Daily Papers

Despite substantial investment in safety alignment, the vulnerability of large language models to sophisticated multi-turn adversarial attacks remains poorly characterized, and whether model scale or inference mode affects robustness is unknown. This study employed the TEMPEST multi-turn attack framework to evaluate ten frontier models from eight vendors across 1,000 harmful behaviors, generating over 97,000 API queries across adversarial conversations with automated evaluation by independent safety classifiers. Results demonstrated a spectrum of vulnerability: six models achieved 96% to 100% attack success rate (ASR), while four showed meaningful resistance, with ASR ranging from 42% to 78%; enabling extended reasoning on identical architecture reduced ASR from 97% to 42%. These findings indicate that safety alignment quality varies substantially across vendors, that model scale does not predict adversarial robustness, and that thinking mode provides a deployable safety enhancement. Collectively, this work establishes that current alignment techniques remain fundamentally vulnerable to adaptive multi-turn attacks regardless of model scale, while identifying deliberative inference as a promising defense direction.

Large Reasoning Models (LRMs) significantly improve the reasoning ability of Large Language Models (LLMs) by learning to reason, exhibiting promising performance in complex task-solving. However, their deliberative reasoning process leads to inefficiencies in token usage, memory consumption, and inference time. Thus, this survey provides a review of efficient inference methods designed specifically for LRMs, focusing on mitigating token inefficiency while preserving the reasoning quality. First, we introduce a taxonomy to group the recent methods into two main categories: (a) explicit compact Chain-of-Thought (CoT), which reduces tokens while keeping the explicit reasoning structure, and (b) implicit latent CoT, which encodes reasoning steps within hidden representations instead of explicit tokens. Meanwhile, we discuss their strengths and weaknesses. Then, we conduct empirical analyses on existing methods from performance and efficiency aspects. Besides, we present open challenges in this field, including human-centric controllable reasoning, trade-off between interpretability and efficiency of reasoning, ensuring safety of efficient reasoning, and broader applications of efficient reasoning. In addition, we highlight key insights for enhancing LRMs' inference efficiency via techniques such as model merging, new architectures, and agent routers. We hope this work serves as a valuable guide, helping researchers overcome challenges in this vibrant fieldhttps://github.com/yueliu1999/Awesome-Efficient-Inference-for-LRMs.

We introduce SafeWork-R1, a cutting-edge multimodal reasoning model that demonstrates the coevolution of capabilities and safety. It is developed by our proposed SafeLadder framework, which incorporates large-scale, progressive, safety-oriented reinforcement learning post-training, supported by a suite of multi-principled verifiers. Unlike previous alignment methods such as RLHF that simply learn human preferences, SafeLadder enables SafeWork-R1 to develop intrinsic safety reasoning and self-reflection abilities, giving rise to safety `aha' moments. Notably, SafeWork-R1 achieves an average improvement of 46.54% over its base model Qwen2.5-VL-72B on safety-related benchmarks without compromising general capabilities, and delivers state-of-the-art safety performance compared to leading proprietary models such as GPT-4.1 and Claude Opus 4. To further bolster its reliability, we implement two distinct inference-time intervention methods and a deliberative search mechanism, enforcing step-level verification. Finally, we further develop SafeWork-R1-InternVL3-78B, SafeWork-R1-DeepSeek-70B, and SafeWork-R1-Qwen2.5VL-7B. All resulting models demonstrate that safety and capability can co-evolve synergistically, highlighting the generalizability of our framework in building robust, reliable, and trustworthy general-purpose AI.

Despite significant advancements, current large language models (LLMs) and vision-language models (LVLMs) continue to struggle with complex, multi-step, cross-modal common sense reasoning tasks, often exhibiting a lack of "deliberative thinking." They tend to rely on superficial associations rather than deep, chained inference, particularly when integrating visual information with abstract concepts. To address this, we propose the Coherent Multimodal Reasoning Framework (CMRF), a novel approach that enhances LVLMs' common sense reasoning capabilities through an iterative, self-evaluating inference mechanism. CMRF mimics human problem-solving by decomposing complex queries, generating step-by-step inferences, and self-correcting errors. Our framework integrates three key modules: a Reasoning Decomposition Unit (RDU) for breaking down problems into sub-questions, a Contextual Inference Engine (CIE) for contextual inference, and a Coherence Assessment Module (CAM) for evaluating logical consistency and confidence. Coupled with an Adaptive Iterative Refinement strategy, CMRF systematically refines its reasoning paths. Built upon LLaVA-1.6-34B and trained on a novel Multimodal Daily Activity Reasoning (MDAR) dataset, CMRF achieves state-of-the-art performance among open-source LVLMs on challenging benchmarks like VCR, A-OKVQA, and DailyLife-MRC. It attains an average accuracy of 69.4%, surpassing the best open-source baseline by +2.4 percentage points, with particular strength in complex reasoning scenarios. Extensive ablation studies and human evaluations confirm the critical contributions of each module and the effectiveness of iterative refinement in fostering more coherent and accurate reasoning.

In AI-assisted decision-making, humans often passively review AI's suggestion and decide whether to accept or reject it as a whole. In such a paradigm, humans are found to rarely trigger analytical thinking and face difficulties in communicating the nuances of conflicting opinions to the AI when disagreements occur. To tackle this challenge, we propose Human-AI Deliberation, a novel framework to promote human reflection and discussion on conflicting human-AI opinions in decision-making. Based on theories in human deliberation, this framework engages humans and AI in dimension-level opinion elicitation, deliberative discussion, and decision updates. To empower AI with deliberative capabilities, we designed Deliberative AI, which leverages large language models (LLMs) as a bridge between humans and domain-specific models to enable flexible conversational interactions and faithful information provision. An exploratory evaluation on a graduate admissions task shows that Deliberative AI outperforms conventional explainable AI (XAI) assistants in improving humans' appropriate reliance and task performance. Based on a mixed-methods analysis of participant behavior, perception, user experience, and open-ended feedback, we draw implications for future AI-assisted decision tool design.

Chain-of-thought (CoT) prompting has become a widely used strategy for working with large language and multimodal models. While CoT has been shown to improve performance across many tasks, determining the settings in which it is effective remains an ongoing effort. In particular, it is still an open question in what settings CoT systematically reduces model performance. In this paper, we seek to identify the characteristics of tasks where CoT reduces performance by drawing inspiration from cognitive psychology, looking at cases where (i) verbal thinking or deliberation hurts performance in humans, and (ii) the constraints governing human performance generalize to language models. Three such cases are implicit statistical learning, visual recognition, and classifying with patterns containing exceptions. In extensive experiments across all three settings, we find that a diverse collection of state-of-the-art models exhibit significant drop-offs in performance (e.g., up to 36.3% absolute accuracy for OpenAI o1-preview compared to GPT-4o) when using inference-time reasoning compared to zero-shot counterparts. We also identify three tasks that satisfy condition (i) but not (ii), and find that while verbal thinking reduces human performance in these tasks, CoT retains or increases model performance. Overall, our results show that while there is not an exact parallel between the cognitive processes of models and those of humans, considering cases where thinking has negative consequences for human performance can help us identify settings where it negatively impacts models. By connecting the literature on human deliberation with evaluations of CoT, we offer a new tool that can be used in understanding the impact of prompt choices and inference-time reasoning.

