Daily Papers

Accurately anticipating how complex, diverse scenes will evolve requires models that represent uncertainty, simulate along extended interaction chains, and efficiently explore many plausible futures. Yet most existing approaches rely on dense video or latent-space prediction, expending substantial capacity on dense appearance rather than on the underlying sparse trajectories of points in the scene. This makes large-scale exploration of future hypotheses costly and limits performance when long-horizon, multi-modal motion is essential. We address this by formulating the prediction of open-set future scene dynamics as step-wise inference over sparse point trajectories. Our autoregressive diffusion model advances these trajectories through short, locally predictable transitions, explicitly modeling the growth of uncertainty over time. This dynamics-centric representation enables fast rollout of thousands of diverse futures from a single image, optionally guided by initial constraints on motion, while maintaining physical plausibility and long-range coherence. We further introduce OWM, a benchmark for open-set motion prediction based on diverse in-the-wild videos, to evaluate accuracy and variability of predicted trajectory distributions under real-world uncertainty. Our method matches or surpasses dense simulators in predictive accuracy while achieving orders-of-magnitude higher sampling speed, making open-set future prediction both scalable and practical. Project page: http://compvis.github.io/myriad.

Diffusion language models (DLMs) have recently emerged as a promising alternative to autoregressive (AR) models, offering parallel decoding and controllable sampling dynamics while achieving competitive generation quality at scale. Despite this progress, the role of sampling mechanisms in shaping refusal behavior and jailbreak robustness remains poorly understood. In this work, we present a fundamental analytical framework for step-wise refusal dynamics, enabling comparison between AR and diffusion sampling. Our analysis reveals that the sampling strategy itself plays a central role in safety behavior, as a factor distinct from the underlying learned representations. Motivated by this analysis, we introduce the Step-Wise Refusal Internal Dynamics (SRI) signal, which supports interpretability and improved safety for both AR and DLMs. We demonstrate that the geometric structure of SRI captures internal recovery dynamics, and identifies anomalous behavior in harmful generations as cases of incomplete internal recovery that are not observable at the text level. This structure enables lightweight inference-time detectors that generalize to unseen attacks while matching or outperforming existing defenses with over 100times lower inference overhead.

This paper identifies significant redundancy in the query-key interactions within self-attention mechanisms of diffusion transformer models, particularly during the early stages of denoising diffusion steps. In response to this observation, we present a novel diffusion transformer framework incorporating an additional set of mediator tokens to engage with queries and keys separately. By modulating the number of mediator tokens during the denoising generation phases, our model initiates the denoising process with a precise, non-ambiguous stage and gradually transitions to a phase enriched with detail. Concurrently, integrating mediator tokens simplifies the attention module's complexity to a linear scale, enhancing the efficiency of global attention processes. Additionally, we propose a time-step dynamic mediator token adjustment mechanism that further decreases the required computational FLOPs for generation, simultaneously facilitating the generation of high-quality images within the constraints of varied inference budgets. Extensive experiments demonstrate that the proposed method can improve the generated image quality while also reducing the inference cost of diffusion transformers. When integrated with the recent work SiT, our method achieves a state-of-the-art FID score of 2.01. The source code is available at https://github.com/LeapLabTHU/Attention-Mediators.

Diffusion-based generative models have shown great potential for image synthesis, but there is a lack of research on the security and privacy risks they may pose. In this paper, we investigate the vulnerability of diffusion models to Membership Inference Attacks (MIAs), a common privacy concern. Our results indicate that existing MIAs designed for GANs or VAE are largely ineffective on diffusion models, either due to inapplicable scenarios (e.g., requiring the discriminator of GANs) or inappropriate assumptions (e.g., closer distances between synthetic samples and member samples). To address this gap, we propose Step-wise Error Comparing Membership Inference (SecMI), a query-based MIA that infers memberships by assessing the matching of forward process posterior estimation at each timestep. SecMI follows the common overfitting assumption in MIA where member samples normally have smaller estimation errors, compared with hold-out samples. We consider both the standard diffusion models, e.g., DDPM, and the text-to-image diffusion models, e.g., Latent Diffusion Models and Stable Diffusion. Experimental results demonstrate that our methods precisely infer the membership with high confidence on both of the two scenarios across multiple different datasets. Code is available at https://github.com/jinhaoduan/SecMI.

Long-context LLMs demand accurate inference at low latency, yet decoding becomes primarily constrained by KV cache as context grows. Prior pruning methods are largely context-agnostic: their token selection ignores step-wise relevance and local semantics, which undermines quality. Moreover, their irregular accesses and selection overheads yield only limited wall-clock speedups. To address this, we propose CHESS, an algorithm-system co-design KV-cache management system. Algorithmically, CHESS introduces a context-aware, hierarchical selection policy that dynamically reconstructs a coherent context for the current decoding. System-wise, coarse granularity selection eliminates expensive data movement, fully realizing practical acceleration from theoretical sparsity. Extensive evaluations demonstrate that CHESS surpasses Full-KV quality using only 1\% of the KV cache, delivers low-latency stable inference with up to 4.56times higher throughput, and consistently outperforms other strong baselines. Code is available at https://anonymous.4open.science/r/CHESS-9958/{https://anonymous.4open.science/r/CHESS/}.

Large Reasoning Models (LRMs) achieve remarkable performance by explicitly generating multi-step chains of thought, but this capability incurs substantial inference latency and computational cost. Collaborative inference offers a promising solution by selectively allocating work between lightweight and large models, yet a fundamental challenge remains: determining when a reasoning step requires the capacity of a large model or the efficiency of a small model. Existing routing strategies either rely on local token probabilities or post-hoc verification, introducing significant inference overhead. In this work, we propose a novel perspective on step-wise collaboration: the difficulty of a reasoning step can be inferred from its very first token. Inspired by the "Aha Moment" phenomenon in LRMs, we show that the entropy of the initial token serves as a strong predictor of step difficulty. Building on this insight, we introduce GlimpRouter, a training-free step-wise collaboration framework. GlimpRouter employs a lightweight model to generate only the first token of each reasoning step and routes the step to a larger model only when the initial token entropy exceeds a threshold. Experiments on multiple benchmarks demonstrate that our approach significantly reduces inference latency while preserving accuracy. For instance, GlimpRouter attains a substantial 10.7% improvement in accuracy while reducing inference latency by 25.9% compared to a standalone large model on AIME25. These results suggest a simple yet effective mechanism for reasoning: allocating computation based on a glimpse of thought rather than full-step evaluation.

Tool-augmented large language models (LLMs) leverage tools, often in the form of APIs, to enhance their reasoning capabilities on complex tasks, thus taking on the role of intelligent agents interacting with the real world. The recently introduced ToolLLaMA model by Qin et al. [2024] utilizes the depth-first search-based decision tree (DFSDT) method for reasoning with 16000+ real-world APIs, which effectively improves the planning and inferencing performance of tool-augmented LLMs compared to traditional chain reasoning approaches. However, their approach only employs successful paths from decision trees (also called inference trees) for supervised fine-tuning (SFT) during training, which does not fully exploit the advantages of the tree of thought. In this study, we propose an inference trajectory optimization framework based on the preference data extracted from decision trees to address this limitation. We first introduce a novel method for constructing preference data from the tree of thought, capitalizing on the failed explorations previously overlooked in the trees. Specifically, we generate an effective step-wise preference dataset, named ToolPreference, for tool use based on the ToolBench dataset. In the subsequent training phase, we first fine-tune the LLM with tool-usage expert trajectories and then use these step-wise preference pairs for direct preference optimization (DPO) to update the policy of the LLM, resulting in our ToolPrefer-LLaMA (TP-LLaMA) model. Our experiments demonstrate that by obtaining insights from errors in inference trees, TP-LLaMA significantly outperforms the baselines across almost all test scenarios by a large margin and exhibits better generalization capabilities with unseen APIs. At the same time, TP-LLaMA has also demonstrated superior reasoning efficiency compared to the baselines, making it more suitable for complex tool-usage reasoning tasks.

Diffusion Transformers (DiTs) have gained prominence for outstanding scalability and extraordinary performance in generative tasks. However, their considerable inference costs impede practical deployment. The feature cache mechanism, which involves storing and retrieving redundant computations across timesteps, holds promise for reducing per-step inference time in diffusion models. Most existing caching methods for DiT are manually designed. Although the learning-based approach attempts to optimize strategies adaptively, it suffers from discrepancies between training and inference, which hampers both the performance and acceleration ratio. Upon detailed analysis, we pinpoint that these discrepancies primarily stem from two aspects: (1) Prior Timestep Disregard, where training ignores the effect of cache usage at earlier timesteps, and (2) Objective Mismatch, where the training target (align predicted noise in each timestep) deviates from the goal of inference (generate the high-quality image). To alleviate these discrepancies, we propose HarmoniCa, a novel method that Harmonizes training and inference with a novel learning-based Caching framework built upon Step-Wise Denoising Training (SDT) and Image Error Proxy-Guided Objective (IEPO). Compared to the traditional training paradigm, the newly proposed SDT maintains the continuity of the denoising process, enabling the model to leverage information from prior timesteps during training, similar to the way it operates during inference. Furthermore, we design IEPO, which integrates an efficient proxy mechanism to approximate the final image error caused by reusing the cached feature. Therefore, IEPO helps balance final image quality and cache utilization, resolving the issue of training that only considers the impact of cache usage on the predicted output at each timestep.

Recent work has explored optimizing image signal processing (ISP) pipelines for various tasks by composing predefined modules and adapting them to task-specific objectives. However, jointly optimizing module sequences and parameters remains challenging. Existing approaches rely on neural architecture search (NAS) or step-wise reinforcement learning (RL), but NAS suffers from a training-inference mismatch, while step-wise RL leads to unstable training and high computational overhead due to stage-wise decision-making. We propose POS-ISP, a sequence-level RL framework that formulates modular ISP optimization as a global sequence prediction problem. Our method predicts the entire module sequence and its parameters in a single forward pass and optimizes the pipeline using a terminal task reward, eliminating the need for intermediate supervision and redundant executions. Experiments across multiple downstream tasks show that POS-ISP improves task performance while reducing computational cost, highlighting sequence-level optimization as a stable and efficient paradigm for task-aware ISP. The project page is available at https://w1jyun.github.io/POS-ISP

Recently, Test-Time Scaling (TTS) has gained increasing attention for improving LLM reasoning performance at test time without retraining the model. A notable TTS technique is Self-Consistency (SC), which generates multiple reasoning chains in parallel and selects the final answer via majority voting. While effective, the order-of-magnitude computational overhead limits its broad deployment. Prior attempts to accelerate SC mainly rely on model-based confidence scores or heuristics with limited empirical support. For the first time, we theoretically and empirically analyze the inefficiencies of SC and reveal actionable opportunities for improvement. Building on these insights, we propose Slim-SC, a step-wise pruning strategy that identifies and removes redundant chains using inter-chain similarity at the thought level. Experiments on three STEM reasoning datasets and two recent LLM architectures show that Slim-SC reduces inference latency and KVC usage by up to 45% and 26%, respectively, with R1-Distill, while maintaining or improving accuracy, thus offering a simple yet efficient TTS alternative for SC.

Test-time scaling has emerged as a promising paradigm in language modeling, leveraging additional computational resources at inference time to enhance model performance. In this work, we introduce R2-LLMs, a novel and versatile hierarchical retrieval-augmented reasoning framework designed to improve test-time scaling in large language models (LLMs) without requiring distillation from more advanced models to obtain chain-of-thought (CoT) training data. R2-LLMs enhances inference-time generalization by integrating dual-level retrieval-based in-context learning: (1) At the coarse level, our approach extracts abstract templates from complex reasoning problems and retrieves similar problem-answer pairs to facilitate high-level in-context learning; (2) At the fine level, during Monte Carlo Tree Search (MCTS), R2-LLMs efficiently retrieves analogous intermediate solution steps from reference mathematical problem datasets, refining step-wise reasoning with the aid of a process reward model (PRM) for scoring. R2-LLMs is a robust hierarchical reasoning-augmentation method that enhances in-context-level reasoning while seamlessly integrating with step-level tree search methods. Utilizing PRM, it refines both candidate generation and decision-making for improved reasoning accuracy. Empirical evaluations on the MATH500, GSM8K, and OlympiadBench-TO datasets achieve substantial relative improvement with an increase of up to 16% using LLaMA-3.1-8B compared to the baselines, showcasing the effectiveness of our approach in complex reasoning tasks.

Reasoning is an essential capacity for large language models (LLMs) to address complex tasks, where the identification of process errors is vital for improving this ability. Recently, process-level reward models (PRMs) were proposed to provide step-wise rewards that facilitate reinforcement learning and data production during training and guide LLMs toward correct steps during inference, thereby improving reasoning accuracy. However, existing benchmarks of PRMs are text-based and focus on error detection, neglecting other scenarios like reasoning search. To address this gap, we introduce MPBench, a comprehensive, multi-task, multimodal benchmark designed to systematically assess the effectiveness of PRMs in diverse scenarios. MPBench employs three evaluation paradigms, each targeting a specific role of PRMs in the reasoning process: (1) Step Correctness, which assesses the correctness of each intermediate reasoning step; (2) Answer Aggregation, which aggregates multiple solutions and selects the best one; and (3) Reasoning Process Search, which guides the search for optimal reasoning steps during inference. Through these paradigms, MPBench makes comprehensive evaluations and provides insights into the development of multimodal PRMs.

