and actionable insights are crucial.

There has been considerable recent interest in scoring properties on the basis of eviction risk. The success of methods for eviction prediction is typically evaluated using different measures of predictive accuracy. However, the underlying goal of such prediction is to direct appropriate assistance to households that may be at greater risk so they remain stably housed. Thus, we must ask the question of how useful such predictions are in targeting outreach efforts - informing action. In this paper, we investigate this question using a novel dataset that matches information on properties, evictions, and owners. We perform an eviction prediction task to produce risk scores and then use these risk scores to plan targeted outreach policies. We show that the risk scores are, in fact, useful, enabling a theoretical team of caseworkers to reach more eviction-prone properties in the same amount of time, compared to outreach policies that are either neighborhood-based or focus on buildings with a recent history of evictions. We also discuss the importance of neighborhood and ownership features in both risk prediction and targeted outreach.

Given a video with aligned dialogue, people can often infer what is more likely to happen next. Making such predictions requires not only a deep understanding of the rich dynamics underlying the video and dialogue, but also a significant amount of commonsense knowledge. In this work, we explore whether AI models are able to learn to make such multimodal commonsense next-event predictions. To support research in this direction, we collect a new dataset, named Video-and-Language Event Prediction (VLEP), with 28,726 future event prediction examples (along with their rationales) from 10,234 diverse TV Show and YouTube Lifestyle Vlog video clips. In order to promote the collection of non-trivial challenging examples, we employ an adversarial human-and-model-in-the-loop data collection procedure. We also present a strong baseline incorporating information from video, dialogue, and commonsense knowledge. Experiments show that each type of information is useful for this challenging task, and that compared to the high human performance on VLEP, our model provides a good starting point but leaves large room for future work. Our dataset and code are available at: https://github.com/jayleicn/VideoLanguageFuturePred

We investigate large language model performance across five orders of magnitude of compute scaling in eleven recent model architectures. We show that average benchmark performance, aggregating over many individual tasks and evaluations as in the commonly-used BIG-Bench dataset, is decently predictable as a function of training compute scale. Specifically, when extrapolating BIG-Bench Hard performance across one order of magnitude in compute, we observe average absolute errors of 6 percentage points (pp). By contrast, extrapolation for individual BIG-Bench tasks across an order of magnitude in compute yields higher average errors of 18pp. Nonetheless, individual task performance remains significantly more predictable than chance. Overall, our work suggests compute scaling provides a promising basis to forecast AI capabilities in diverse benchmarks, though predicting performance in specific tasks poses challenges.

Machine learning models in modern mass-market applications are often updated over time. One of the foremost challenges faced is that, despite increasing overall performance, these updates may flip specific model predictions in unpredictable ways. In practice, researchers quantify the number of unstable predictions between models pre and post update -- i.e., predictive churn. In this paper, we study this effect through the lens of predictive multiplicity -- i.e., the prevalence of conflicting predictions over the set of near-optimal models (the Rashomon set). We show how traditional measures of predictive multiplicity can be used to examine expected churn over this set of prospective models -- i.e., the set of models that may be used to replace a baseline model in deployment. We present theoretical results on the expected churn between models within the Rashomon set from different perspectives. And we characterize expected churn over model updates via the Rashomon set, pairing our analysis with empirical results on real-world datasets -- showing how our approach can be used to better anticipate, reduce, and avoid churn in consumer-facing applications. Further, we show that our approach is useful even for models enhanced with uncertainty awareness.

Large Language Models (LLMs) demonstrate partial forecasting competence across social, political, and economic events. Yet, their predictive ability varies sharply with domain structure and prompt framing. We investigate how forecasting performance varies with different model families on real-world questions about events that happened beyond the model cutoff date. We analyze how context, question type, and external knowledge affect accuracy and calibration, and how adding factual news context modifies belief formation and failure modes. Our results show that forecasting ability is highly variable as it depends on what, and how, we ask.