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

As large-scale language models increasingly impact safety-critical domains, ensuring their reliable adherence to well-defined principles remains a fundamental challenge. We introduce Deliberative Alignment, a new paradigm that directly teaches the model safety specifications and trains it to explicitly recall and accurately reason over the specifications before answering. We used this approach to align OpenAI's o-series models, and achieved highly precise adherence to OpenAI's safety policies, without requiring human-written chain-of-thoughts or answers. Deliberative Alignment pushes the Pareto frontier by simultaneously increasing robustness to jailbreaks while decreasing overrefusal rates, and also improves out-of-distribution generalization. We demonstrate that reasoning over explicitly specified policies enables more scalable, trustworthy, and interpretable alignment.

Multi-agent debate (MAD) has recently emerged as a promising framework for improving the reasoning performance of large language models (LLMs). Yet, whether LLM agents can genuinely engage in deliberative reasoning, beyond simple ensembling or majority voting, remains unclear. We address this question through a controlled study using the Knight--Knave--Spy logic puzzle, which enables precise, step-wise evaluation of debate outcomes and processes under verifiable ground truth. We systematically set up six structural and cognitive factors, including agent team size, composition, confidence visibility, debate order, debate depth, and task difficulty, to disentangle their respective effects on collective reasoning. Our results show that intrinsic reasoning strength and group diversity are the dominant drivers of debate success, while structural parameters such as order or confidence visibility offer limited gains. Beyond outcomes, process-level analyses identify key behavioral patterns: majority pressure suppresses independent correction, effective teams overturn incorrect consensus, and rational, validity-aligned reasoning most strongly predicts improvement. These findings provide valuable insights into how and why LLM debates succeed or fail, offering guidance for designing interpretable and truth-seeking multi-agent reasoning systems.

Theory-of-Mind (ToM) tasks pose a unique challenge for small language models (SLMs) with limited scale, which often lack the capacity to perform deep social reasoning. In this work, we propose DEL-ToM, a framework that improves ToM reasoning through inference-time scaling rather than architectural changes. Our approach decomposes ToM tasks into a sequence of belief updates grounded in Dynamic Epistemic Logic (DEL), enabling structured and transparent reasoning. We train a verifier, called the Process Belief Model (PBM), to score each belief update step using labels generated automatically via a DEL simulator. During inference, candidate belief traces generated by a language model are evaluated by the PBM, and the highest-scoring trace is selected. This allows SLMs to emulate more deliberate reasoning by allocating additional compute at test time. Experiments across multiple model scales and benchmarks show that DEL-ToM consistently improves performance, demonstrating that verifiable belief supervision can significantly enhance ToM abilities of SLMs without retraining.

While recent advancements in aligning Large Language Models (LLMs) with recommendation tasks have shown great potential and promising performance overall, these aligned recommendation LLMs still face challenges in complex scenarios. This is primarily due to the current alignment approach focusing on optimizing LLMs to generate user feedback directly, without incorporating deliberation. To overcome this limitation and develop more reliable LLMs for recommendations, we propose a new Deliberative Recommendation task, which incorporates explicit reasoning about user preferences as an additional alignment goal. We then introduce the Reasoning-powered Recommender framework for deliberative user preference alignment, designed to enhance reasoning capabilities by utilizing verbalized user feedback in a step-wise manner to tackle this task. The framework employs collaborative step-wise experts and tailored training strategies for each expert. Experimental results across three real-world datasets demonstrate the rationality of the deliberative task formulation and the superior performance of the proposed framework in improving both prediction accuracy and reasoning quality.

Knowledge graph-based retrieval-augmented generation seeks to mitigate hallucinations in Large Language Models (LLMs) caused by insufficient or outdated knowledge. However, existing methods often fail to fully exploit the prior knowledge embedded in knowledge graphs (KGs), particularly their structural information and explicit or implicit constraints. The former can enhance the faithfulness of LLMs' reasoning, while the latter can improve the reliability of response generation. Motivated by these, we propose a trustworthy reasoning framework, termed Deliberation over Priors (DP), which sufficiently utilizes the priors contained in KGs. Specifically, DP adopts a progressive knowledge distillation strategy that integrates structural priors into LLMs through a combination of supervised fine-tuning and Kahneman-Tversky optimization, thereby improving the faithfulness of relation path generation. Furthermore, our framework employs a reasoning-introspection strategy, which guides LLMs to perform refined reasoning verification based on extracted constraint priors, ensuring the reliability of response generation. Extensive experiments on three benchmark datasets demonstrate that DP achieves new state-of-the-art performance, especially a Hit@1 improvement of 13% on the ComplexWebQuestions dataset, and generates highly trustworthy responses. We also conduct various analyses to verify its flexibility and practicality. The code is available at https://github.com/reml-group/Deliberation-on-Priors.

There is intense interest in investigating how inference time compute (ITC) (e.g. repeated sampling, refinements, etc) can improve large language model (LLM) capabilities. At the same time, recent breakthroughs in reasoning models, such as Deepseek-R1, unlock the opportunity for reinforcement learning to improve LLM reasoning skills. An in-depth understanding of how ITC interacts with reasoning across different models could provide important guidance on how to further advance the LLM frontier. This work conducts a comprehensive analysis of inference-time scaling methods for both reasoning and non-reasoning models on challenging reasoning tasks. Specifically, we focus our research on verifier-free inference time-scaling methods due to its generalizability without needing a reward model. We construct the Pareto frontier of quality and efficiency. We find that non-reasoning models, even with an extremely high inference budget, still fall substantially behind reasoning models. For reasoning models, majority voting proves to be a robust inference strategy, generally competitive or outperforming other more sophisticated ITC methods like best-of-N and sequential revisions, while the additional inference compute offers minimal improvements. We further perform in-depth analyses of the association of key response features (length and linguistic markers) with response quality, with which we can improve the existing ITC methods. We find that correct responses from reasoning models are typically shorter and have fewer hedging and thinking markers (but more discourse markers) than the incorrect responses.

Recent studies show that the reasoning capabilities of Large Language Models (LLMs) can be improved by applying Reinforcement Learning (RL) to question-answering (QA) tasks in areas such as math and coding. With a long context length, LLMs may learn to perform search, as indicated by the self-correction behavior observed in DeepSeek R1. However, this search behavior is often imprecise and lacks confidence, resulting in long, redundant responses and highlighting deficiencies in intuition and verification. Inspired by the Dual Process Theory in psychology, we introduce a simple modification to the QA task that includes four stages: Fast Thinking, where the LLM must answer within a strict token budget; Verification, where the model evaluates its initial response; Slow Thinking, where it refines the initial response with more deliberation; and Summarization, where it distills the refinement from the previous stage into precise steps. Our proposed task improves average accuracy from 24.9% to 27.9% for Qwen2.5-1.5B, and from 45.9% to 49.8% for DeepSeek-R1-Qwen-1.5B. Notably, for Qwen2.5-1.5B, the Fast Thinking mode alone achieves 26.8% accuracy using fewer than 1000 tokens, demonstrating substantial inference efficiency gains. These findings suggest that intuition and deliberative reasoning are distinct, complementary systems benefiting from targeted training.