Diffusion models have emerged as a powerful class of generative models across various modalities, including image, video, and audio synthesis. However, their deployment is often limited by significant inference latency, primarily due to the inherently sequential nature of the denoising process. While existing parallelization strategies attempt to accelerate inference by distributing computation across multiple devices, they typically incur high communication overhead, hindering deployment on commercial hardware. To address this challenge, we propose ParaStep, a novel parallelization method based on a reuse-then-predict mechanism that parallelizes diffusion inference by exploiting similarity between adjacent denoising steps. Unlike prior approaches that rely on layer-wise or stage-wise communication, ParaStep employs lightweight, step-wise communication, substantially reducing overhead. ParaStep achieves end-to-end speedups of up to 3.88times on SVD, 2.43times on CogVideoX-2b, and 6.56times on AudioLDM2-large, while maintaining generation quality. These results highlight ParaStep as a scalable and communication-efficient solution for accelerating diffusion inference, particularly in bandwidth-constrained environments.

Reasoning and strategic behavior in social interactions is a hallmark of intelligence. This form of reasoning is significantly more sophisticated than isolated planning or reasoning tasks in static settings (e.g., math problem solving). In this paper, we present Strategic Planning, Interaction, and Negotiation (SPIN-Bench), a new multi-domain evaluation designed to measure the intelligence of strategic planning and social reasoning. While many existing benchmarks focus on narrow planning or single-agent reasoning, SPIN-Bench combines classical PDDL tasks, competitive board games, cooperative card games, and multi-agent negotiation scenarios in one unified framework. The framework includes both a benchmark as well as an arena to simulate and evaluate the variety of social settings to test reasoning and strategic behavior of AI agents. We formulate the benchmark SPIN-Bench by systematically varying action spaces, state complexity, and the number of interacting agents to simulate a variety of social settings where success depends on not only methodical and step-wise decision making, but also conceptual inference of other (adversarial or cooperative) participants. Our experiments reveal that while contemporary LLMs handle basic fact retrieval and short-range planning reasonably well, they encounter significant performance bottlenecks in tasks requiring deep multi-hop reasoning over large state spaces and socially adept coordination under uncertainty. We envision SPIN-Bench as a catalyst for future research on robust multi-agent planning, social reasoning, and human--AI teaming.

Reverse engineering in the realm of Computer-Aided Design (CAD) has been a longstanding aspiration, though not yet entirely realized. Its primary aim is to uncover the CAD process behind a physical object given its 3D scan. We propose CAD-SIGNet, an end-to-end trainable and auto-regressive architecture to recover the design history of a CAD model represented as a sequence of sketch-and-extrusion from an input point cloud. Our model learns visual-language representations by layer-wise cross-attention between point cloud and CAD language embedding. In particular, a new Sketch instance Guided Attention (SGA) module is proposed in order to reconstruct the fine-grained details of the sketches. Thanks to its auto-regressive nature, CAD-SIGNet not only reconstructs a unique full design history of the corresponding CAD model given an input point cloud but also provides multiple plausible design choices. This allows for an interactive reverse engineering scenario by providing designers with multiple next-step choices along with the design process. Extensive experiments on publicly available CAD datasets showcase the effectiveness of our approach against existing baseline models in two settings, namely, full design history recovery and conditional auto-completion from point clouds.

Large language models (LLMs) excel in many tasks but struggle to accurately quantify uncertainty in their generated responses. This limitation makes it challenging to detect misinformation and ensure reliable decision-making. Existing uncertainty quantification (UQ) methods for LLMs are primarily prompt-wise rather than response-wise, often requiring multiple response samples, which incurs high computational costs. Moreover, LLMs have been shown to be overconfident, particularly when using reasoning steps to derive their answers. In this work, we propose CoT-UQ, a response-wise UQ framework that integrates LLMs' inherent reasoning capabilities through Chain-of-Thought (CoT) into the UQ process. CoT-UQ captures critical information during inference by extracting keywords from each reasoning step and assessing their importance to the final answer. This key reasoning information is then aggregated to produce a final uncertainty estimate. We conduct extensive experiments based on LLaMA Family with model sizes varying from 8B to 13B across logical and mathematical reasoning tasks. Experimental results demonstrate that CoT-UQ significantly outperforms existing UQ methods, achieving an average improvement of 5.9% AUROC compared to current UQ methods. The code is available at: https://github.com/ZBox1005/CoT-UQ.

Pretrained Vision-Language-Action (VLA) policies have achieved strong single-step manipulation, but their inference remains largely memoryless, which is brittle in non-Markovian long-horizon settings with occlusion, state aliasing, and subtle post-action changes. Prior approaches inject history either by stacking frames, which scales visual tokens and latency while adding near-duplicate pixels, or by learning additional temporal interfaces that require (re-)training and may break the original single-frame inference graph. We present TempoFit, a training-free temporal retrofit that upgrades frozen VLAs through state-level memory. Our key insight is that prefix attention K/V already form a model-native, content-addressable runtime state; reusing them across timesteps introduces history without new tokens or trainable modules. TempoFit stores layer-wise FIFO prefix K/V at selected intermediate layers, performs parameter-free K-to-K retrieval with Frame-Gap Temporal Bias (FGTB), a fixed recency bias inspired by positional biases in NLP, to keep decisions present-dominant, and injects the retrieved context via pre-attention residual loading with norm-preserving rescaling to avoid distribution shift under frozen weights. On LIBERO-LONG, TempoFit improves strong pretrained backbones by up to +4.0% average success rate while maintaining near-real-time latency, and it transfers consistently to CALVIN and real-robot long-horizon tasks.

Recent studies on inverse problems have proposed posterior samplers that leverage the pre-trained diffusion models as powerful priors. These attempts have paved the way for using diffusion models in a wide range of inverse problems. However, the existing methods entail computationally demanding iterative sampling procedures and optimize a separate solution for each measurement, which leads to limited scalability and lack of generalization capability across unseen samples. To address these limitations, we propose a novel approach, Diffusion prior-based Amortized Variational Inference (DAVI) that solves inverse problems with a diffusion prior from an amortized variational inference perspective. Specifically, instead of separate measurement-wise optimization, our amortized inference learns a function that directly maps measurements to the implicit posterior distributions of corresponding clean data, enabling a single-step posterior sampling even for unseen measurements. Extensive experiments on image restoration tasks, e.g., Gaussian deblur, 4times super-resolution, and box inpainting with two benchmark datasets, demonstrate our approach's superior performance over strong baselines. Code is available at https://github.com/mlvlab/DAVI.

Transformer-based language models excel at both recall (retrieving memorized facts) and reasoning (performing multi-step inference), but whether these abilities rely on distinct internal mechanisms remains unclear. Distinguishing recall from reasoning is crucial for predicting model generalization, designing targeted evaluations, and building safer interventions that affect one ability without disrupting the other.We approach this question through mechanistic interpretability, using controlled datasets of synthetic linguistic puzzles to probe transformer models at the layer, head, and neuron level. Our pipeline combines activation patching and structured ablations to causally measure component contributions to each task type. Across two model families (Qwen and LLaMA), we find that interventions on distinct layers and attention heads lead to selective impairments: disabling identified "recall circuits" reduces fact-retrieval accuracy by up to 15\% while leaving reasoning intact, whereas disabling "reasoning circuits" reduces multi-step inference by a comparable margin. At the neuron level, we observe task-specific firing patterns, though these effects are less robust, consistent with neuronal polysemanticity.Our results provide the first causal evidence that recall and reasoning rely on separable but interacting circuits in transformer models. These findings advance mechanistic interpretability by linking circuit-level structure to functional specialization and demonstrate how controlled datasets and causal interventions can yield mechanistic insights into model cognition, informing safer deployment of large language models.

Masked diffusion language models (MDLMs) have recently emerged as a promising alternative to autoregressive (AR) language models, offering properties such as parallel decoding, flexible generation orders, and the potential for fewer inference steps. Despite these advantages, decoding strategies and reinforcement learning (RL) algorithms tailored for MDLMs remain underexplored. A naive approach is to directly transfer techniques well-established for AR models to MDLMs. However, this raises an immediate question: Is such a naive transfer truly optimal? For example, 1) Block-wise and semi-AR decoding strategies are not employed during the training of MDLMs, so why do they outperform full diffusion-style decoding during inference? 2) Applying RL algorithms designed for AR models directly to MDLMs exhibits a training-inference inconsistency, since MDLM decoding are non-causal (parallel). This results in inconsistencies between the rollout trajectory and the optimization trajectory. To address these challenges, we propose EOS Early Rejection (EOSER) and Ascending Step-Size (ASS) decoding scheduler, which unlock the potential of MDLMs to perform full diffusion-style decoding, achieving competitive performance with fewer decoding steps. Additionally, we introduce Consistency Trajectory Group Relative Policy Optimization (CJ-GRPO) for taming MDLMs, which emphasizes the consistency between rollout trajectory and optimization trajectory, and reduces the optimization errors caused by skip-step optimization. We conduct extensive experiments on reasoning tasks, such as mathematical and planning benchmarks, using LLaDA-8B-Instruct. The results demonstrate that the proposed EOSER and ASS mechanisms, together with CJ-GRPO, hold significant promise for effectively and efficiently taming MDLMs. Code: https://github.com/yjyddq/EOSER-ASS-RL.

Diffusion models deliver high-fidelity synthesis but remain slow due to iterative sampling. We empirically observe there exists feature invariance in deterministic sampling, and present InvarDiff, a training-free acceleration method that exploits the relative temporal invariance across timestep-scale and layer-scale. From a few deterministic runs, we compute a per-timestep, per-layer, per-module binary cache plan matrix and use a re-sampling correction to avoid drift when consecutive caches occur. Using quantile-based change metrics, this matrix specifies which module at which step is reused rather than recomputed. The same invariance criterion is applied at the step scale to enable cross-timestep caching, deciding whether an entire step can reuse cached results. During inference, InvarDiff performs step-first and layer-wise caching guided by this matrix. When applied to DiT and FLUX, our approach reduces redundant compute while preserving fidelity. Experiments show that InvarDiff achieves 2-3times end-to-end speed-ups with minimal impact on standard quality metrics. Qualitatively, we observe almost no degradation in visual quality compared with full computations.

Stepwise inference protocols, such as scratchpads and chain-of-thought, help language models solve complex problems by decomposing them into a sequence of simpler subproblems. Despite the significant gain in performance achieved via these protocols, the underlying mechanisms of stepwise inference have remained elusive. To address this, we propose to study autoregressive Transformer models on a synthetic task that embodies the multi-step nature of problems where stepwise inference is generally most useful. Specifically, we define a graph navigation problem wherein a model is tasked with traversing a path from a start to a goal node on the graph. Despite is simplicity, we find we can empirically reproduce and analyze several phenomena observed at scale: (i) the stepwise inference reasoning gap, the cause of which we find in the structure of the training data; (ii) a diversity-accuracy tradeoff in model generations as sampling temperature varies; (iii) a simplicity bias in the model's output; and (iv) compositional generalization and a primacy bias with in-context exemplars. Overall, our work introduces a grounded, synthetic framework for studying stepwise inference and offers mechanistic hypotheses that can lay the foundation for a deeper understanding of this phenomenon.

Inference-time optimization scales computation to derive deliberate reasoning steps for effective performance. While previous search-based strategies address the short-sightedness of auto-regressive generation, the vast search space leads to excessive exploration and insufficient exploitation. To strike an efficient balance to derive the optimal step, we frame the decoding strategy as foresight sampling, leveraging simulated future steps to obtain globally optimal step estimation. Built on it, we propose a novel decoding strategy, named phi-Decoding. To provide a precise and expressive estimation of step value, phi-Decoding approximates two distributions via foresight and clustering. Sampling from the joint distribution, the optimal steps can be selected for exploitation. To support adaptive computation allocation, we propose in-width and in-depth pruning strategies, featuring a light-weight solution to achieve inference efficiency. Extensive experiments across seven benchmarks show phi-Decoding outperforms strong baselines in both performance and efficiency. Additional analysis demonstrates its generalization across various LLMs and scalability across a wide range of computing budgets. The code will be released at https://github.com/xufangzhi/phi-Decoding, and the open-source PyPI package is coming soon.

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

Recent studies generally enhance MLLMs' reasoning capabilities via supervised fine-tuning on high-quality chain-of-thought reasoning data, which often leads models to merely imitate successful reasoning paths without understanding what the wrong reasoning paths are. In this work, we aim to enhance the MLLMs' reasoning ability beyond passively imitating positive reasoning paths. To this end, we design Step-wise Group Relative Policy Optimization (StepGRPO), a new online reinforcement learning framework that enables MLLMs to self-improve reasoning ability via simple, effective and dense step-wise rewarding. Specifically, StepGRPO introduces two novel rule-based reasoning rewards: Step-wise Reasoning Accuracy Reward (StepRAR) and Step-wise Reasoning Validity Reward (StepRVR). StepRAR rewards the reasoning paths that contain necessary intermediate reasoning steps via a soft key-step matching technique, while StepRAR rewards reasoning paths that follow a well-structured and logically consistent reasoning process through a reasoning completeness and logic evaluation strategy. With the proposed StepGRPO, we introduce R1-VL, a series of MLLMs with outstanding capabilities in step-by-step reasoning. Extensive experiments over 8 benchmarks demonstrate the superiority of our methods.