Machine learning models are often used to inform real world risk assessment tasks: predicting consumer default risk, predicting whether a person suffers from a serious illness, or predicting a person's risk to appear in court. Given multiple models that perform almost equally well for a prediction task, to what extent do predictions vary across these models? If predictions are relatively consistent for similar models, then the standard approach of choosing the model that optimizes a penalized loss suffices. But what if predictions vary significantly for similar models? In machine learning, this is referred to as predictive multiplicity i.e. the prevalence of conflicting predictions assigned by near-optimal competing models. In this paper, we present a framework for measuring predictive multiplicity in probabilistic classification (predicting the probability of a positive outcome). We introduce measures that capture the variation in risk estimates over the set of competing models, and develop optimization-based methods to compute these measures efficiently and reliably for convex empirical risk minimization problems. We demonstrate the incidence and prevalence of predictive multiplicity in real-world tasks. Further, we provide insight into how predictive multiplicity arises by analyzing the relationship between predictive multiplicity and data set characteristics (outliers, separability, and majority-minority structure). Our results emphasize the need to report predictive multiplicity more widely.

We study the problem of online prediction, in which at each time step t, an individual x_t arrives, whose label we must predict. Each individual is associated with various groups, defined based on their features such as age, sex, race etc., which may intersect. Our goal is to make predictions that have regret guarantees not just overall but also simultaneously on each sub-sequence comprised of the members of any single group. Previous work such as [Blum & Lykouris] and [Lee et al] provide attractive regret guarantees for these problems; however, these are computationally intractable on large model classes. We show that a simple modification of the sleeping experts technique of [Blum & Lykouris] yields an efficient reduction to the well-understood problem of obtaining diminishing external regret absent group considerations. Our approach gives similar regret guarantees compared to [Blum & Lykouris]; however, we run in time linear in the number of groups, and are oracle-efficient in the hypothesis class. This in particular implies that our algorithm is efficient whenever the number of groups is polynomially bounded and the external-regret problem can be solved efficiently, an improvement on [Blum & Lykouris]'s stronger condition that the model class must be small. Our approach can handle online linear regression and online combinatorial optimization problems like online shortest paths. Beyond providing theoretical regret bounds, we evaluate this algorithm with an extensive set of experiments on synthetic data and on two real data sets -- Medical costs and the Adult income dataset, both instantiated with intersecting groups defined in terms of race, sex, and other demographic characteristics. We find that uniformly across groups, our algorithm gives substantial error improvements compared to running a standard online linear regression algorithm with no groupwise regret guarantees.

Large Language Models (LLMs) have recently been successfully applied to regression tasks -- such as time series forecasting and tabular prediction -- by leveraging their in-context learning abilities. However, their autoregressive decoding process may be ill-suited to continuous-valued outputs, where obtaining predictive distributions over numerical targets requires repeated sampling, leading to high computational cost and inference time. In this work, we investigate whether distributional properties of LLM predictions can be recovered without explicit autoregressive generation. To this end, we study a set of regression probes trained to predict statistical functionals (e.g., mean, median, quantiles) of the LLM's numerical output distribution directly from its internal representations. Our results suggest that LLM embeddings carry informative signals about summary statistics of their predictive distributions, including the numerical uncertainty. This investigation opens up new questions about how LLMs internally encode uncertainty in numerical tasks, and about the feasibility of lightweight alternatives to sampling-based approaches for uncertainty-aware numerical predictions.

The 100 MW cryogenic liquid oxygen/hydrogen multi-injector combustor BKD operated by the DLR Institute of Space Propulsion is a research platform that allows the study of thermoacoustic instabilities under realistic conditions, representative of small upper stage rocket engines. We use data from BKD experimental campaigns in which the static chamber pressure and fuel-oxidizer ratio are varied such that the first tangential mode of the combustor is excited under some conditions. We train an autoregressive Bayesian neural network model to forecast the amplitude of the dynamic pressure time series, inputting multiple sensor measurements (injector pressure/ temperature measurements, static chamber pressure, high-frequency dynamic pressure measurements, high-frequency OH* chemiluminescence measurements) and future flow rate control signals. The Bayesian nature of our algorithms allows us to work with a dataset whose size is restricted by the expense of each experimental run, without making overconfident extrapolations. We find that the networks are able to accurately forecast the evolution of the pressure amplitude and anticipate instability events on unseen experimental runs 500 milliseconds in advance. We compare the predictive accuracy of multiple models using different combinations of sensor inputs. We find that the high-frequency dynamic pressure signal is particularly informative. We also use the technique of integrated gradients to interpret the influence of different sensor inputs on the model prediction. The negative log-likelihood of data points in the test dataset indicates that predictive uncertainties are well-characterized by our Bayesian model and simulating a sensor failure event results as expected in a dramatic increase in the epistemic component of the uncertainty.