Large Language Models (LLMs) trained with reinforcement learning and verifiable rewards have achieved strong results on complex reasoning tasks. Recent work extends this paradigm to a multi-agent setting, where a meta-thinking agent proposes plans and monitors progress while a reasoning agent executes subtasks through sequential conversational turns. Despite promising performance, we identify a critical limitation: lazy agent behavior, in which one agent dominates while the other contributes little, undermining collaboration and collapsing the setup to an ineffective single agent. In this paper, we first provide a theoretical analysis showing why lazy behavior naturally arises in multi-agent reasoning. We then introduce a stable and efficient method for measuring causal influence, helping mitigate this issue. Finally, as collaboration intensifies, the reasoning agent risks getting lost in multi-turn interactions and trapped by previous noisy responses. To counter this, we propose a verifiable reward mechanism that encourages deliberation by allowing the reasoning agent to discard noisy outputs, consolidate instructions, and restart its reasoning process when necessary. Extensive experiments demonstrate that our framework alleviates lazy agent behavior and unlocks the full potential of multi-agent framework for complex reasoning tasks.

Multiple types of inference are available for probabilistic graphical models, e.g., marginal, maximum-a-posteriori, and even marginal maximum-a-posteriori. Which one do researchers mean when they talk about ``planning as inference''? There is no consistency in the literature, different types are used, and their ability to do planning is further entangled with specific approximations or additional constraints. In this work we use the variational framework to show that, just like all commonly used types of inference correspond to different weightings of the entropy terms in the variational problem, planning corresponds exactly to a different set of weights. This means that all the tricks of variational inference are readily applicable to planning. We develop an analogue of loopy belief propagation that allows us to perform approximate planning in factored-state Markov decisions processes without incurring intractability due to the exponentially large state space. The variational perspective shows that the previous types of inference for planning are only adequate in environments with low stochasticity, and allows us to characterize each type by its own merits, disentangling the type of inference from the additional approximations that its practical use requires. We validate these results empirically on synthetic MDPs and tasks posed in the International Planning Competition.

The capacity of Large Language Models (LLMs) to reason is fundamental to their application in complex, knowledge-intensive domains. In real-world scenarios, LLMs are often augmented with external information that can be helpful, irrelevant, or even misleading. This paper investigates the causal impact of such auxiliary information on the reasoning process of LLMs with explicit step-by-step thinking capabilities. We introduce SciAux, a new dataset derived from ScienceQA, to systematically test the robustness of the model against these types of information. Our findings reveal a critical vulnerability: the model's deliberative "thinking mode" is a double-edged sword. While helpful context improves accuracy, misleading information causes a catastrophic drop in performance, which is amplified by the thinking process. Instead of conferring robustness, thinking reinforces the degree of error when provided with misinformation. This highlights that the challenge is not merely to make models "think", but to endow them with the critical faculty to evaluate the information upon which their reasoning is based. The SciAux dataset is available at https://huggingface.co/datasets/billhdzhao/SciAux.

Multimodal Large Language Models (MLLMs) have powered Graphical User Interface (GUI) Agents, showing promise in automating tasks on computing devices. Recent works have begun exploring reasoning in GUI tasks with encouraging results. However, many current approaches rely on manually designed reasoning templates, which may result in reasoning that is not sufficiently robust and adaptive for complex GUI environments. Meanwhile, some existing agents continue to operate as Reactive Actors, relying primarily on implicit reasoning that may lack sufficient depth for GUI tasks demanding planning and error recovery. We argue that advancing these agents requires a shift from reactive acting towards acting based on deliberate reasoning. To facilitate this transformation, we introduce InfiGUI-R1, an MLLM-based GUI agent developed through our Actor2Reasoner framework, a reasoning-centric, two-stage training approach designed to progressively evolve agents from Reactive Actors to Deliberative Reasoners. The first stage, Reasoning Injection, focuses on establishing a basic reasoner. We employ Spatial Reasoning Distillation to transfer cross-modal spatial reasoning capabilities from teacher models to MLLMs through trajectories with explicit reasoning steps, enabling models to integrate GUI visual-spatial information with logical reasoning before action generation. The second stage, Deliberation Enhancement, refines the basic reasoner into a deliberative one using Reinforcement Learning. This stage introduces two approaches: Sub-goal Guidance, which rewards models for generating accurate intermediate sub-goals, and Error Recovery Scenario Construction, which creates failure-and-recovery training scenarios from identified prone-to-error steps. Experimental results show InfiGUI-R1 achieves strong performance in GUI grounding and trajectory tasks. Resources at https://github.com/Reallm-Labs/InfiGUI-R1.

Large language models (LLMs) are widely applied in chatbots, code generators, and search engines. Workloads such as chain-of-thought, complex reasoning, and agent services significantly increase the inference cost by invoking the model repeatedly. Optimization methods such as parallelism, compression, and caching have been adopted to reduce costs, but the diverse service requirements make it hard to select the right method. Recently, specialized LLM inference engines have emerged as a key component for integrating the optimization methods into service-oriented infrastructures. However, a systematic study on inference engines is still lacking. This paper provides a comprehensive evaluation of 25 open-source and commercial inference engines. We examine each inference engine in terms of ease-of-use, ease-of-deployment, general-purpose support, scalability, and suitability for throughput- and latency-aware computation. Furthermore, we explore the design goals of each inference engine by investigating the optimization techniques it supports. In addition, we assess the ecosystem maturity of open source inference engines and handle the performance and cost policy of commercial solutions. We outline future research directions that include support for complex LLM-based services, support of various hardware, and enhanced security, offering practical guidance to researchers and developers in selecting and designing optimized LLM inference engines. We also provide a public repository to continually track developments in this fast-evolving field: https://github.com/sihyeong/Awesome-LLM-Inference-Engine

Inference, especially those derived from inductive processes, is a crucial component in our conversation to complement the information implicitly or explicitly conveyed by a speaker. While recent large language models show remarkable advances in inference tasks, their performance in inductive reasoning, where not all information is present in the context, is far behind deductive reasoning. In this paper, we analyze the behavior of the models based on the task difficulty defined by the semantic information gap -- which distinguishes inductive and deductive reasoning (Johnson-Laird, 1988, 1993). Our analysis reveals that the disparity in information between dialogue contexts and desired inferences poses a significant challenge to the inductive inference process. To mitigate this information gap, we investigate a contrastive learning approach by feeding negative samples. Our experiments suggest negative samples help models understand what is wrong and improve their inference generations.