As models increasingly leverage multi-step reasoning strategies to solve complex problems, supervising the logical validity of these intermediate steps has become a critical research challenge. Process reward models address this by providing step-by-step feedback, but current approaches have two major drawbacks: they typically function as classifiers without providing explanations, and their reliance on supervised fine-tuning with static datasets limits generalization. Inspired by recent advances, we reframe stepwise reward modeling from a classification task to a reasoning task itself. We thus propose a generative judge that reasons about the policy model's reasoning steps (i.e., meta-reasons), outputting thinking tokens before delivering a final verdict. Our model, StepWiser, is trained by reinforcement learning using relative outcomes of rollouts. We show it provides (i) better judgment accuracy on intermediate steps than existing methods; (ii) can be used to improve the policy model at training time; and (iii) improves inference-time search.

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

Recent advancements in large language models (LLMs) have substantially enhanced their mathematical reasoning abilities. However, these models still struggle with complex problems that require multiple reasoning steps, frequently leading to logical or numerical errors. While numerical mistakes can be largely addressed by integrating a code interpreter, identifying logical errors within intermediate steps is more challenging. Moreover, manually annotating these steps for training is not only expensive but also labor-intensive, requiring the expertise of professional annotators. In our study, we introduce an innovative approach that bypasses the need for process annotations (from human or GPTs) by utilizing the Monte Carlo Tree Search (MCTS) framework. This technique automatically generates both the process supervision and the step-level evaluation signals. Our method iteratively trains the policy and value models, leveraging the capabilities of a well-pretrained LLM to progressively enhance its mathematical reasoning skills. Furthermore, we propose an efficient inference strategy-step-level beam search, where the value model is crafted to assist the policy model (i.e., LLM) in navigating more effective reasoning paths, rather than solely relying on prior probabilities. The experimental results on both in-domain and out-of-domain datasets demonstrate that even without GPT-4 or human-annotated process supervision, our AlphaMath framework achieves comparable or superior results to previous state-of-the-art methods.

Recent large language models (LLMs) can generate long Chain-of-Thought (CoT) at test time, enabling them to solve complex tasks. These reasoning steps in CoT are often assumed as a faithful reflection of the model's internal thinking process, and used to monitor unsafe intentions. However, we find many reasoning steps don't truly contribute to LLMs' prediction. We measure the step-wise causal influence of each reasoning step on the model's final prediction with a proposed True Thinking Score (TTS). We reveal that LLMs often interleave between true-thinking steps (which are genuinely used to produce the final output) and decorative-thinking steps (which only give the appearance of reasoning but have minimal causal impact). Notably, only a small subset of the total reasoning steps have a high TTS that causally drive the model's prediction: e.g., for the AIME dataset, only an average of 2.3% of reasoning steps in CoT have a TTS >= 0.7 (range: 0-1) under the Qwen-2.5 model. Furthermore, we identify a TrueThinking direction in the latent space of LLMs. By steering along or against this direction, we can force the model to perform or disregard certain CoT steps when computing the final result. Finally, we highlight that self-verification steps in CoT (i.e., aha moments) can also be decorative, where LLMs do not truly verify their solution. Steering along the TrueThinking direction can force internal reasoning over these steps, resulting in a change in the final results. Overall, our work reveals that LLMs often verbalize reasoning steps without actually performing them internally, which undermines both the efficiency of LLM reasoning and the trustworthiness of CoT.

Large Language Models (LLMs) can enhance reasoning capabilities through test-time scaling by generating multiple traces. However, the combination of lengthy reasoning traces with multiple sampling introduces substantial computation and high end-to-end latency. Prior work on accelerating this process has relied on similarity-based or confidence-based pruning, but these signals do not reliably indicate trace quality. To address these limitations, we propose STEP: Step-level Trace Evaluation and Pruning, a novel pruning framework that evaluates reasoning steps using hidden states and dynamically prunes unpromising traces during generation. We train a lightweight step scorer to estimate trace quality, and design a GPU memory-aware pruning strategy that triggers pruning as the GPU memory is saturated by KV cache to reduce end-to-end latency. Experiments across challenging reasoning benchmarks demonstrate that STEP reduces end-to-end inference latency by 45%-70% on average compared to self-consistency while also improving reasoning accuracy. Our code is released at: https://github.com/Supercomputing-System-AI-Lab/STEP

Large Reasoning Models have demonstrated remarkable performance with the advancement of test-time scaling techniques, which enhances prediction accuracy by generating multiple candidate responses and selecting the most reliable answer. While prior work has analyzed that internal model signals like confidence scores can partly indicate response correctness and exhibit a distributional correlation with accuracy, such distributional information has not been fully utilized to guide answer selection. Motivated by this, we propose DistriVoting, which incorporates distributional priors as another signal alongside confidence during voting. Specifically, our method (1) first decomposes the mixed confidence distribution into positive and negative components using Gaussian Mixture Models, (2) then applies a reject filter based on positive/negative samples from them to mitigate overlap between the two distributions. Besides, to further alleviate the overlap from the perspective of distribution itself, we propose SelfStepConf, which uses step-level confidence to dynamically adjust inference process, increasing the separation between the two distributions to improve the reliability of confidences in voting. Experiments across 16 models and 5 benchmarks demonstrate that our method significantly outperforms state-of-the-art approaches.

Efficient multi-hop reasoning requires Large Language Models (LLMs) based agents to acquire high-value external knowledge iteratively. Previous work has explored reinforcement learning (RL) to train LLMs to perform search-based document retrieval, achieving notable improvements in QA performance, but underperform on complex, multi-hop QA resulting from the sparse rewards from global signal only. To address this gap in existing research, we introduce StepSearch, a framework for search LLMs that trained with step-wise proximal policy optimization method. It consists of richer and more detailed intermediate search rewards and token-level process supervision based on information gain and redundancy penalties to better guide each search step. We constructed a fine-grained question-answering dataset containing sub-question-level search trajectories based on open source datasets through a set of data pipeline method. On standard multi-hop QA benchmarks, it significantly outperforms global-reward baselines, achieving 11.2% and 4.2% absolute improvements for 3B and 7B models over various search with RL baselines using only 19k training data, demonstrating the effectiveness of fine-grained, stepwise supervision in optimizing deep search LLMs. Our code will be released on https://github.com/Zillwang/StepSearch.

We introduce HRMCR (HAE-RAE Multi-Step Commonsense Reasoning), a benchmark designed to evaluate large language models' ability to perform multi-step reasoning in culturally specific contexts, focusing on Korean. The questions are automatically generated via templates and algorithms, requiring LLMs to integrate Korean cultural knowledge into sequential reasoning steps. Consistent with prior observations on emergent abilities, our experiments reveal that models trained on fewer than \(2 \cdot 10^{25}\) training FLOPs struggle to solve any questions, showing near-zero performance. Beyond this threshold, performance improves sharply. State-of-the-art models (e.g., O1) still score under 50\%, underscoring the difficulty of our tasks. Notably, stepwise analysis suggests the observed emergent behavior may stem from compounding errors across multiple steps rather than reflecting a genuinely new capability. We publicly release the benchmark and commit to regularly updating the dataset to prevent contamination.

Best-of-N decoding methods instruct large language models (LLMs) to generate multiple solutions, score each using a scoring function, and select the highest scored as the final answer to mathematical reasoning problems. However, this repeated independent process often leads to the same mistakes, making the selected solution still incorrect. We propose a novel prompting method named Stepwise Correction (StepCo) that helps LLMs identify and revise incorrect steps in their generated reasoning paths. It iterates verification and revision phases that employ a process-supervised verifier. The verify-then-revise process not only improves answer correctness but also reduces token consumption with fewer paths needed to generate. With StepCo, a series of LLMs demonstrate exceptional performance. Notably, using GPT-4o as the backend LLM, StepCo achieves an average accuracy of 94.1 across eight datasets, significantly outperforming the state-of-the-art Best-of-N method by +2.4, while reducing token consumption by 77.8%.

Large Language Models (LLMs) using Chain-of-Thought (CoT) prompting excel at complex reasoning but generate verbose thought processes with considerable redundancy, leading to increased inference costs and reduced efficiency. We introduce a novel CoT compression framework based on step entropy, a metric that quantifies the informational contribution of individual reasoning steps to identify redundancy. Through theoretical analysis and extensive empirical validation on mathematical reasoning benchmarks, we demonstrate that steps with low entropy are indeed highly redundant. Our experiments reveal that an astonishing 80\% of low-entropy intermediate steps can be pruned with minor degradation in the final answer accuracy across DeepSeek-R1-7B, 14B and Qwen3-8B. This finding sharply contrasts with random or high-entropy pruning, which severely impairs reasoning performance. Building on this, we propose a novel two-stage training strategy combining Supervised Fine-Tuning (SFT) and Group Relative Policy Optimization (GRPO) reinforcement learning. This approach enables LLMs to autonomously learn to generate compressed COTs during inference by strategically incorporating [SKIP] tokens. Our method significantly enhances LLM inference efficiency while rigorously preserving accuracy, offering profound implications for practical LLM deployment and a deeper understanding of reasoning structures.

Flow-based vision-language-action (VLA) models excel in embodied control but suffer from intractable likelihoods during multi-step sampling, hindering online reinforcement learning. We propose \textit{boldsymbolπ-StepNFT} (Step-wise Negative-aware Fine-Tuning), a critic-and-likelihood-free framework that requires only a single forward pass per optimization step and eliminates auxiliary value networks. We identify that wider exploration spaces necessitate finer-grained, step-wise guidance for alignment. Empirically, π-StepNFT unlocks latent potential on LIBERO with competitive few-shot robustness. Moreover, it achieves superior generalization on ManiSkill, outperforming value-based baselines in OOD scenarios by preventing overfitting to multimodal features. This property offers a scalable solution promising for complex real-world applications.

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

Large reasoning models improve with more test-time computation, but often overthink, producing unnecessarily long chains-of-thought that raise cost without improving accuracy. Prior reinforcement learning approaches typically rely on a single outcome reward with trajectory-level length penalties, which cannot distinguish essential from redundant reasoning steps and therefore yield blunt compression. Although recent work incorporates step-level signals, such as offline pruning, supervised data construction, or verifier-based intermediate rewards, reasoning length is rarely treated as an explicit step-level optimization objective during RL. We propose Step-wise Adaptive Penalization (SWAP), a fine-grained framework that allocates length reduction across steps based on intrinsic contribution. We estimate step importance from the model's on-policy log-probability improvement toward the correct answer, then treat excess length as a penalty mass redistributed to penalize low-importance steps more heavily while preserving high-importance reasoning. We optimize with a unified outcome-process advantage within group-relative policy optimization. Extensive experiments demonstrate that SWAP reduces reasoning length by 64.3% on average while improving accuracy by 5.7% relative to the base model.

Reasoning large language models (LLMs) have demonstrated superior capacities in solving complicated problems by generating long chain-of-thoughts (CoT), but such a lengthy CoT incurs high inference costs. In this study, we introduce ES-CoT, an inference-time method that shortens CoT generation by detecting answer convergence and stopping early with minimal performance loss. At the end of each reasoning step, we prompt the LLM to output its current final answer, denoted as a step answer. We then track the run length of consecutive identical step answers as a measure of answer convergence. Once the run length exhibits a sharp increase and exceeds a minimum threshold, the generation is terminated. We provide both empirical and theoretical support for this heuristic: step answers steadily converge to the final answer, and large run-length jumps reliably mark this convergence. Experiments on five reasoning datasets across three LLMs show that ES-CoT reduces the number of inference tokens by about 41\% on average while maintaining accuracy comparable to standard CoT. Further, ES-CoT integrates seamlessly with self-consistency prompting and remains robust across hyperparameter choices, highlighting it as a practical and effective approach for efficient reasoning.

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

Large language models (LLMs) have revolutionized the field of AI, demonstrating unprecedented capacity across various tasks. However, the inference process for LLMs comes with significant computational costs. In this paper, we propose an efficient LLM inference pipeline that harnesses the power of LLMs. Our approach begins by tapping into the potential of LLMs to accurately perceive and predict the response length with minimal overhead. By leveraging this information, we introduce an efficient sequence scheduling technique that groups queries with similar response lengths into micro-batches. We evaluate our approach on real-world instruction datasets using the LLaMA-based model, and our results demonstrate an impressive 86% improvement in inference throughput without compromising effectiveness. Notably, our method is orthogonal to other inference acceleration techniques, making it a valuable addition to many existing toolkits (e.g., FlashAttention, Quantization) for LLM inference.