Large language models (LLMs) excel at processing information reactively but lack the ability to systemically explore hypothetical futures. They cannot ask, "what if we take this action? how will it affect the final outcome" and forecast its potential consequences before acting. This critical gap limits their utility in dynamic, high-stakes scenarios like strategic planning, risk assessment, and real-time decision making. To bridge this gap, we propose WiA-LLM, a new paradigm that equips LLMs with proactive thinking capabilities. Our approach integrates What-If Analysis (WIA), a systematic approach for evaluating hypothetical scenarios by changing input variables. By leveraging environmental feedback via reinforcement learning, WiA-LLM moves beyond reactive thinking. It dynamically simulates the outcomes of each potential action, enabling the model to anticipate future states rather than merely react to the present conditions. We validate WiA-LLM in Honor of Kings (HoK), a complex multiplayer game environment characterized by rapid state changes and intricate interactions. The game's real-time state changes require precise multi-step consequence prediction, making it an ideal testbed for our approach. Experimental results demonstrate WiA-LLM achieves a remarkable 74.2% accuracy in forecasting game-state changes (up to two times gain over baselines). The model shows particularly significant gains in high-difficulty scenarios where accurate foresight is critical. To our knowledge, this is the first work to formally explore and integrate what-if analysis capabilities within LLMs. WiA-LLM represents a fundamental advance toward proactive reasoning in LLMs, providing a scalable framework for robust decision-making in dynamic environments with broad implications for strategic applications.

Many classic Reinforcement Learning (RL) algorithms rely on a Bellman operator, which involves an expectation over the next states, leading to the concept of bootstrapping. To introduce a form of pessimism, we propose to replace this expectation with an expectile. In practice, this can be very simply done by replacing the L_2 loss with a more general expectile loss for the critic. Introducing pessimism in RL is desirable for various reasons, such as tackling the overestimation problem (for which classic solutions are double Q-learning or the twin-critic approach of TD3) or robust RL (where transitions are adversarial). We study empirically these two cases. For the overestimation problem, we show that the proposed approach, ExpectRL, provides better results than a classic twin-critic. On robust RL benchmarks, involving changes of the environment, we show that our approach is more robust than classic RL algorithms. We also introduce a variation of ExpectRL combined with domain randomization which is competitive with state-of-the-art robust RL agents. Eventually, we also extend \ExpectRL with a mechanism for choosing automatically the expectile value, that is the degree of pessimism

Machine learning shows promise in predicting the outcome of legal cases, but most research has concentrated on civil law cases rather than case law systems. We identified two unique challenges in making legal case outcome predictions with case law. First, it is crucial to identify relevant precedent cases that serve as fundamental evidence for judges during decision-making. Second, it is necessary to consider the evolution of legal principles over time, as early cases may adhere to different legal contexts. In this paper, we proposed a new framework named PILOT (PredictIng Legal case OuTcome) for case outcome prediction. It comprises two modules for relevant case retrieval and temporal pattern handling, respectively. To benchmark the performance of existing legal case outcome prediction models, we curated a dataset from a large-scale case law database. We demonstrate the importance of accurately identifying precedent cases and mitigating the temporal shift when making predictions for case law, as our method shows a significant improvement over the prior methods that focus on civil law case outcome predictions.

The paper studies the linear model for Bitcoin price which includes regression features based on Bitcoin currency statistics, mining processes, Google search trends, Wikipedia pages visits. The pattern of deviation of regression model prediction from real prices is simpler comparing to price time series. It is assumed that this pattern can be predicted by an experienced expert. In such a way, using the combination of the regression model and expert correction, one can receive better results than with either regression model or expert opinion only. It is shown that Bayesian approach makes it possible to utilize the probabilistic approach using distributions with fat tails and take into account the outliers in Bitcoin price time series.