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.

Recent Large Reasoning Models (LRMs), such as DeepSeek-R1 and OpenAI o1, have demonstrated strong performance gains by scaling up the length of Chain-of-Thought (CoT) reasoning during inference. However, a growing concern lies in their tendency to produce excessively long reasoning traces, which are often filled with redundant content (e.g., repeated definitions), over-analysis of simple problems, and superficial exploration of multiple reasoning paths for harder tasks. This inefficiency introduces significant challenges for training, inference, and real-world deployment (e.g., in agent-based systems), where token economy is critical. In this survey, we provide a comprehensive overview of recent efforts aimed at improving reasoning efficiency in LRMs, with a particular focus on the unique challenges that arise in this new paradigm. We identify common patterns of inefficiency, examine methods proposed across the LRM lifecycle, i.e., from pretraining to inference, and discuss promising future directions for research. To support ongoing development, we also maintain a real-time GitHub repository tracking recent progress in the field. We hope this survey serves as a foundation for further exploration and inspires innovation in this rapidly evolving area.

Building upon our previous investigations of O1 replication (Part 1: Journey Learning [Qin et al., 2024] and Part 2: Distillation [Huang et al., 2024]), this work explores the potential of inference-time scaling in large language models (LLMs) for medical reasoning tasks, ranging from diagnostic decision-making to treatment planning. Through extensive experiments on medical benchmarks of varying complexity (MedQA, Medbullets, and JAMA Clinical Challenges), our investigation reveals several key insights: (1) Increasing inference time does lead to improved performance. With a modest training set of 500 samples, our model yields substantial performance improvements of 6%-11%. (2) Task complexity directly correlates with the required length of reasoning chains, confirming the necessity of extended thought processes for challenging problems. (3) The differential diagnoses generated by our model adhere to the principles of the hypothetico-deductive method, producing a list of potential conditions that may explain a patient's symptoms and systematically narrowing these possibilities by evaluating the evidence. These findings demonstrate the promising synergy between inference-time scaling and journey learning in advancing LLMs' real-world clinical reasoning capabilities.

We present Klear-Reasoner, a model with long reasoning capabilities that demonstrates careful deliberation during problem solving, achieving outstanding performance across multiple benchmarks. Although there are already many excellent works related to inference models in the current community, there are still many problems with reproducing high-performance inference models due to incomplete disclosure of training details. This report provides an in-depth analysis of the reasoning model, covering the entire post-training workflow from data preparation and long Chain-of-Thought supervised fine-tuning (long CoT SFT) to reinforcement learning (RL), along with detailed ablation studies for each experimental component. For SFT data, our experiments show that a small number of high-quality data sources are more effective than a large number of diverse data sources, and that difficult samples can achieve better results without accuracy filtering. In addition, we investigate two key issues with current clipping mechanisms in RL: Clipping suppresses critical exploration signals and ignores suboptimal trajectories. To address these challenges, we propose Gradient-Preserving clipping Policy Optimization (GPPO) that gently backpropagates gradients from clipped tokens. GPPO not only enhances the model's exploration capacity but also improves its efficiency in learning from negative samples. Klear-Reasoner exhibits exceptional reasoning abilities in mathematics and programming, scoring 90.5\% on AIME 2024, 83.2\% on AIME 2025, 66.0\% on LiveCodeBench V5 and 58.1\% on LiveCodeBench V6.

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.

Reasoning protocols such as Chain of Thought (CoT) and Tree of Thought (ToT) organize internal deliberation but lack an explicit mechanism for external questioning that elicits self-revision. We present FOR-Prompting (From Objection to Revision Prompting), an asymmetric protocol where a Defender proposes an answer, an Objectioner raises question-style objections with no direct fixes, and a Host enforces consistency and closure. On GSM8K we observe about a 22% point gain over single-prompt and accuracy on par with CoT, with more than 10% higher ratings in reasoning and coherence from a uniform GPT 4.1 judge. FOR-Prompting also corrects mistakes without tools or human supervision on tricky queries, and improves performance for small-scale model (approx. 19% accuracy improved on Llama3.2:1b for GSM8K task), highlighting promise for small models and on personal device use. Beyond factual QA, qualitative analyses on open-ended tasks show enhanced exploration and refinement, with dialogue traces that make assumptions and trade-offs explicit. The protocol is model agnostic and operates purely at the prompt level through role-structured turns, so it works with hosted and local models of different sizes without retraining, and it supports large-scale study of objection-guided reasoning.

Chain-of-Thought (CoT) prompting has been shown to improve Large Language Model (LLM) performance on various tasks. With this approach, LLMs appear to produce human-like reasoning steps before providing answers (a.k.a., CoT reasoning), which often leads to the perception that they engage in deliberate inferential processes. However, some initial findings suggest that CoT reasoning may be more superficial than it appears, motivating us to explore further. In this paper, we study CoT reasoning via a data distribution lens and investigate if CoT reasoning reflects a structured inductive bias learned from in-distribution data, allowing the model to conditionally generate reasoning paths that approximate those seen during training. Thus, its effectiveness is fundamentally bounded by the degree of distribution discrepancy between the training data and the test queries. With this lens, we dissect CoT reasoning via three dimensions: task, length, and format. To investigate each dimension, we design DataAlchemy, an isolated and controlled environment to train LLMs from scratch and systematically probe them under various distribution conditions. Our results reveal that CoT reasoning is a brittle mirage that vanishes when it is pushed beyond training distributions. This work offers a deeper understanding of why and when CoT reasoning fails, emphasizing the ongoing challenge of achieving genuine and generalizable reasoning.

Large Language Models (LLMs) have achieved impressive performance on complex reasoning tasks with Chain-of-Thought (CoT) prompting. However, conventional CoT relies on reasoning steps explicitly verbalized in natural language, introducing inefficiencies and limiting its applicability to abstract reasoning. To address this, there has been growing research interest in latent CoT reasoning, where inference occurs within latent spaces. By decoupling reasoning from language, latent reasoning promises richer cognitive representations and more flexible, faster inference. Researchers have explored various directions in this promising field, including training methodologies, structural innovations, and internal reasoning mechanisms. This paper presents a comprehensive overview and analysis of this reasoning paradigm. We begin by proposing a unified taxonomy from four perspectives: token-wise strategies, internal mechanisms, analysis, and applications. We then provide in-depth discussions and comparative analyses of representative methods, highlighting their design patterns, strengths, and open challenges. We aim to provide a structured foundation for advancing this emerging direction in LLM reasoning. The relevant papers will be regularly updated at https://github.com/EIT-NLP/Awesome-Latent-CoT.