The abundance of instructional videos and their narrations over the Internet offers an exciting avenue for understanding procedural activities. In this work, we propose to learn video representation that encodes both action steps and their temporal ordering, based on a large-scale dataset of web instructional videos and their narrations, without using human annotations. Our method jointly learns a video representation to encode individual step concepts, and a deep probabilistic model to capture both temporal dependencies and immense individual variations in the step ordering. We empirically demonstrate that learning temporal ordering not only enables new capabilities for procedure reasoning, but also reinforces the recognition of individual steps. Our model significantly advances the state-of-the-art results on step classification (+2.8% / +3.3% on COIN / EPIC-Kitchens) and step forecasting (+7.4% on COIN). Moreover, our model attains promising results in zero-shot inference for step classification and forecasting, as well as in predicting diverse and plausible steps for incomplete procedures. Our code is available at https://github.com/facebookresearch/ProcedureVRL.

Recent large language model (LLM) reasoning, despite its success, suffers from limited domain knowledge, susceptibility to hallucinations, and constrained reasoning depth, particularly in small-scale models deployed in resource-constrained environments. This paper presents the first investigation into integrating step-wise knowledge graph retrieval with step-wise reasoning to address these challenges, introducing a novel paradigm termed as graph-augmented reasoning. Our goal is to enable frozen, small-scale LLMs to retrieve and process relevant mathematical knowledge in a step-wise manner, enhancing their problem-solving abilities without additional training. To this end, we propose KG-RAR, a framework centered on process-oriented knowledge graph construction, a hierarchical retrieval strategy, and a universal post-retrieval processing and reward model (PRP-RM) that refines retrieved information and evaluates each reasoning step. Experiments on the Math500 and GSM8K benchmarks across six models demonstrate that KG-RAR yields encouraging results, achieving a 20.73\% relative improvement with Llama-3B on Math500.

How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case. Our contributions are two-fold. First, we show that a reparameterization of the variational lower bound yields a lower bound estimator that can be straightforwardly optimized using standard stochastic gradient methods. Second, we show that for i.i.d. datasets with continuous latent variables per datapoint, posterior inference can be made especially efficient by fitting an approximate inference model (also called a recognition model) to the intractable posterior using the proposed lower bound estimator. Theoretical advantages are reflected in experimental results.

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

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

Modern Large Language Models achieve impressive reasoning capabilities with long Chain of Thoughts, but they incur substantial computational cost during inference, and this motivates techniques to improve the performance-cost ratio. Among these techniques, Speculative Decoding accelerates inference by employing a fast but inaccurate draft model to autoregressively propose tokens, which are then verified in parallel by a more capable target model. However, due to unnecessary rejections caused by token mismatches in semantically equivalent steps, traditional token-level Speculative Decoding struggles in reasoning tasks. Although recent works have shifted to step-level semantic verification, which improve efficiency by accepting or rejecting entire reasoning steps, existing step-level methods still regenerate many rejected steps with little improvement, wasting valuable target compute. To address this challenge, we propose Arbitrage, a novel step-level speculative generation framework that routes generation dynamically based on the relative advantage between draft and target models. Instead of applying a fixed acceptance threshold, Arbitrage uses a lightweight router trained to predict when the target model is likely to produce a meaningfully better step. This routing approximates an ideal Arbitrage Oracle that always chooses the higher-quality step, achieving near-optimal efficiency-accuracy trade-offs. Across multiple mathematical reasoning benchmarks, Arbitrage consistently surpasses prior step-level Speculative Decoding baselines, reducing inference latency by up to sim2times at matched accuracy.

Recent years have seen considerable advancements in multi-step reasoning with Large Language Models (LLMs). The previous studies have elucidated the merits of integrating feedback or search mechanisms during model inference to improve the reasoning accuracy. The Process-Supervised Reward Model (PRM), typically furnishes LLMs with step-by-step feedback during the training phase, akin to Proximal Policy Optimization (PPO) or reject sampling. Our objective is to examine the efficacy of PRM in the inference phase to help discern the optimal solution paths for multi-step tasks such as mathematical reasoning and code generation. To this end, we propose a heuristic greedy search algorithm that employs the step-level feedback from PRM to optimize the reasoning pathways explored by LLMs. This tailored PRM demonstrated enhanced results compared to the Chain of Thought (CoT) on mathematical benchmarks like GSM8K and MATH. Additionally, to explore the versatility of our approach, we develop a novel method to automatically generate step-level reward dataset for coding tasks and observed similar improved performance in the code generation tasks. Thus highlighting the robust nature of our reward-model-based approach to inference for reasoning tasks.

Evaluating large language models (LLMs) on final-answer correctness is the dominant paradigm. This approach, however, provides a coarse signal for model improvement and overlooks the quality of the underlying reasoning process. We argue that a more granular evaluation of reasoning offers a more effective path to building robust models. We decompose reasoning quality into two dimensions: relevance and coherence. Relevance measures if a step is grounded in the problem; coherence measures if it follows logically from prior steps. To measure these aspects reliably, we introduce causal stepwise evaluation (CaSE). This method assesses each reasoning step using only its preceding context, which avoids hindsight bias. We validate CaSE against human judgments on our new expert-annotated benchmarks, MRa-GSM8K and MRa-MATH. More importantly, we show that curating training data with CaSE-evaluated relevance and coherence directly improves final task performance. Our work provides a scalable framework for analyzing, debugging, and improving LLM reasoning, demonstrating the practical value of moving beyond validity checks.

Current approaches for training Process Reward Models (PRMs) often involve breaking down responses into multiple reasoning steps using rule-based techniques, such as using predefined placeholder tokens or setting the reasoning step's length into a fixed size. These approaches overlook the fact that specific words do not typically mark true decision points in a text. To address this, we propose AdaptiveStep, a method that divides reasoning steps based on the model's confidence in predicting the next word. This division method provides more decision-making information at each step, enhancing downstream tasks, such as reward model learning. Moreover, our method does not require manual annotation. We demonstrate its effectiveness through experiments with AdaptiveStep-trained PRMs in mathematical reasoning and code generation tasks. Experimental results indicate that the outcome PRM achieves state-of-the-art Best-of-N performance, surpassing greedy search strategy with token-level value-guided decoding, while also reducing construction costs by over 30% compared to existing open-source PRMs. In addition, we provide a thorough analysis and case study on the PRM's performance, transferability, and generalization capabilities.

Large Language Models (LLMs) have achieved strong complex reasoning capabilities through Chain-of-Thought (CoT) reasoning. However, their reasoning patterns remain too complicated to analyze. While Sparse Autoencoders (SAEs) have emerged as a powerful tool for interpretability, existing approaches predominantly operate at the token level, creating a granularity mismatch when capturing more critical step-level information, such as reasoning direction and semantic transitions. In this work, we propose step-level sparse autoencoder (SSAE), which serves as an analytical tool to disentangle different aspects of LLMs' reasoning steps into sparse features. Specifically, by precisely controlling the sparsity of a step feature conditioned on its context, we form an information bottleneck in step reconstruction, which splits incremental information from background information and disentangles it into several sparsely activated dimensions. Experiments on multiple base models and reasoning tasks show the effectiveness of the extracted features. By linear probing, we can easily predict surface-level information, such as generation length and first token distribution, as well as more complicated properties, such as the correctness and logicality of the step. These observations indicate that LLMs should already at least partly know about these properties during generation, which provides the foundation for the self-verification ability of LLMs. The code is available at https://github.com/Miaow-Lab/SSAE

Large Reasoning Models (LRMs) demonstrate strong performance on complex tasks but often suffer from excessive verbosity, known as "overthinking." Existing solutions via reinforcement learning (RL) typically penalize generated tokens to promote conciseness. However, these methods encounter two challenges: responses with fewer tokens do not always correspond to fewer reasoning steps, and models may develop hacking behavior in later stages of training by discarding reasoning steps to minimize token usage. In this work, we introduce Step Pruner (SP), an RL framework that steers LRMs toward more efficient reasoning by favoring compact reasoning steps. Our step-aware reward function prioritizes correctness while imposing penalties for redundant steps, and withholds rewards for incorrect responses to prevent the reinforcement of erroneous reasoning. Moreover, we propose a dynamic stopping mechanism: when the length of any output step exceeds the upper limit, we halt updates to prevent hacking behavior caused by merging steps. Extensive experiments across four reasoning benchmarks demonstrate that SP achieves state-of-the-art accuracy while significantly reducing response length. For instance, on AIME24, SP reduces token usage by 69.7\%.

Recent advances in Chain-of-Thought (CoT) prompting have substantially improved the reasoning capabilities of Large Language Models (LLMs). However, these methods often suffer from overthinking, leading to unnecessarily lengthy or redundant reasoning traces. Existing approaches attempt to mitigate this issue through curating multiple reasoning chains for training LLMs, but their effectiveness is often constrained by the quality of the generated data and prone to overfitting. To address the challenge, we propose Reasoning Compression ThroUgh Stepwise Trials (ReCUT), a novel method aimed at balancing the accuracy and length of reasoning trajectory. Specifically, ReCUT employs a stepwise exploration mechanism and a long-short switched sampling strategy, enabling LLMs to incrementally generate diverse reasoning paths. These paths are evaluated and used to construct preference pairs to train two specialized models (Gemini LLMs)-one optimized for reasoning accuracy, the other for shorter reasoning. A final integrated model is obtained by interpolating the parameters of these two models. Experimental results across multiple math reasoning datasets and backbone models demonstrate that ReCUT significantly reduces reasoning lengths by approximately 30-50%, while maintaining or improving reasoning accuracy compared to various baselines. All codes and data will be released via https://github.com/NEUIR/ReCUT.

Recent large language models (LLMs) have witnessed significant advancement in various tasks, including mathematical reasoning and theorem proving. As these two tasks require strict and formal multi-step inference, they are appealing domains for exploring the reasoning ability of LLMs but still face important challenges. Previous studies such as Chain-of-Thought (CoT) have revealed the effectiveness of intermediate steps guidance. However, such step-wise annotation requires heavy labor, leading to insufficient training steps for current benchmarks. To fill this gap, this work introduces MUSTARD, a data generation framework that masters uniform synthesis of theorem and proof data of high quality and diversity. MUSTARD synthesizes data in three stages: (1) It samples a few mathematical concept seeds as the problem category. (2) Then, it prompts a generative language model with the sampled concepts to obtain both the problems and their step-wise formal solutions. (3) Lastly, the framework utilizes a proof assistant (e.g., Lean Prover) to filter the valid proofs. With the proposed MUSTARD, we present a theorem-and-proof benchmark MUSTARDSAUCE with 5,866 valid data points. Each data point contains an informal statement, an informal proof, and a translated formal proof that passes the prover validation. We perform extensive analysis and demonstrate that MUSTARD generates validated high-quality step-by-step data. We further apply the MUSTARDSAUCE for fine-tuning smaller language models. The fine-tuned Llama 2-7B achieves a 15.41% average relative performance gain in automated theorem proving, and 8.18% in math word problems. Codes and data are available at https://github.com/Eleanor-H/MUSTARD.

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

Training of the neural autoregressive density estimator (NADE) can be viewed as doing one step of probabilistic inference on missing values in data. We propose a new model that extends this inference scheme to multiple steps, arguing that it is easier to learn to improve a reconstruction in k steps rather than to learn to reconstruct in a single inference step. The proposed model is an unsupervised building block for deep learning that combines the desirable properties of NADE and multi-predictive training: (1) Its test likelihood can be computed analytically, (2) it is easy to generate independent samples from it, and (3) it uses an inference engine that is a superset of variational inference for Boltzmann machines. The proposed NADE-k is competitive with the state-of-the-art in density estimation on the two datasets tested.

Parameter inference, i.e. inferring the posterior distribution of the parameters of a statistical model given some data, is a central problem to many scientific disciplines. Generative models can be used as an alternative to Markov Chain Monte Carlo methods for conducting posterior inference, both in likelihood-based and simulation-based problems. However, assessing the accuracy of posteriors encoded in generative models is not straightforward. In this paper, we introduce `Tests of Accuracy with Random Points' (TARP) coverage testing as a method to estimate coverage probabilities of generative posterior estimators. Our method differs from previously-existing coverage-based methods, which require posterior evaluations. We prove that our approach is necessary and sufficient to show that a posterior estimator is accurate. We demonstrate the method on a variety of synthetic examples, and show that TARP can be used to test the results of posterior inference analyses in high-dimensional spaces. We also show that our method can detect inaccurate inferences in cases where existing methods fail.

Large Language Models (LLMs) have demonstrated remarkable potential in handling complex reasoning tasks by generating step-by-step rationales.Some methods have proven effective in boosting accuracy by introducing extra verifiers to assess these paths. However, existing verifiers, typically trained on binary-labeled reasoning paths, fail to fully utilize the relative merits of intermediate steps, thereby limiting the effectiveness of the feedback provided. To overcome this limitation, we propose Tree-based Preference Learning Verifier (Tree-PLV), a novel approach that constructs reasoning trees via a best-first search algorithm and collects step-level paired data for preference training. Compared to traditional binary classification, step-level preferences more finely capture the nuances between reasoning steps, allowing for a more precise evaluation of the complete reasoning path. We empirically evaluate Tree-PLV across a range of arithmetic and commonsense reasoning tasks, where it significantly outperforms existing benchmarks. For instance, Tree-PLV achieved substantial performance gains over the Mistral-7B self-consistency baseline on GSM8K (67.55% to 82.79%), MATH (17.00% to 26.80%), CSQA (68.14% to 72.97%), and StrategyQA (82.86% to 83.25%).Additionally, our study explores the appropriate granularity for applying preference learning, revealing that step-level guidance provides feedback that better aligns with the evaluation of the reasoning process.