Transformers, currently the state-of-the-art in natural language understanding (NLU) tasks, are prone to generate uncalibrated predictions or extreme probabilities, making the process of taking different decisions based on their output relatively difficult. In this paper we propose to build several inductive Venn--ABERS predictors (IVAP), which are guaranteed to be well calibrated under minimal assumptions, based on a selection of pre-trained transformers. We test their performance over a set of diverse NLU tasks and show that they are capable of producing well-calibrated probabilistic predictions that are uniformly spread over the [0,1] interval -- all while retaining the original model's predictive accuracy.

Prior-data fitted networks (PFNs) were recently proposed as a new paradigm for machine learning. Instead of training the network to an observed training set, a fixed model is pre-trained offline on small, simulated training sets from a variety of tasks. The pre-trained model is then used to infer class probabilities in-context on fresh training sets with arbitrary size and distribution. Empirically, PFNs achieve state-of-the-art performance on tasks with similar size to the ones used in pre-training. Surprisingly, their accuracy further improves when passed larger data sets during inference. This article establishes a theoretical foundation for PFNs and illuminates the statistical mechanisms governing their behavior. While PFNs are motivated by Bayesian ideas, a purely frequentistic interpretation of PFNs as pre-tuned, but untrained predictors explains their behavior. A predictor's variance vanishes if its sensitivity to individual training samples does and the bias vanishes only if it is appropriately localized around the test feature. The transformer architecture used in current PFN implementations ensures only the former. These findings shall prove useful for designing architectures with favorable empirical behavior.

Forecasting what will happen next is a critical skill for general-purpose systems that plan or act in the world at different levels of abstraction. In this paper, we identify a strong correlation between a vision model's perceptual ability and its generalist forecasting performance over short time horizons. This trend holds across a diverse set of pretrained models-including those trained generatively-and across multiple levels of abstraction, from raw pixels to depth, point tracks, and object motion. The result is made possible by a novel generalist forecasting framework that operates on any frozen vision backbone: we train latent diffusion models to forecast future features in the frozen representation space, which are then decoded via lightweight, task-specific readouts. To enable consistent evaluation across tasks, we introduce distributional metrics that compare distributional properties directly in the space of downstream tasks and apply this framework to nine models and four tasks. Our results highlight the value of bridging representation learning and generative modeling for temporally grounded video understanding.

Mathematical reasoning models are widely deployed in education, automated tutoring, and decision support systems despite exhibiting fundamental computational instabilities. We demonstrate that state-of-the-art models (Qwen2.5-Math-7B) achieve 61% accuracy through a mixture of reliable and unreliable reasoning pathways: 18.4% of correct predictions employ stable, faithful reasoning while 81.6% emerge through computationally inconsistent pathways. Additionally, 8.8% of all predictions are silent failures -- confident yet incorrect outputs. Through comprehensive analysis using novel faithfulness metrics, we reveal: (1) reasoning quality shows weak negative correlation with correctness (r=-0.21, p=0.002), reflecting a binary classification threshold artifact rather than a monotonic inverse relationship; (2) scaling from 1.5B to 7B parameters (4.7x increase) provides zero accuracy benefit on our evaluated subset (6% of GSM8K), requiring validation on the complete benchmark; and (3) latent reasoning employs diverse computational strategies, with ~20% sharing CoT-like patterns. These findings highlight that benchmark accuracy can mask computational unreliability, demanding evaluation reforms measuring stability beyond single-sample metrics.

When users can benefit from certain predictive outcomes, they may be prone to act to achieve those outcome, e.g., by strategically modifying their features. The goal in strategic classification is therefore to train predictive models that are robust to such behavior. However, the conventional framework assumes that changing features does not change actual outcomes, which depicts users as "gaming" the system. Here we remove this assumption, and study learning in a causal strategic setting where true outcomes do change. Focusing on accuracy as our primary objective, we show how strategic behavior and causal effects underlie two complementing forms of distribution shift. We characterize these shifts, and propose a learning algorithm that balances between these two forces and over time, and permits end-to-end training. Experiments on synthetic and semi-synthetic data demonstrate the utility of our approach.