Automated evaluation of free-form outputs from large language models (LLMs) is challenging because many distinct answers can be equally valid. A common practice is to use LLMs themselves as judges, but the theoretical properties of this approach are not yet well understood. We show that a geometric framework that represents both judges and candidates as points on a probability simplex can provide helpful insight on what is or is not identifiable using LLM judges. Our theoretical analysis uncovers a "phase transition" in ranking identifiability: for binary scoring systems, true rankings are identifiable even with weak judges under mild assumptions, while rankings become non-identifiable for three or more scoring levels even with infinite data, absent additional prior knowledge. This non-identifiability highlights how uncertainty in rankings stems from not only aleatoric uncertainty (i.e., inherent stochasticity in the data) but also epistemic uncertainty regarding which assumptions hold, an aspect that has received limited attention until now. To integrate both types of uncertainty, we use Bayesian inference to encode assumptions as priors and conduct sensitivity analysis of ranking estimates and credible intervals. Empirical evaluations across multiple benchmarks demonstrate that Bayesian inference yields more accurate rankings and substantially improves coverage rates. These results underscore the importance of taking a more holistic approach to uncertainty quantification when using LLMs as judges.

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

Recent advancements in large reasoning models (LRMs) have significantly enhanced language models' capabilities in complex problem-solving by emulating human-like deliberative thinking. However, these models often exhibit overthinking (i.e., the generation of unnecessarily verbose and redundant content), which hinders efficiency and inflates inference cost. In this work, we explore the representational and behavioral origins of this inefficiency, revealing that LRMs inherently possess the capacity for more concise reasoning. Empirical analyses show that correct reasoning paths vary significantly in length, and the shortest correct responses often suffice, indicating untapped efficiency potential. Exploiting these findings, we propose two lightweight methods to enhance LRM efficiency. First, we introduce Efficiency Steering, a training-free activation steering technique that modulates reasoning behavior via a single direction in the model's representation space. Second, we develop Self-Rewarded Efficiency RL, a reinforcement learning framework that dynamically balances task accuracy and brevity by rewarding concise correct solutions. Extensive experiments on seven LRM backbones across multiple mathematical reasoning benchmarks demonstrate that our methods significantly reduce reasoning length while preserving or improving task performance. Our results highlight that reasoning efficiency can be improved by leveraging and guiding the intrinsic capabilities of existing models in a self-guided manner.

LLM inference often generates a batch of candidates for a prompt and selects one via strategies like majority voting or Best-of- N (BoN). For difficult tasks, this single-shot selection often underperforms. Consequently, evaluations commonly report Pass@k: the agent may submit up to k responses, and only the best of them is used when computing regret. Motivated by this, we study inference scaling in the more general Pass@k inference setting, and prove that neither majority voting nor BoN exhibits the desirable scaling with k and the sampling budget N. Combining the advantages of majority voting and BoN, we propose a new inference strategy called Best-of-Majority (BoM), with a pivotal step that restricts the candidates to the responses with high frequency in the N samples before selecting the top-k rewards. We prove that when the sampling budget is N=tildeOmega(C^*), the regret of BoM is O(epsilon_{opt}+epsilon_{mathrm{RM}^2C^*/k}), where C^* is the coverage coefficient, epsilon_{RM} is the estimation error of the reward model, and epsilon_{opt} is the estimation error of reward at the optimal response. We further establish a matching lower bound, certifying that our algorithm is minimax optimal. Beyond optimality, BoM has a key advantage: unlike majority voting and BoN, its performance does not degrade when increasing N. Experimental results of inference on math problems show BoM outperforming both majority voting and BoN.

Large Language Models (LLMs) have demonstrated the ability to tackle increasingly complex tasks through advanced reasoning, long-form content generation, and tool use. Solving these tasks often involves long inference-time computations. In human problem solving, a common strategy to expedite work is collaboration: by dividing the problem into sub-tasks, exploring different strategies concurrently, etc. Recent research has shown that LLMs can also operate in parallel by implementing explicit cooperation frameworks, such as voting mechanisms or the explicit creation of independent sub-tasks that can be executed in parallel. However, each of these frameworks may not be suitable for all types of tasks, which can hinder their applicability. In this work, we propose a different design approach: we run LLM "workers" in parallel , allowing them to synchronize via a concurrently-updated attention cache and prompt these workers to decide how best to collaborate. Our approach allows the instances to come up with their own collaboration strategy for the problem at hand, all the while "seeing" each other's partial progress in the concurrent cache. We implement this approach via Hogwild! Inference: a parallel LLM inference engine where multiple instances of the same LLM run in parallel with the same attention cache, with "instant" access to each other's generated tokens. Hogwild! inference takes advantage of Rotary Position Embeddings (RoPE) to avoid recomputation while improving parallel hardware utilization. We find that modern reasoning-capable LLMs can perform inference with shared Key-Value cache out of the box, without additional fine-tuning.

Current inference scaling methods, such as Self-consistency and Best-of-N, have proven effective in improving the accuracy of LLMs on complex reasoning tasks. However, these methods rely heavily on the quality of candidate responses and are unable to produce correct answers when all candidates are incorrect. In this paper, we propose a novel inference scaling strategy, CoT-based Synthesizer, which leverages CoT reasoning to synthesize superior answers by analyzing complementary information from multiple candidate responses, even when all candidate responses are flawed. To enable a lightweight and cost-effective implementation, we introduce an automated data generation pipeline that creates diverse training data. This allows smaller LLMs trained on this data to improve the inference accuracy of larger models, including API-based LLMs. Experimental results across four benchmark datasets with seven policy models demonstrate that our method significantly enhances performance, with gains of 11.8% for Llama3-8B and 10.3% for GPT-4o on the MATH dataset. The corresponding training data and code are publicly available on https://github.com/RUCKBReasoning/CoT-based-Synthesizer.

We explore uncertainty quantification in large language models (LLMs), with the goal to identify when uncertainty in responses given a query is large. We simultaneously consider both epistemic and aleatoric uncertainties, where the former comes from the lack of knowledge about the ground truth (such as about facts or the language), and the latter comes from irreducible randomness (such as multiple possible answers). In particular, we derive an information-theoretic metric that allows to reliably detect when only epistemic uncertainty is large, in which case the output of the model is unreliable. This condition can be computed based solely on the output of the model obtained simply by some special iterative prompting based on the previous responses. Such quantification, for instance, allows to detect hallucinations (cases when epistemic uncertainty is high) in both single- and multi-answer responses. This is in contrast to many standard uncertainty quantification strategies (such as thresholding the log-likelihood of a response) where hallucinations in the multi-answer case cannot be detected. We conduct a series of experiments which demonstrate the advantage of our formulation. Further, our investigations shed some light on how the probabilities assigned to a given output by an LLM can be amplified by iterative prompting, which might be of independent interest.