State-of-the-art text-to-image models produce high-quality images, but inference remains expensive as generation requires several sequential ODE or denoising steps. Native one-step models aim to reduce this cost by mapping noise to an image in a single step, yet fair comparisons to multi-step systems are difficult because studies use mismatched sampling steps and different classifier-free guidance (CFG) settings, where CFG can shift FID, Inception Score, and CLIP-based alignment in opposing directions. It is also unclear how well one-step models scale to multi-step inference, and there is limited standardized out-of-distribution evaluation for label-ID-conditioned generators beyond ImageNet. To address this, We benchmark eight models spanning one-step flows (MeanFlow, Improved MeanFlow, SoFlow), multi-step baselines (RAE, Scale-RAE), and established systems (SiT, Stable Diffusion 3.5, FLUX.1) under a controlled class-conditional protocol on ImageNet validation, ImageNetV2, and reLAIONet, our new proofread out-of-distribution dataset aligned to ImageNet label IDs. Using FID, Inception Score, CLIP Score, and Pick Score, we show that FID-focused model development and CFG selection can be misleading in few-step regimes, where guidance changes can improve FID while degrading text-image alignment and human preference signals and worsening perceived quality. We further show that leading one-step models benefit from step scaling and become substantially more competitive under multi-step inference, although they still exhibit characteristic local distortions. To capture these tradeoffs, we introduce MinMax Harmonic Mean (MMHM), a composite proxy over all four metrics that stabilizes hyperparameter selection across guidance and step sweeps.

Chain-of-thought (CoT) reasoning has advanced medical visual question answering (VQA), yet most existing CoT rationales are free-form and fail to capture the structured reasoning process clinicians actually follow. This work asks: Can traceable, multi-step reasoning supervision improve reasoning accuracy and the interpretability of Medical VQA? To this end, we introduce Step-CoT, a large-scale medical reasoning dataset with expert-curated, structured multi-step CoT aligned to clinical diagnostic workflows, implicitly grounding the model's reasoning in radiographic evidence. Step-CoT comprises more than 10K real clinical cases and 70K VQA pairs organized around diagnostic workflows, providing supervised intermediate steps that guide models to follow valid reasoning trajectories. To effectively learn from Step-CoT, we further introduce a teacher-student framework with a dynamic graph-structured focusing mechanism that prioritizes diagnostically informative steps while filtering out less relevant contexts. Our experiments show that using Step-CoT can improve reasoning accuracy and interpretability. Benchmark: github.com/hahaha111111/Step-CoT. Dataset Card: huggingface.co/datasets/fl-15o/Step-CoT

Large language models (LLMs) have been shown to be capable of impressive few-shot generalisation to new tasks. However, they still tend to perform poorly on multi-step logical reasoning problems. Here we carry out a comprehensive evaluation of LLMs on 50 tasks that probe different aspects of logical reasoning. We show that language models tend to perform fairly well at single step inference or entailment tasks, but struggle to chain together multiple reasoning steps to solve more complex problems. In light of this, we propose a Selection-Inference (SI) framework that exploits pre-trained LLMs as general processing modules, and alternates between selection and inference to generate a series of interpretable, casual reasoning steps leading to the final answer. We show that a 7B parameter LLM used within the SI framework in a 5-shot generalisation setting, with no fine-tuning, yields a performance improvement of over 100% compared to an equivalent vanilla baseline on a suite of 10 logical reasoning tasks. The same model in the same setting even outperforms a significantly larger 280B parameter baseline on the same suite of tasks. Moreover, answers produced by the SI framework are accompanied by a causal natural-language-based reasoning trace, which has important implications for the safety and trustworthiness of the system.

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 introduce an approach aimed at enhancing the reasoning capabilities of Large Language Models (LLMs) through an iterative preference learning process inspired by the successful strategy employed by AlphaZero. Our work leverages Monte Carlo Tree Search (MCTS) to iteratively collect preference data, utilizing its look-ahead ability to break down instance-level rewards into more granular step-level signals. To enhance consistency in intermediate steps, we combine outcome validation and stepwise self-evaluation, continually updating the quality assessment of newly generated data. The proposed algorithm employs Direct Preference Optimization (DPO) to update the LLM policy using this newly generated step-level preference data. Theoretical analysis reveals the importance of using on-policy sampled data for successful self-improving. Extensive evaluations on various arithmetic and commonsense reasoning tasks demonstrate remarkable performance improvements over existing models. For instance, our approach outperforms the Mistral-7B Supervised Fine-Tuning (SFT) baseline on GSM8K, MATH, and ARC-C, with substantial increases in accuracy to 81.8% (+5.9%), 34.7% (+5.8%), and 76.4% (+15.8%), respectively. Additionally, our research delves into the training and inference compute tradeoff, providing insights into how our method effectively maximizes performance gains. Our code is publicly available at https://github.com/YuxiXie/MCTS-DPO.

Most Reading Comprehension methods limit themselves to queries which can be answered using a single sentence, paragraph, or document. Enabling models to combine disjoint pieces of textual evidence would extend the scope of machine comprehension methods, but currently there exist no resources to train and test this capability. We propose a novel task to encourage the development of models for text understanding across multiple documents and to investigate the limits of existing methods. In our task, a model learns to seek and combine evidence - effectively performing multi-hop (alias multi-step) inference. We devise a methodology to produce datasets for this task, given a collection of query-answer pairs and thematically linked documents. Two datasets from different domains are induced, and we identify potential pitfalls and devise circumvention strategies. We evaluate two previously proposed competitive models and find that one can integrate information across documents. However, both models struggle to select relevant information, as providing documents guaranteed to be relevant greatly improves their performance. While the models outperform several strong baselines, their best accuracy reaches 42.9% compared to human performance at 74.0% - leaving ample room for improvement.

Large language models (LLMs) have achieved significant performance gains via scaling up model sizes and/or data. However, recent evidence suggests diminishing returns from such approaches, motivating scaling the computation spent at inference time. Existing inference-time scaling methods, usually with reward models, cast the task as a search problem, which tends to be vulnerable to reward hacking as a consequence of approximation errors in reward models. In this paper, we instead cast inference-time scaling as a probabilistic inference task and leverage sampling-based techniques to explore the typical set of the state distribution of a state-space model with an approximate likelihood, rather than optimize for its mode directly. We propose a novel inference-time scaling approach by adapting particle-based Monte Carlo methods to this task. Our empirical evaluation demonstrates that our methods have a 4-16x better scaling rate over our deterministic search counterparts on various challenging mathematical reasoning tasks. Using our approach, we show that Qwen2.5-Math-1.5B-Instruct can surpass GPT-4o accuracy in only 4 rollouts, while Qwen2.5-Math-7B-Instruct scales to o1 level accuracy in only 32 rollouts. Our work not only presents an effective method to inference-time scaling, but also connects the rich literature in probabilistic inference with inference-time scaling of LLMs to develop more robust algorithms in future work. Code and further information is available at https://probabilistic-inference-scaling.github.io.

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

Mathematical reasoning represents a critical frontier in advancing large language models (LLMs). While step-by-step approaches have emerged as the dominant paradigm for mathematical problem-solving in LLMs, the quality of reasoning steps in training data fundamentally constrains the performance of the models. Recent studies has demonstrated that more detailed intermediate steps can enhance model performance, yet existing methods for step expansion either require more powerful external models or incur substantial computational costs. In this paper, we introduce MathFimer, a novel framework for mathematical reasoning step expansion inspired by the "Fill-in-the-middle" task from code completion. By decomposing solution chains into prefix-suffix pairs and training models to reconstruct missing intermediate steps, we develop a specialized model, MathFimer-7B, on our carefully curated NuminaMath-FIM dataset. We then apply these models to enhance existing mathematical reasoning datasets by inserting detailed intermediate steps into their solution chains, creating MathFimer-expanded versions. Through comprehensive experiments on multiple mathematical reasoning datasets, including MathInstruct, MetaMathQA and etc., we demonstrate that models trained on MathFimer-expanded data consistently outperform their counterparts trained on original data across various benchmarks such as GSM8K and MATH. Our approach offers a practical, scalable solution for enhancing mathematical reasoning capabilities in LLMs without relying on powerful external models or expensive inference procedures.

Large reasoning models have recently demonstrated strong performance on complex tasks that require long chain-of-thought reasoning, through supervised fine-tuning on large-scale and high-quality datasets. To construct such datasets, existing pipelines generate long reasoning data from more capable Large Language Models (LLMs) and apply manually heuristic or naturalness-based selection methods to filter high-quality samples. Despite the proven effectiveness of naturalness-based data selection, which ranks data by the average log probability assigned by LLMs, our analysis shows that, when applied to LLM reasoning datasets, it systematically prefers samples with longer reasoning steps (i.e., more tokens per step) rather than higher-quality ones, a phenomenon we term step length confounding. Through quantitative analysis, we attribute this phenomenon to low-probability first tokens in reasoning steps; longer steps dilute their influence, thereby inflating the average log probabilities. To address this issue, we propose two variant methods: ASLEC-DROP, which drops first-token probabilities when computing average log probability, and ASLEC-CASL, which applies a causal debiasing regression to remove the first tokens' confounding effect. Experiments across four LLMs and five evaluation benchmarks demonstrate the effectiveness of our approach in mitigating the step length confounding problem.

Multimodal Retrieval-Augmented Generation (MRAG) has shown promise in mitigating hallucinations in Multimodal Large Language Models (MLLMs) by incorporating external knowledge during generation. Existing MRAG methods typically adopt a static retrieval pipeline that fetches relevant information from multiple Knowledge Bases (KBs), followed by a refinement step. However, these approaches overlook the reasoning and planning capabilities of MLLMs to dynamically determine how to interact with different KBs during the reasoning process. To address this limitation, we propose R1-Router, a novel MRAG framework that learns to decide when and where to retrieve knowledge based on the evolving reasoning state. Specifically, R1-Router can generate follow-up queries according to the current reasoning step, routing these intermediate queries to the most suitable KB, and integrating external knowledge into a coherent reasoning trajectory to answer the original query. Furthermore, we introduce Step-wise Group Relative Policy Optimization (Step-GRPO), a tailored reinforcement learning algorithm that assigns step-specific rewards to optimize the reasoning behavior of MLLMs. Experimental results on various open-domain QA benchmarks across multiple modalities demonstrate that R1-Router outperforms baseline models by over 7%. Further analysis shows that R1-Router can adaptively and effectively leverage diverse KBs, reducing unnecessary retrievals and improving both efficiency and accuracy.

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

Test-time scaling has proven effective in further enhancing the performance of pretrained Large Language Models (LLMs). However, mainstream post-training methods (i.e., reinforcement learning (RL) with chain-of-thought (CoT) reasoning) often incur substantial computational overhead due to auxiliary models and overthinking. In this paper, we empirically reveal that the incorrect answers partially stem from verbose reasoning processes lacking correct self-fix, where errors accumulate across multiple reasoning steps. To this end, we propose Self-traced Step-wise Preference Optimization (SSPO), a pluggable RL process supervision framework that enables fine-grained optimization of each reasoning step. Specifically, SSPO requires neither auxiliary models nor stepwise manual annotations. Instead, it leverages step-wise preference signals generated by the model itself to guide the optimization process for reasoning compression. Experiments demonstrate that the generated reasoning sequences from SSPO are both accurate and succinct, effectively mitigating overthinking behaviors without compromising model performance across diverse domains and languages.

We propose a novel hierarchical Bayesian model for learning with a large (possibly infinite) number of tasks/episodes, which suits well the few-shot meta learning problem. We consider episode-wise random variables to model episode-specific target generative processes, where these local random variables are governed by a higher-level global random variate. The global variable helps memorize the important information from historic episodes while controlling how much the model needs to be adapted to new episodes in a principled Bayesian manner. Within our model framework, the prediction on a novel episode/task can be seen as a Bayesian inference problem. However, a main obstacle in learning with a large/infinite number of local random variables in online nature, is that one is not allowed to store the posterior distribution of the current local random variable for frequent future updates, typical in conventional variational inference. We need to be able to treat each local variable as a one-time iterate in the optimization. We propose a Normal-Inverse-Wishart model, for which we show that this one-time iterate optimization becomes feasible due to the approximate closed-form solutions for the local posterior distributions. The resulting algorithm is more attractive than the MAML in that it is not required to maintain computational graphs for the whole gradient optimization steps per episode. Our approach is also different from existing Bayesian meta learning methods in that unlike dealing with a single random variable for the whole episodes, our approach has a hierarchical structure that allows one-time episodic optimization, desirable for principled Bayesian learning with many/infinite tasks. The code is available at https://github.com/minyoungkim21/niwmeta.