Inference-time scaling techniques have significantly bolstered the reasoning capabilities of large language models (LLMs) by harnessing additional computational effort at inference without retraining. Similarly, Chain-of-Thought (CoT) prompting and its extension, Long CoT, improve accuracy by generating rich intermediate reasoning trajectories, but these approaches incur substantial token costs that impede their deployment in latency-sensitive settings. In this work, we first show that truncated CoT, which stops reasoning before completion and directly generates the final answer, often matches full CoT sampling while using dramatically fewer tokens. Building on this insight, we introduce Fractured Sampling, a unified inference-time strategy that interpolates between full CoT and solution-only sampling along three orthogonal axes: (1) the number of reasoning trajectories, (2) the number of final solutions per trajectory, and (3) the depth at which reasoning traces are truncated. Through extensive experiments on five diverse reasoning benchmarks and several model scales, we demonstrate that Fractured Sampling consistently achieves superior accuracy-cost trade-offs, yielding steep log-linear scaling gains in Pass@k versus token budget. Our analysis reveals how to allocate computation across these dimensions to maximize performance, paving the way for more efficient and scalable LLM reasoning.

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.

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

Chain-of-thought prompting~(CoT) and tool augmentation have been validated in recent work as effective practices for improving large language models~(LLMs) to perform step-by-step reasoning on complex math-related tasks. However, most existing math reasoning datasets may be not able to fully evaluate and analyze the ability of LLMs in manipulating tools and performing reasoning, as they may only require very few invocations of tools or miss annotations for evaluating intermediate reasoning steps. To address the issue, we construct CARP, a new Chinese dataset consisting of 4,886 computation-intensive algebra problems with formulated annotations on intermediate steps. In CARP, we test four LLMs with CoT prompting, and find that they are all prone to make mistakes at the early steps of the solution, leading to wrong answers. Based on this finding, we propose a new approach that can deliberate the reasoning steps with tool interfaces, namely DELI. In DELI, we first initialize a step-by-step solution based on retrieved exemplars, then iterate two deliberation procedures that check and refine the intermediate steps of the generated solution, from the perspectives of tool manipulation and natural language reasoning, until obtaining converged solutions or reaching the maximum turn. Experimental results on CARP and six other datasets show that the proposed DELI mostly outperforms competitive baselines, and can further boost the performance of existing CoT methods. Our data and code are available in https://github.com/RUCAIBox/CARP.

Social reasoning - inferring unobservable beliefs and intentions from partial observations of other agents - remains a challenging task for large language models (LLMs). We evaluate the limits of current reasoning language models in the social deduction game Avalon and find that while the largest models demonstrate strong performance, they require extensive test-time inference and degrade sharply when distilled to smaller, real-time-capable variants. To address this, we introduce a hybrid reasoning framework that externalizes belief inference to a structured probabilistic model, while using an LLM for language understanding and interaction. Our approach achieves competitive performance with much larger models in Agent-Agent play and, notably, is the first language agent to defeat human players in a controlled study - achieving a 67% win rate and receiving higher qualitative ratings than both reasoning baselines and human teammates. We release code, models, and a dataset to support future work on social reasoning in LLM agents, which can be found at https://camp-lab-purdue.github.io/bayesian-social-deduction/

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

Explanatory inference is the creation and evaluation of hypotheses that provide explanations, and is sometimes known as abduction or abductive inference. Generative AI is a new set of artificial intelligence models based on novel algorithms for generating text, images, and sounds. This paper proposes a set of benchmarks for assessing the ability of AI programs to perform explanatory inference, and uses them to determine the extent to which ChatGPT, a leading generative AI model, is capable of making explanatory inferences. Tests on the benchmarks reveal that ChatGPT performs creative and evaluative inferences in many domains, although it is limited to verbal and visual modalities. Claims that ChatGPT and similar models are incapable of explanation, understanding, causal reasoning, meaning, and creativity are rebutted.

A prominent challenge of offline reinforcement learning (RL) is the issue of hidden confounding: unobserved variables may influence both the actions taken by the agent and the observed outcomes. Hidden confounding can compromise the validity of any causal conclusion drawn from data and presents a major obstacle to effective offline RL. In the present paper, we tackle the problem of hidden confounding in the nonidentifiable setting. We propose a definition of uncertainty due to hidden confounding bias, termed delphic uncertainty, which uses variation over world models compatible with the observations, and differentiate it from the well-known epistemic and aleatoric uncertainties. We derive a practical method for estimating the three types of uncertainties, and construct a pessimistic offline RL algorithm to account for them. Our method does not assume identifiability of the unobserved confounders, and attempts to reduce the amount of confounding bias. We demonstrate through extensive experiments and ablations the efficacy of our approach on a sepsis management benchmark, as well as on electronic health records. Our results suggest that nonidentifiable hidden confounding bias can be mitigated to improve offline RL solutions in practice.

Scaling model size and training data has led to great advances in the performance of Large Language Models (LLMs). However, the diminishing returns of this approach necessitate alternative methods to improve model capabilities, particularly in tasks requiring advanced reasoning. Large reasoning models, which leverage long chain-of-thoughts, bring unprecedented breakthroughs in problem-solving capabilities but at a substantial deployment cost associated to longer generations. Reducing inference costs is crucial for the economic feasibility, user experience, and environmental sustainability of these models. In this work, we propose to train large reasoning models to reason efficiently. More precisely, we use reinforcement learning (RL) to train reasoning models to dynamically allocate inference-time compute based on task complexity. Our method incentivizes models to minimize unnecessary computational overhead while maintaining accuracy, thereby achieving substantial efficiency gains. It enables the derivation of a family of reasoning models with varying efficiency levels, controlled via a single hyperparameter. Experiments on two open-weight large reasoning models demonstrate significant reductions in inference cost while preserving most of the accuracy.

We study the problem of modeling a population of agents pursuing unknown goals subject to unknown computational constraints. In standard models of bounded rationality, sub-optimal decision-making is simulated by adding homoscedastic noise to optimal decisions rather than explicitly simulating constrained inference. In this work, we introduce a latent inference budget model (L-IBM) that models agents' computational constraints explicitly, via a latent variable (inferred jointly with a model of agents' goals) that controls the runtime of an iterative inference algorithm. L-IBMs make it possible to learn agent models using data from diverse populations of suboptimal actors. In three modeling tasks -- inferring navigation goals from routes, inferring communicative intents from human utterances, and predicting next moves in human chess games -- we show that L-IBMs match or outperform Boltzmann models of decision-making under uncertainty. Inferred inference budgets are themselves meaningful, efficient to compute, and correlated with measures of player skill, partner skill and task difficulty.

Large Language Models (LLMs) have exhibited an impressive capability to perform reasoning tasks, especially if they are encouraged to generate a sequence of intermediate steps. Reasoning performance can be improved by suitably combining multiple LLM responses, generated either in parallel in a single query, or via sequential interactions with LLMs throughout the reasoning process. Existing strategies for combination, such as self-consistency and progressive-hint-prompting, make inefficient usage of the LLM responses. We present Hint Marginalization, a novel and principled algorithmic framework to enhance the reasoning capabilities of LLMs. Our approach can be viewed as an iterative sampling strategy for forming a Monte Carlo approximation of an underlying distribution of answers, with the goal of identifying the mode the most likely answer. Empirical evaluation on several benchmark datasets for arithmetic reasoning demonstrates the superiority of the proposed approach.