We present extensive empirical evidence showing that current Bayesian simulation-based inference algorithms can produce computationally unfaithful posterior approximations. Our results show that all benchmarked algorithms -- (Sequential) Neural Posterior Estimation, (Sequential) Neural Ratio Estimation, Sequential Neural Likelihood and variants of Approximate Bayesian Computation -- can yield overconfident posterior approximations, which makes them unreliable for scientific use cases and falsificationist inquiry. Failing to address this issue may reduce the range of applicability of simulation-based inference. For this reason, we argue that research efforts should be made towards theoretical and methodological developments of conservative approximate inference algorithms and present research directions towards this objective. In this regard, we show empirical evidence that ensembling posterior surrogates provides more reliable approximations and mitigates the issue.

Solving complex tasks usually requires LLMs to generate long multi-step reasoning chains. Previous work has shown that verifying the correctness of individual reasoning steps can further improve the performance and efficiency of LLMs on such tasks and enhance solution interpretability. However, existing verification approaches, such as Process Reward Models (PRMs), are either computationally expensive, limited to specific domains, or require large-scale human or model-generated annotations. Thus, we propose a lightweight alternative for step-level reasoning verification based on data-driven uncertainty scores. We train transformer-based uncertainty quantification heads (UHeads) that use the internal states of a frozen LLM to estimate the uncertainty of its reasoning steps during generation. The approach is fully automatic: target labels are generated either by another larger LLM (e.g., DeepSeek R1) or in a self-supervised manner by the original model itself. UHeads are both effective and lightweight, containing less than 10M parameters. Across multiple domains, including mathematics, planning, and general knowledge question answering, they match or even surpass the performance of PRMs that are up to 810x larger. Our findings suggest that the internal states of LLMs encode their uncertainty and can serve as reliable signals for reasoning verification, offering a promising direction toward scalable and generalizable introspective LLMs.

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.

Learning dynamics, which describes how the learning of specific training examples influences the model's predictions on other examples, gives us a powerful tool for understanding the behavior of deep learning systems. We study the learning dynamics of large language models during different types of finetuning, by analyzing the step-wise decomposition of how influence accumulates among different potential responses. Our framework allows a uniform interpretation of many interesting observations about the training of popular algorithms for both instruction tuning and preference tuning. In particular, we propose a hypothetical explanation of why specific types of hallucination are strengthened after finetuning, e.g., the model might use phrases or facts in the response for question B to answer question A, or the model might keep repeating similar simple phrases when generating responses. We also extend our framework and highlight a unique "squeezing effect" to explain a previously observed phenomenon in off-policy direct preference optimization (DPO), where running DPO for too long makes even the desired outputs less likely. This framework also provides insights into where the benefits of on-policy DPO and other variants come from. The analysis not only provides a novel perspective of understanding LLM's finetuning but also inspires a simple, effective method to improve alignment performance.

Training large language models to reason with search engines via reinforcement learning is hindered by a fundamental credit assignment problem: existing methods such as Search-R1 provide only a sparse outcome reward after an entire multi-step trajectory, making it infeasible to attribute success or failure to individual reasoning and retrieval decisions. Process-reward methods like StepSearch alleviate this by introducing step-level supervision, but rely on heuristic rewards such as TF-IDF overlap with gold documents, and still sample k complete trajectories per example, retaining high gradient variance. We propose SLATE, a framework built on two complementary ideas: (1) truncated step-level sampling, which generates k trajectories that share a common prefix and differ only at the next step, and (2) dense LLM-as-judge rewards, which replace heuristic scoring with a capable LLM evaluator that assesses the quality of each reasoning step, search query, and answer, providing richer and more reliable supervision. We theoretically prove that under the same dense reward structure, truncated sampling reduces the variance of advantage estimates by up to a factor of T compared to full-trajectory sampling for T-step trajectories, yielding lower-variance, better-targeted policy gradients. Experiments on seven QA benchmarks confirm that SLATE consistently outperforms both sparse-reward and process-reward baselines, with the largest gains on harder multi-hop tasks and smaller models.

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

We introduce the Self-Evaluating Model (Self-E), a novel, from-scratch training approach for text-to-image generation that supports any-step inference. Self-E learns from data similarly to a Flow Matching model, while simultaneously employing a novel self-evaluation mechanism: it evaluates its own generated samples using its current score estimates, effectively serving as a dynamic self-teacher. Unlike traditional diffusion or flow models, it does not rely solely on local supervision, which typically necessitates many inference steps. Unlike distillation-based approaches, it does not require a pretrained teacher. This combination of instantaneous local learning and self-driven global matching bridges the gap between the two paradigms, enabling the training of a high-quality text-to-image model from scratch that excels even at very low step counts. Extensive experiments on large-scale text-to-image benchmarks show that Self-E not only excels in few-step generation, but is also competitive with state-of-the-art Flow Matching models at 50 steps. We further find that its performance improves monotonically as inference steps increase, enabling both ultra-fast few-step generation and high-quality long-trajectory sampling within a single unified model. To our knowledge, Self-E is the first from-scratch, any-step text-to-image model, offering a unified framework for efficient and scalable generation.

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

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

Sequential Bayesian inference can be used for continual learning to prevent catastrophic forgetting of past tasks and provide an informative prior when learning new tasks. We revisit sequential Bayesian inference and test whether having access to the true posterior is guaranteed to prevent catastrophic forgetting in Bayesian neural networks. To do this we perform sequential Bayesian inference using Hamiltonian Monte Carlo. We propagate the posterior as a prior for new tasks by fitting a density estimator on Hamiltonian Monte Carlo samples. We find that this approach fails to prevent catastrophic forgetting demonstrating the difficulty in performing sequential Bayesian inference in neural networks. From there we study simple analytical examples of sequential Bayesian inference and CL and highlight the issue of model misspecification which can lead to sub-optimal continual learning performance despite exact inference. Furthermore, we discuss how task data imbalances can cause forgetting. From these limitations, we argue that we need probabilistic models of the continual learning generative process rather than relying on sequential Bayesian inference over Bayesian neural network weights. In this vein, we also propose a simple baseline called Prototypical Bayesian Continual Learning, which is competitive with state-of-the-art Bayesian continual learning methods on class incremental continual learning vision benchmarks.

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.

Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as process reward models (PRMs) or self-consistency operate as opaque boxes and do not provide checkable evidence for their judgments, possibly limiting their effectiveness. To address this issue, we draw inspiration from the idea that "the gold standard for supporting a mathematical claim is to provide a proof". We propose a retrospective, step-aware formal verification framework Safe. Rather than assigning arbitrary scores, we strive to articulate mathematical claims in formal mathematical language Lean 4 at each reasoning step and provide formal proofs to identify hallucinations. We evaluate our framework Safe across multiple language models and various mathematical datasets, demonstrating a significant performance improvement while offering interpretable and verifiable evidence. We also propose FormalStep as a benchmark for step correctness theorem proving with 30,809 formal statements. To the best of our knowledge, our work represents the first endeavor to utilize formal mathematical language Lean 4 for verifying natural language content generated by LLMs, aligning with the reason why formal mathematical languages were created in the first place: to provide a robust foundation for hallucination-prone human-written proofs.

Diffusion Probabilistic Models (DPM) have shown remarkable efficacy in the synthesis of high-quality images. However, their inference process characteristically requires numerous, potentially hundreds, of iterative steps, which could exaggerate the problem of exposure bias due to the training and inference discrepancy. Previous work has attempted to mitigate this issue by perturbing inputs during training, which consequently mandates the retraining of the DPM. In this work, we conduct a systematic study of exposure bias in DPM and, intriguingly, we find that the exposure bias could be alleviated with a novel sampling method that we propose, without retraining the model. We empirically and theoretically show that, during inference, for each backward time step t and corresponding state x_t, there might exist another time step t_s which exhibits superior coupling with x_t. Based on this finding, we introduce a sampling method named Time-Shift Sampler. Our framework can be seamlessly integrated to existing sampling algorithms, such as DDPM, DDIM and other high-order solvers, inducing merely minimal additional computations. Experimental results show our method brings significant and consistent improvements in FID scores on different datasets and sampling methods. For example, integrating Time-Shift Sampler to F-PNDM yields a FID=3.88, achieving 44.49\% improvements as compared to F-PNDM, on CIFAR-10 with 10 sampling steps, which is more performant than the vanilla DDIM with 100 sampling steps. Our code is available at https://github.com/Mingxiao-Li/TS-DPM.

Chain-of-thought (CoT) reasoning enables large language models (LLMs) to move beyond fast System-1 responses and engage in deliberative System-2 reasoning. However, this comes at the cost of significant inefficiency due to verbose intermediate output. Recent latent-space reasoning methods improve efficiency by operating on hidden states without decoding into language, yet they treat all steps uniformly, failing to distinguish critical deductions from auxiliary steps and resulting in suboptimal use of computational resources. In this paper, we propose System-1.5 Reasoning, an adaptive reasoning framework that dynamically allocates computation across reasoning steps through shortcut paths in latent space. Specifically, System-1.5 Reasoning introduces two types of dynamic shortcuts. The model depth shortcut (DS) adaptively reasons along the vertical depth by early exiting non-critical tokens through lightweight adapter branches, while allowing critical tokens to continue through deeper Transformer layers. The step shortcut (SS) reuses hidden states across the decoding steps to skip trivial steps and reason horizontally in latent space. Training System-1.5 Reasoning involves a two-stage self-distillation process: first distilling natural language CoT into latent-space continuous thought, and then distilling full-path System-2 latent reasoning into adaptive shortcut paths (System-1.5 Reasoning). Experiments on reasoning tasks demonstrate the superior performance of our method. For example, on GSM8K, System-1.5 Reasoning achieves reasoning performance comparable to traditional CoT fine-tuning methods while accelerating inference by over 20x and reducing token generation by 92.31% on average.

Chain of thought reasoning has demonstrated remarkable success in large language models, yet its adaptation to vision-language reasoning remains an open challenge with unclear best practices. Existing attempts typically employ reasoning chains at a coarse-grained level, which struggles to perform fine-grained structured reasoning and, more importantly, are difficult to evaluate the reward and quality of intermediate reasoning. In this work, we delve into chain of step reasoning for vision-language models, enabling assessing reasoning step quality accurately and leading to effective reinforcement learning and inference-time scaling with fine-grained rewards. We present a simple, effective, and fully transparent framework, including the step-level reasoning data, process reward model (PRM), and reinforcement learning training. With the proposed approaches, our models set strong baselines with consistent improvements on challenging vision-language benchmarks. More importantly, we conduct a thorough empirical analysis and ablation study, unveiling the impact of each component and several intriguing properties of inference-time scaling. We believe this paper serves as a baseline for vision-language models and offers insights into more complex multimodal reasoning. Our dataset, PRM, and code will be available at https://github.com/baaivision/CoS.

Long-form generation is crucial for academic writing papers and repo-level code generation. Despite this, current models, including GPT-4o, still exhibit unsatisfactory performance. Existing methods that utilize preference learning with outcome supervision often fail to provide detailed feedback for extended contexts. This shortcoming can lead to content that does not fully satisfy query requirements, resulting in issues like length deviations, and diminished quality. In this paper, we propose enhancing long-form generation by incorporating process supervision. We employ Monte Carlo Tree Search to gather stepwise preference pairs, utilizing a global memory pool to maintain consistency. To address the issue of suboptimal candidate selection, we integrate external critiques to refine and improve the quality of the preference pairs. Finally, we apply step-level DPO using the collected stepwise preference pairs. Experimental results show that our method improves length and quality on long-form generation benchmarks, with almost lossless performance on general benchmarks across various model backbones.

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

Recent innovations on hardware (e.g. Nvidia A100) have motivated learning N:M structured sparsity masks from scratch for fast model inference. However, state-of-the-art learning recipes in this regime (e.g. SR-STE) are proposed for non-adaptive optimizers like momentum SGD, while incurring non-trivial accuracy drop for Adam-trained models like attention-based LLMs. In this paper, we first demonstrate such gap origins from poorly estimated second moment (i.e. variance) in Adam states given by the masked weights. We conjecture that learning N:M masks with Adam should take the critical regime of variance estimation into account. In light of this, we propose STEP, an Adam-aware recipe that learns N:M masks with two phases: first, STEP calculates a reliable variance estimate (precondition phase) and subsequently, the variance remains fixed and is used as a precondition to learn N:M masks (mask-learning phase). STEP automatically identifies the switching point of two phases by dynamically sampling variance changes over the training trajectory and testing the sample concentration. Empirically, we evaluate STEP and other baselines such as ASP and SR-STE on multiple tasks including CIFAR classification, machine translation and LLM fine-tuning (BERT-Base, GPT-2). We show STEP mitigates the accuracy drop of baseline recipes and is robust to aggressive structured sparsity ratios.

The rapid advancements in large Language models (LLMs) have significantly enhanced their reasoning capabilities, driven by various strategies such as multi-agent collaboration. However, unlike the well-established performance improvements achieved through scaling data and model size, the scaling of reasoning in LLMs is more complex and can even negatively impact reasoning performance, introducing new challenges in model alignment and robustness. In this survey, we provide a comprehensive examination of scaling in LLM reasoning, categorizing it into multiple dimensions and analyzing how and to what extent different scaling strategies contribute to improving reasoning capabilities. We begin by exploring scaling in input size, which enables LLMs to process and utilize more extensive context for improved reasoning. Next, we analyze scaling in reasoning steps that improves multi-step inference and logical consistency. We then examine scaling in reasoning rounds, where iterative interactions refine reasoning outcomes. Furthermore, we discuss scaling in training-enabled reasoning, focusing on optimization through iterative model improvement. Finally, we review applications of scaling across domains and outline future directions for further advancing LLM reasoning. By synthesizing these diverse perspectives, this survey aims to provide insights into how scaling strategies fundamentally enhance the reasoning capabilities of LLMs and further guide the development of next-generation AI systems.

When leveraging language models for reasoning tasks, generating explicit chain-of-thought (CoT) steps often proves essential for achieving high accuracy in final outputs. In this paper, we investigate if models can be taught to internalize these CoT steps. To this end, we propose a simple yet effective method for internalizing CoT steps: starting with a model trained for explicit CoT reasoning, we gradually remove the intermediate steps and finetune the model. This process allows the model to internalize the intermediate reasoning steps, thus simplifying the reasoning process while maintaining high performance. Our approach enables a GPT-2 Small model to solve 9-by-9 multiplication with up to 99% accuracy, whereas standard training cannot solve beyond 4-by-4 multiplication. Furthermore, our method proves effective on larger language models, such as Mistral 7B, achieving over 50% accuracy on GSM8K without producing any intermediate steps.

The outstanding capabilities of large language models (LLMs) render them a crucial component in various autonomous agent systems. While traditional methods depend on the inherent knowledge of LLMs without fine-tuning, more recent approaches have shifted toward the reinforcement learning strategy to further enhance agents' ability to solve complex interactive tasks with environments and tools. However, previous approaches are constrained by the sparse reward issue, where existing datasets solely provide a final scalar reward for each multi-step reasoning chain, potentially leading to ineffectiveness and inefficiency in policy learning. In this paper, we introduce StepAgent, which utilizes step-wise reward to optimize the agent's reinforcement learning process. Inheriting the spirit of novice-to-expert theory, we first compare the actions of the expert and the agent to automatically generate intermediate rewards for fine-grained optimization. Additionally, we propose implicit-reward and inverse reinforcement learning techniques to facilitate agent reflection and policy adjustment. Further theoretical analysis demonstrates that the action distribution of the agent can converge toward the expert action distribution over multiple training cycles. Experimental results across various datasets indicate that StepAgent outperforms existing baseline methods.

Reinforcement Learning with Verifiable Rewards (RLVR) elicits long chain-of-thought reasoning in large language models (LLMs), but outcome-based rewards lead to coarse-grained advantage estimation. While existing approaches improve RLVR via token-level entropy or sequence-level length control, they lack a semantically grounded, step-level measure of reasoning progress. As a result, LLMs fail to distinguish necessary deduction from redundant verification: they may continue checking after reaching a correct solution and, in extreme cases, overturn a correct trajectory into an incorrect final answer. To remedy the lack of process supervision, we introduce a training-free probing mechanism that extracts intermediate confidence and correctness and combines them into a Step Potential signal that explicitly estimates the reasoning state at each step. Building on this signal, we propose Step Potential Advantage Estimation (SPAE), a fine-grained credit assignment method that amplifies potential gains, penalizes potential drops, and applies penalty after potential saturates to encourage timely termination. Experiments across multiple benchmarks show SPAE consistently improves accuracy while substantially reducing response length, outperforming strong RL baselines and recent efficient reasoning and token-level advantage estimation methods. The code is available at https://github.com/cii030/SPAE-RL.

Language agents have become a promising solution to complex interactive tasks. One of the key ingredients to the success of language agents is the reward model on the trajectory of the agentic workflow, which provides valuable guidance during training or inference. However, due to the lack of annotations of intermediate interactions, most existing works use an outcome reward model to optimize policies across entire trajectories. This may lead to sub-optimal policies and hinder the overall performance. To address this, we propose QLASS (Q-guided Language Agent Stepwise Search), to automatically generate annotations by estimating Q-values in a stepwise manner for open language agents. By introducing a reasoning tree and performing process reward modeling, QLASS provides effective intermediate guidance for each step. With the stepwise guidance, we propose a Q-guided generation strategy to enable language agents to better adapt to long-term value, resulting in significant performance improvement during model inference on complex interactive agent tasks. Notably, even with almost half the annotated data, QLASS retains strong performance, demonstrating its efficiency in handling limited supervision. We also empirically demonstrate that QLASS can lead to more effective decision making through qualitative analysis. We will release our code and data.

We introduce MorphNLI, a modular step-by-step approach to natural language inference (NLI). When classifying the premise-hypothesis pairs into {entailment, contradiction, neutral}, we use a language model to generate the necessary edits to incrementally transform (i.e., morph) the premise into the hypothesis. Then, using an off-the-shelf NLI model we track how the entailment progresses with these atomic changes, aggregating these intermediate labels into a final output. We demonstrate the advantages of our proposed method particularly in realistic cross-domain settings, where our method always outperforms strong baselines with improvements up to 12.6% (relative). Further, our proposed approach is explainable as the atomic edits can be used to understand the overall NLI label.

Failure attribution in multi-agent systems -- pinpointing the exact step where a decisive error occurs -- is a critical yet unsolved challenge. Current methods treat this as a pattern recognition task over long conversation logs, leading to critically low step-level accuracy (below 17\%), which renders them impractical for debugging complex systems. Their core weakness is a fundamental inability to perform robust counterfactual reasoning: to determine if correcting a single action would have actually averted the task failure. To bridge this counterfactual inference gap, we introduce Abduct-Act-Predict (A2P) Scaffolding, a novel agent framework that transforms failure attribution from pattern recognition into a structured causal inference task. A2P explicitly guides a large language model through a formal three-step reasoning process within a single inference pass: (1) Abduction, to infer the hidden root causes behind an agent's actions; (2) Action, to define a minimal corrective intervention; and (3) Prediction, to simulate the subsequent trajectory and verify if the intervention resolves the failure. This structured approach leverages the holistic context of the entire conversation while imposing a rigorous causal logic on the model's analysis. Our extensive experiments on the Who\&When benchmark demonstrate its efficacy. On the Algorithm-Generated dataset, A2P achieves 47.46\% step-level accuracy, a 2.85times improvement over the 16.67\% of the baseline. On the more complex Hand-Crafted dataset, it achieves 29.31\% step accuracy, a 2.43times improvement over the baseline's 12.07\%. By reframing the problem through a causal lens, A2P Scaffolding provides a robust, verifiable, and significantly more accurate solution for automated failure attribution. Ours code are released at https://github.com/ResearAI/A2P.

It has been well-known that Chain-of-Thought can remarkably enhance LLMs' performance on complex tasks. However, because it also introduces slower inference speeds and higher computational costs, many researches have attempted to use implicit CoT, which does not need LLMs to explicitly generate the intermediate steps. But there is still gap between their efficacy and typical explicit CoT methods. This leaves us a doubt that, does implicit CoT really equal to explicit CoT? Therefore, in this study, we address this question through experiments. We probe the information of intermediate steps from the model's hidden states when it is performing implicit CoT. The results surprisingly indicate that LLMs hardly think about intermediate steps, suggesting they may just rely on experience rather than strict step-by-step reasoning. Moreover, we find LLMs' implicit reasoning capabilities are susceptible and unstable, reaffirming the necessity of explicit CoT to effectively support complex tasks.

Recent advancements in large language models (LLMs) often rely on generating intermediate reasoning steps to enhance accuracy. However, little work has examined how reasoning utility contributes to the final answer's correctness. Due to the stochastic nature of autoregressive generation, generating more context does not guarantee increased confidence in the answer. If we could predict, during generation, whether a reasoning step will be useful, we could stop early or prune ineffective steps, avoiding distractions in the final decision. We present an oracle study on MATH dataset, using Qwen2.5-32B and GPT-4o to generate reasoning chains, and then employing a separate model (Qwen3-8B) to quantify the utility of these chains for final accuracy. Specifically, we measure the model's uncertainty on the answer span Y at each reasoning step using conditional entropy (expected negative log-likelihood over the vocabulary) with context expanding step by step. Our results show a clear pattern: conditional entropy that decreases over steps is strongly associated with correct answers, whereas flat or increasing entropy often results in wrong answers. We also corroborate that incorrect reasoning paths tend to be longer than correct ones, suggesting that longer reasoning does not necessarily yield better outcomes. These findings serve as a foundation to inspire future work on designing efficient reasoning pipelines that detect and avoid unproductive reasoning early.

Inspired by the foundational works by Spivak and Fong and Cruttwell et al., we introduce a categorical framework to formalize Bayesian inference and learning. The two key ideas at play here are the notions of Bayesian inversions and the functor GL as constructed by Cruttwell et al.. In this context, we find that Bayesian learning is the simplest case of the learning paradigm. We then obtain categorical formulations of batch and sequential Bayes updates while also verifying that the two coincide in a specific example.

Test-Time Scaling (TTS) is a promising approach to progressively elicit the model's intelligence during inference. Recently, training-based TTS methods, such as continued reinforcement learning (RL), have further surged in popularity, while training-free TTS methods are gradually fading from prominence. However, the additional computation overhead of training amplifies the burden on test-time scaling. In this paper, we focus on training-free TTS methods for reasoning. We first design Conditional Step-level Self-refinement, a fine-grained sequential scaling method guided by process verification. On top of its effectiveness, we further combine it with other classical parallel scaling methods at the step level, to introduce a novel inference paradigm called Hybrid Test-Time Scaling. Extensive experiments on five instruction-tuned LLMs across different scales (3B-14B) and families demonstrate that hybrid strategy incorporating various training-free TTS methods at a fine granularity has considerable potential for expanding the reasoning performance boundaries of LLMs.

Prompting-based large language models (LLMs) are surprisingly powerful at generating natural language reasoning steps or Chains-of-Thoughts (CoT) for multi-step question answering (QA). They struggle, however, when the necessary knowledge is either unavailable to the LLM or not up-to-date within its parameters. While using the question to retrieve relevant text from an external knowledge source helps LLMs, we observe that this one-step retrieve-and-read approach is insufficient for multi-step QA. Here, what to retrieve depends on what has already been derived, which in turn may depend on what was previously retrieved. To address this, we propose IRCoT, a new approach for multi-step QA that interleaves retrieval with steps (sentences) in a CoT, guiding the retrieval with CoT and in turn using retrieved results to improve CoT. Using IRCoT with GPT3 substantially improves retrieval (up to 21 points) as well as downstream QA (up to 15 points) on four datasets: HotpotQA, 2WikiMultihopQA, MuSiQue, and IIRC. We observe similar substantial gains in out-of-distribution (OOD) settings as well as with much smaller models such as Flan-T5-large without additional training. IRCoT reduces model hallucination, resulting in factually more accurate CoT reasoning. Code, data, and prompts are available at https://github.com/stonybrooknlp/ircot

We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models with latent and observed variables. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al., 2021) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approximates the actual conditional model with known likelihood-ratio between the two. The backward filter and the forward change of measure are suitable to be incorporated into a probabilistic programming context because they can be formulated as a set of transformation rules. The guided generative model can be incorporated in different approaches to efficiently sample latent states and parameters conditional on observations. We show applicability in a variety of settings, including Markov chains with discrete state space, interacting particle systems, state space models, branching diffusions and Gamma processes.

Artificial intelligence (AI) has made remarkable progress across various domains, with large language models like ChatGPT gaining substantial attention for their human-like text-generation capabilities. Despite these achievements, spatial reasoning remains a significant challenge for these models. Benchmarks like StepGame evaluate AI spatial reasoning, where ChatGPT has shown unsatisfactory performance. However, the presence of template errors in the benchmark has an impact on the evaluation results. Thus there is potential for ChatGPT to perform better if these template errors are addressed, leading to more accurate assessments of its spatial reasoning capabilities. In this study, we refine the StepGame benchmark, providing a more accurate dataset for model evaluation. We analyze GPT's spatial reasoning performance on the rectified benchmark, identifying proficiency in mapping natural language text to spatial relations but limitations in multi-hop reasoning. We provide a flawless solution to the benchmark by combining template-to-relation mapping with logic-based reasoning. This combination demonstrates proficiency in performing qualitative reasoning on StepGame without encountering any errors. We then address the limitations of GPT models in spatial reasoning. We deploy Chain-of-thought and Tree-of-thoughts prompting strategies, offering insights into GPT's ``cognitive process", and achieving remarkable improvements in accuracy. Our investigation not only sheds light on model deficiencies but also proposes enhancements, contributing to the advancement of AI with more robust spatial reasoning capabilities.

We examine the reasoning and planning capabilities of large language models (LLMs) in solving complex tasks. Recent advances in inference-time techniques demonstrate the potential to enhance LLM reasoning without additional training by exploring intermediate steps during inference. Notably, OpenAI's o1 model shows promising performance through its novel use of multi-step reasoning and verification. Here, we explore how scaling inference-time techniques can improve reasoning and planning, focusing on understanding the tradeoff between computational cost and performance. To this end, we construct a comprehensive benchmark, known as Sys2Bench, and perform extensive experiments evaluating existing inference-time techniques on eleven diverse tasks across five categories, including arithmetic reasoning, logical reasoning, common sense reasoning, algorithmic reasoning, and planning. Our findings indicate that simply scaling inference-time computation has limitations, as no single inference-time technique consistently performs well across all reasoning and planning tasks.