Research on emergent patterns in Large Language Models (LLMs) has gained significant traction in both psychology and artificial intelligence, motivating the need for a comprehensive review that offers a synthesis of this complex landscape. In this article, we systematically review LLMs' capabilities across three important cognitive domains: decision-making biases, reasoning, and creativity. We use empirical studies drawing on established psychological tests and compare LLMs' performance to human benchmarks. On decision-making, our synthesis reveals that while LLMs demonstrate several human-like biases, some biases observed in humans are absent, indicating cognitive patterns that only partially align with human decision-making. On reasoning, advanced LLMs like GPT-4 exhibit deliberative reasoning akin to human System-2 thinking, while smaller models fall short of human-level performance. A distinct dichotomy emerges in creativity: while LLMs excel in language-based creative tasks, such as storytelling, they struggle with divergent thinking tasks that require real-world context. Nonetheless, studies suggest that LLMs hold considerable potential as collaborators, augmenting creativity in human-machine problem-solving settings. Discussing key limitations, we also offer guidance for future research in areas such as memory, attention, and open-source model development.

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.

Reasoning training incentivizes LLMs to produce long chains of thought (long CoT), which among other things, allows them to explore solution strategies with self-checking. This results in higher accuracy, but inflates context length, token/compute cost, and answer latency. We ask: Can current models leverage their metacognition to provide other combinations on this Pareto frontier, e.g., better accuracy with lower context length and/or latency? Abstractly, we view the model as an improvement operator on its own "thoughts" with a continuum of possible strategies. We identify an interesting inference family Parallel-Distill-Refine (PDR), which performs the following: (i) generate diverse drafts in parallel; (ii) distill them into a bounded, textual workspace; and (iii) refine conditioned on this workspace, producing an output that seeds the next round. Importantly, context length (hence compute cost) is controllable via degree of parallelism, and is no longer conflated with the total number of generated tokens. We report PDR instantiations of current models that give better accuracy than long CoT while incurring lower latency. Setting degree of parallelism to 1 yields an interesting subcase, Sequential Refinement (SR) (iteratively improve a single candidate answer) which provides performance superior to long CoT. Success of such model orchestrations raises the question whether further training could shift the Pareto frontier. To this end, we train an 8B thinking model with Reinforcement Learning (RL) to make it consistent with PDR as the inference method. On math tasks with verifiable answers, iterative pipelines surpass single-pass baselines at matched sequential budgets, with PDR delivering the largest gains (e.g., +11% on AIME 2024 and +9% on AIME 2025).

Reasoning is a fundamental cognitive process that enables logical inference, problem-solving, and decision-making. With the rapid advancement of large language models (LLMs), reasoning has emerged as a key capability that distinguishes advanced AI systems from conventional models that empower chatbots. In this survey, we categorize existing methods along two orthogonal dimensions: (1) Regimes, which define the stage at which reasoning is achieved (either at inference time or through dedicated training); and (2) Architectures, which determine the components involved in the reasoning process, distinguishing between standalone LLMs and agentic compound systems that incorporate external tools, and multi-agent collaborations. Within each dimension, we analyze two key perspectives: (1) Input level, which focuses on techniques that construct high-quality prompts that the LLM condition on; and (2) Output level, which methods that refine multiple sampled candidates to enhance reasoning quality. This categorization provides a systematic understanding of the evolving landscape of LLM reasoning, highlighting emerging trends such as the shift from inference-scaling to learning-to-reason (e.g., DeepSeek-R1), and the transition to agentic workflows (e.g., OpenAI Deep Research, Manus Agent). Additionally, we cover a broad spectrum of learning algorithms, from supervised fine-tuning to reinforcement learning such as PPO and GRPO, and the training of reasoners and verifiers. We also examine key designs of agentic workflows, from established patterns like generator-evaluator and LLM debate to recent innovations. ...

Chain-of-thought (CoT) reasoning is critical for improving the interpretability and reliability of Large Vision-Language Models (LVLMs). However, existing training algorithms such as SFT, PPO, and GRPO may not generalize well across unseen reasoning tasks and heavily rely on a biased reward model. To address this challenge, we reformulate reasoning in LVLMs as posterior inference and propose a scalable training algorithm based on amortized variational inference. By leveraging diversity-seeking reinforcement learning algorithms, we introduce a novel sparse reward function for token-level learning signals that encourage diverse, high-likelihood latent CoT, overcoming deterministic sampling limitations and avoiding reward hacking. Additionally, we implement a Bayesian inference-scaling strategy that replaces costly Best-of-N and Beam Search with a marginal likelihood to efficiently rank optimal rationales and answers. We empirically demonstrate that the proposed method enhances the state-of-the-art LVLMs on seven reasoning benchmarks, in terms of effectiveness, generalization, and interpretability.

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

Accelerating the inference of large language models (LLMs) is an important challenge in artificial intelligence. This paper introduces distributed speculative inference (DSI), a novel distributed inference algorithm that is provably faster than speculative inference (SI) [leviathan2023fast, chen2023accelerating, miao2023specinfer] and traditional autoregressive inference (non-SI). Like other SI algorithms, DSI works on frozen LLMs, requiring no training or architectural modifications, and it preserves the target distribution. Prior studies on SI have demonstrated empirical speedups (compared to non-SI) but require a fast and accurate drafter LLM. In practice, off-the-shelf LLMs often do not have matching drafters that are sufficiently fast and accurate. We show a gap: SI gets slower than non-SI when using slower or less accurate drafters. We close this gap by proving that DSI is faster than both SI and non-SI given any drafters. By orchestrating multiple instances of the target and drafters, DSI is not only faster than SI but also supports LLMs that cannot be accelerated with SI. Our simulations show speedups of off-the-shelf LLMs in realistic settings: DSI is 1.29-1.92x faster than SI.

Deductive reasoning is the process of deriving conclusions strictly from the given premises, without relying on external knowledge. We define honesty in this setting as a model's ability to respond only when the conclusion is logically entailed by the premises, and to abstain otherwise. However, current language models often fail to reason honestly, producing unwarranted answers when the input is insufficient. To study this challenge, we formulate honest deductive reasoning as multi-step tasks where models must either derive the correct conclusion or abstain. We curate two datasets from graph structures, one for linear algebra and one for logical inference, and introduce unanswerable cases by randomly perturbing an edge in half of the instances. We find that prompting and existing training methods, including GRPO with or without supervised fine-tuning initialization, struggle on these tasks. In particular, GRPO optimize only for final task outcomes, leaving models vulnerable to collapse when negative rewards dominate early training. To address this, we propose ACNCHOR, a reinforcement learning method that injects ground truth trajectories into rollouts, preventing early training collapse. Our results demonstrate that this method stabilizes learning and significantly improves the overall reasoning performance, underscoring the importance of training dynamics for enabling honest deductive reasoning in language models.