Discrete diffusion models have emerged as a powerful generative modeling framework for discrete data with successful applications spanning from text generation to image synthesis. However, their deployment faces challenges due to the high dimensionality of the state space, necessitating the development of efficient inference algorithms. Current inference approaches mainly fall into two categories: exact simulation and approximate methods such as tau-leaping. While exact methods suffer from unpredictable inference time and redundant function evaluations, tau-leaping is limited by its first-order accuracy. In this work, we advance the latter category by tailoring the first extension of high-order numerical inference schemes to discrete diffusion models, enabling larger step sizes while reducing error. We rigorously analyze the proposed schemes and establish the second-order accuracy of the theta-trapezoidal method in KL divergence. Empirical evaluations on GPT-2 level text and ImageNet-level image generation tasks demonstrate that our method achieves superior sample quality compared to existing approaches under equivalent computational constraints.

With current state-of-the-art approaches aimed at enhancing the reasoning capabilities of Large Language Models(LLMs) through iterative preference learning inspired by AlphaZero, we propose to further enhance the step-wise reasoning capabilities through intrinsic self-correction to some extent. Our work leverages step-wise preference learning to enhance self-verification via reinforcement learning. We initially conduct our work through a two-stage training procedure. At the first stage, the self-correction reasoning ability of an LLM is enhanced through its own predictions, relying entirely on self-generated data within the intrinsic self-correction to some extent. At the second stage, the baseline step-wise preference learning is leveraged via the application of the enhanced self-correct policy achieved at the first stage. In the evaluation of arithmetic reasoning tasks, our approach outperforms OpenMath2-Llama3.1-8B, dart-math-mistral-7b-uniform on MATH with increases in accuracy to 71.34%(+4.18%) and 48.06%(+4.94%) and LLama-3.1-8B-Instruct, Mistral-7B-Instruct-v0.1 on GSM8K with increases in accuracy to 86.76%(+2.00%) and 38.06%(+2.28%).

As LLMs shift toward autonomous agents, Deep Research has emerged as a pivotal metric. However, existing academic benchmarks like BrowseComp often fail to meet real-world demands for open-ended research, which requires robust skills in intent recognition, long-horizon decision-making, and cross-source verification. To address this, we introduce Step-DeepResearch, a cost-effective, end-to-end agent. We propose a Data Synthesis Strategy Based on Atomic Capabilities to reinforce planning and report writing, combined with a progressive training path from agentic mid-training to SFT and RL. Enhanced by a Checklist-style Judger, this approach significantly improves robustness. Furthermore, to bridge the evaluation gap in the Chinese domain, we establish ADR-Bench for realistic deep research scenarios. Experimental results show that Step-DeepResearch (32B) scores 61.4% on Scale AI Research Rubrics. On ADR-Bench, it significantly outperforms comparable models and rivals SOTA closed-source models like OpenAI and Gemini DeepResearch. These findings prove that refined training enables medium-sized models to achieve expert-level capabilities at industry-leading cost-efficiency.

Approximate inference in Gaussian process (GP) models with non-conjugate likelihoods gets entangled with the learning of the model hyperparameters. We improve hyperparameter learning in GP models and focus on the interplay between variational inference (VI) and the learning target. While VI's lower bound to the marginal likelihood is a suitable objective for inferring the approximate posterior, we show that a direct approximation of the marginal likelihood as in Expectation Propagation (EP) is a better learning objective for hyperparameter optimization. We design a hybrid training procedure to bring the best of both worlds: it leverages conjugate-computation VI for inference and uses an EP-like marginal likelihood approximation for hyperparameter learning. We compare VI, EP, Laplace approximation, and our proposed training procedure and empirically demonstrate the effectiveness of our proposal across a wide range of data sets.

Automated Theorem Proving (ATP) in formal languages remains a formidable challenge in AI, demanding rigorous logical deduction and navigating vast search spaces. While large language models (LLMs) have shown promising performance, existing stepwise provers often suffer from biased search guidance, leading to inefficiencies and suboptimal proof strategies. This paper introduces the Multi-Perspective Search Prover (MPS-Prover), a novel stepwise ATP system designed to overcome these limitations. MPS-Prover incorporates two key innovations: a highly effective post-training data curation strategy that prunes approximately 40% of redundant training data without sacrificing performance, and a multi-perspective tree search mechanism. This search integrates a learned critic model with strategically designed heuristic rules to diversify tactic selection, prevent getting trapped in unproductive states, and enhance search robustness. Extensive evaluations demonstrate that MPS-Prover achieves state-of-the-art performance on multiple challenging benchmarks, including miniF2F and ProofNet, outperforming prior 7B parameter models. Furthermore, our analyses reveal that MPS-Prover generates significantly shorter and more diverse proofs compared to existing stepwise and whole-proof methods, highlighting its efficiency and efficacy. Our work advances the capabilities of LLM-based formal reasoning and offers a robust framework and a comprehensive analysis for developing more powerful theorem provers.

Frontier reasoning models have exhibited incredible capabilities across a wide array of disciplines, driven by posttraining large language models (LLMs) with reinforcement learning (RL). However, despite the widespread success of this paradigm, much of the literature has been devoted to disentangling truly novel behaviors that emerge during RL but are not present in the base models. In our work, we approach this question from a different angle, instead asking whether comparable reasoning capabilites can be elicited from base models at inference time by pure sampling, without any additional training. Inspired by Markov chain Monte Carlo (MCMC) techniques for sampling from sharpened distributions, we propose a simple iterative sampling algorithm leveraging the base models' own likelihoods. Over different base models, we show that our algorithm offers substantial boosts in reasoning that nearly match and even outperform those from RL on a wide variety of single-shot tasks, including MATH500, HumanEval, and GPQA. Moreover, our sampler avoids the collapse in diversity over multiple samples that is characteristic of RL-posttraining. Crucially, our method does not require training, curated datasets, or a verifier, suggesting broad applicability beyond easily verifiable domains.

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.

Large Language Models (LLMs) have shown promising capabilities for solving Operations Research (OR) problems. While reinforcement learning serves as a powerful paradigm for LLM training on OR problems, existing works generally face two key limitations. First, outcome reward suffers from the credit assignment problem, where correct final answers can reinforce flawed reasoning. Second, conventional discriminative process supervision is myopic, failing to evaluate the interdependent steps of OR modeling holistically. To this end, we introduce StepORLM, a novel self-evolving framework with generative process supervision. At its core, StepORLM features a co-evolutionary loop where a policy model and a generative process reward model (GenPRM) iteratively improve on each other. This loop is driven by a dual-feedback mechanism: definitive, outcome-based verification from an external solver, and nuanced, holistic process evaluation from the GenPRM. The combined signal is used to align the policy via Weighted Direct Preference Optimization (W-DPO) and simultaneously refine the GenPRM. Our resulting 8B-parameter StepORLM establishes a new state-of-the-art across six benchmarks, significantly outperforming vastly larger generalist models, agentic methods, and specialized baselines. Moreover, the co-evolved GenPRM is able to act as a powerful and universally applicable process verifier, substantially boosting the inference scaling performance of both our own model and other existing LLMs.

While Pre-trained Language Models (PLMs) internalize a great amount of world knowledge, they have been shown incapable of recalling these knowledge to solve tasks requiring complex & multi-step reasoning. Similar to how humans develop a "chain of thought" for these tasks, how can we equip PLMs with such abilities? In this work, we explore an iterative prompting framework, a new prompting paradigm which progressively elicits relevant knowledge from PLMs for multi-step inference. We identify key limitations of existing prompting methods, namely they are either restricted to queries with a single identifiable relation/predicate, or being agnostic to input contexts, which makes it difficult to capture variabilities across different inference steps. We propose an iterative context-aware prompter, which addresses these limitations by learning to dynamically synthesize prompts conditioned on the current step's contexts. Experiments on three datasets involving multi-step reasoning show the effectiveness of the iterative scheme and the context-aware prompter design.

Backpropagation (BP) is the most successful and widely used algorithm in deep learning. However, the computations required by BP are challenging to reconcile with known neurobiology. This difficulty has stimulated interest in more biologically plausible alternatives to BP. One such algorithm is the inference learning algorithm (IL). IL has close connections to neurobiological models of cortical function and has achieved equal performance to BP on supervised learning and auto-associative tasks. In contrast to BP, however, the mathematical foundations of IL are not well-understood. Here, we develop a novel theoretical framework for IL. Our main result is that IL closely approximates an optimization method known as implicit stochastic gradient descent (implicit SGD), which is distinct from the explicit SGD implemented by BP. Our results further show how the standard implementation of IL can be altered to better approximate implicit SGD. Our novel implementation considerably improves the stability of IL across learning rates, which is consistent with our theory, as a key property of implicit SGD is its stability. We provide extensive simulation results that further support our theoretical interpretations and also demonstrate IL achieves quicker convergence when trained with small mini-batches while matching the performance of BP for large mini-batches.

Mathematical reasoning has been challenging for large language models (LLMs). However, the introduction of step-by-step Chain-of-Thought (CoT) inference has significantly advanced the mathematical capabilities of LLMs. Despite this progress, current approaches either necessitate extensive inference datasets for training or depend on few-shot methods that frequently compromise computational accuracy. To address these bottlenecks in mathematical reasoning, we propose a novel method called Step Guidied Reasoning, which is more stable and generalizable than few-shot methods and does not involve further fine-tuning of the model. In this approach, LLMs reflect on small reasoning steps, similar to how humans deliberate and focus attention on what to do next. By incorporating this reflective process into the inference stage, LLMs can effectively guide their reasoning from one step to the next. Through extensive experiments, we demonstrate the significant effect of Step Guidied Reasoning in augmenting mathematical performance in state-of-the-art language models. Qwen2-72B-Instruct outperforms its math-specific counterpart, Qwen2.5-72B-Math-Instruct, on MMLU- STEM with a score of 90.9%, compared to 87.3%. The average scores of Qwen2-7B-Instruct and Qwen2-72B-Instruct increase from 27.1% to 36.3% and from 36.5% to 47.4% on the mathematics domain, respectively.

Recently proposed pyramidal models decompose the conventional forward and backward diffusion processes into multiple stages operating at varying resolutions. These models handle inputs with higher noise levels at lower resolutions, while less noisy inputs are processed at higher resolutions. This hierarchical approach significantly reduces the computational cost of inference in multi-step denoising models. However, existing open-source pyramidal video models have been trained from scratch and tend to underperform compared to state-of-the-art systems in terms of visual plausibility. In this work, we present a pipeline that converts a pretrained diffusion model into a pyramidal one through low-cost finetuning, achieving this transformation without degradation in quality of output videos. Furthermore, we investigate and compare various strategies for step distillation within pyramidal models, aiming to further enhance the inference efficiency. Our results are available at https://qualcomm-ai-research.github.io/PyramidalWan.

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

Training on model-generated synthetic data is a promising approach for finetuning LLMs, but it remains unclear when it helps or hurts. In this paper, we investigate this question for math reasoning via an empirical study, followed by building a conceptual understanding of our observations. First, we find that while the typical approach of finetuning a model on synthetic correct or positive problem-solution pairs generated by capable models offers modest performance gains, sampling more correct solutions from the finetuned learner itself followed by subsequent fine-tuning on this self-generated data doubles the efficiency of the same synthetic problems. At the same time, training on model-generated positives can amplify various spurious correlations, resulting in flat or even inverse scaling trends as the amount of data increases. Surprisingly, we find that several of these issues can be addressed if we also utilize negative responses, i.e., model-generated responses that are deemed incorrect by a final answer verifier. Crucially, these negatives must be constructed such that the training can appropriately recover the utility or advantage of each intermediate step in the negative response. With this per-step scheme, we are able to attain consistent gains over only positive data, attaining performance similar to amplifying the amount of synthetic data by 8 times. We show that training on per-step negatives can help to unlearn spurious correlations in the positive data, and is equivalent to advantage-weighted reinforcement learning (RL), implying that it inherits robustness benefits of RL over imitating positive data alone.

Recently, Zaremba et al. demonstrated that increasing inference-time computation improves robustness in large proprietary reasoning LLMs. In this paper, we first show that smaller-scale, open-source models (e.g., DeepSeek R1, Qwen3, Phi-reasoning) can also benefit from inference-time scaling using a simple budget forcing strategy. More importantly, we reveal and critically examine an implicit assumption in prior work: intermediate reasoning steps are hidden from adversaries. By relaxing this assumption, we identify an important security risk, intuitively motivated and empirically verified as an inverse scaling law: if intermediate reasoning steps become explicitly accessible, increased inference-time computation consistently reduces model robustness. Finally, we discuss practical scenarios where models with hidden reasoning chains are still vulnerable to attacks, such as models with tool-integrated reasoning and advanced reasoning extraction attacks. Our findings collectively demonstrate that the robustness benefits of inference-time scaling depend heavily on the adversarial setting and deployment context. We urge practitioners to carefully weigh these subtle trade-offs before applying inference-time scaling in security-sensitive, real-world applications.