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

Inference scaling empowers LLMs with unprecedented reasoning ability, with reinforcement learning as the core technique to elicit complex reasoning. However, key technical details of state-of-the-art reasoning LLMs are concealed (such as in OpenAI o1 blog and DeepSeek R1 technical report), thus the community still struggles to reproduce their RL training results. We propose the Decoupled Clip and Dynamic sAmpling Policy Optimization (DAPO) algorithm, and fully open-source a state-of-the-art large-scale RL system that achieves 50 points on AIME 2024 using Qwen2.5-32B base model. Unlike previous works that withhold training details, we introduce four key techniques of our algorithm that make large-scale LLM RL a success. In addition, we open-source our training code, which is built on the verl framework, along with a carefully curated and processed dataset. These components of our open-source system enhance reproducibility and support future research in large-scale LLM RL.

This paper presents a case study on the design, administration, post-processing, and evaluation of surveys on large language models (LLMs). It comprises two components: (1) A statistical method for eliciting beliefs encoded in LLMs. We introduce statistical measures and evaluation metrics that quantify the probability of an LLM "making a choice", the associated uncertainty, and the consistency of that choice. (2) We apply this method to study what moral beliefs are encoded in different LLMs, especially in ambiguous cases where the right choice is not obvious. We design a large-scale survey comprising 680 high-ambiguity moral scenarios (e.g., "Should I tell a white lie?") and 687 low-ambiguity moral scenarios (e.g., "Should I stop for a pedestrian on the road?"). Each scenario includes a description, two possible actions, and auxiliary labels indicating violated rules (e.g., "do not kill"). We administer the survey to 28 open- and closed-source LLMs. We find that (a) in unambiguous scenarios, most models "choose" actions that align with commonsense. In ambiguous cases, most models express uncertainty. (b) Some models are uncertain about choosing the commonsense action because their responses are sensitive to the question-wording. (c) Some models reflect clear preferences in ambiguous scenarios. Specifically, closed-source models tend to agree with each other.

Reasoning large language models (RLLMs) have recently demonstrated remarkable capabilities through structured and multi-step reasoning. While prior research has primarily focused on improving their training and inference strategies, their potential for in-context learning (ICL) remains largely underexplored. To fill this gap, we propose Thinking with Nothinking Calibration (JointThinking), a new ICL paradigm that leverages the structured difference between two reasoning modes, i.e., Thinking and Nothinking, to improve reasoning accuracy. Specifically, our method prompts the model to generate two answers in parallel: one in Thinking mode and the other in Nothinking mode. A second round of Thinking is triggered only when the two initial responses are inconsistent, using a single prompt that incorporates the original question and both candidate answers. Since such disagreement occurs infrequently (e.g., only 6\% in GSM8K), our method performs just one round of reasoning in most cases, resulting in minimal latency overhead. Extensive experiments across multiple reasoning benchmarks demonstrate that JointThinking significantly outperforms few-shot chain-of-thought (CoT) and majority voting with improved answer robustness. Moreover, It achieves comparable in-distribution performance to training-based SOTA method, while substantially outperforming on out-of-distribution tasks. We further conduct a systematic analysis of the calibration mechanism, showing that leveraging different reasoning modes consistently lowers the error rate and highlights the value of structural thinking diversity. Additionally, we observe that the performance gap between actual and ideal reasoning narrows as model size increases in the second round of thinking, indicating the strong scalability of our approach. Finally, we discuss current limitations and outline promising directions for future ICL research in RLLMs.

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.

Being prompted to engage in reasoning has emerged as a core technique for using large language models (LLMs), deploying additional inference-time compute to improve task performance. However, as LLMs increase in both size and adoption, inference costs are correspondingly becoming increasingly burdensome. How, then, might we optimize reasoning's cost-performance tradeoff? This work introduces a novel approach based on computational models of metareasoning used in cognitive science, training LLMs to selectively use intermediate reasoning steps only when necessary. We first develop a reward function that incorporates the Value of Computation by penalizing unnecessary reasoning, then use this reward function with Expert Iteration to train the LLM. Compared to few-shot chain-of-thought prompting and STaR, our method significantly reduces inference costs (20-37\% fewer tokens generated across three models) while maintaining task performance across diverse datasets.

Epistemic Uncertainty is a measure of the lack of knowledge of a learner which diminishes with more evidence. While existing work focuses on using the variance of the Bayesian posterior due to parameter uncertainty as a measure of epistemic uncertainty, we argue that this does not capture the part of lack of knowledge induced by model misspecification. We discuss how the excess risk, which is the gap between the generalization error of a predictor and the Bayes predictor, is a sound measure of epistemic uncertainty which captures the effect of model misspecification. We thus propose a principled framework for directly estimating the excess risk by learning a secondary predictor for the generalization error and subtracting an estimate of aleatoric uncertainty, i.e., intrinsic unpredictability. We discuss the merits of this novel measure of epistemic uncertainty, and highlight how it differs from variance-based measures of epistemic uncertainty and addresses its major pitfall. Our framework, Direct Epistemic Uncertainty Prediction (DEUP) is particularly interesting in interactive learning environments, where the learner is allowed to acquire novel examples in each round. Through a wide set of experiments, we illustrate how existing methods in sequential model optimization can be improved with epistemic uncertainty estimates from DEUP, and how DEUP can be used to drive exploration in reinforcement learning. We also evaluate the quality of uncertainty estimates from DEUP for probabilistic image classification and predicting synergies of drug combinations.

Large language models (LLMs) have demonstrated remarkable capabilities in complex reasoning tasks. However, existing approaches mainly rely on imitation learning and struggle to achieve effective test-time scaling. While reinforcement learning (RL) holds promise for enabling self-exploration and learning from feedback, recent attempts yield only modest improvements in complex reasoning. In this paper, we present T1 to scale RL by encouraging exploration and understand inference scaling. We first initialize the LLM using synthesized chain-of-thought data that integrates trial-and-error and self-verification. To scale RL training, we promote increased sampling diversity through oversampling. We further employ an entropy bonus as an auxiliary loss, alongside a dynamic anchor for regularization to facilitate reward optimization. We demonstrate that T1 with open LLMs as its base exhibits inference scaling behavior and achieves superior performance on challenging math reasoning benchmarks. For example, T1 with Qwen2.5-32B as the base model outperforms the recent Qwen QwQ-32B-Preview model on MATH500, AIME2024, and Omni-math-500. More importantly, we present a simple strategy to examine inference scaling, where increased inference budgets directly lead to T1's better performance without any additional verification. We will open-source the T1 models and the data used to train them at https://github.com/THUDM/T1.

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

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.

As AI systems progress, we rely more on them to make decisions with us and for us. To ensure that such decisions are aligned with human values, it is imperative for us to understand not only what decisions they make but also how they come to those decisions. Reasoning language models, which provide both final responses and (partially transparent) intermediate thinking traces, present a timely opportunity to study AI procedural reasoning. Unlike math and code problems which often have objectively correct answers, moral dilemmas are an excellent testbed for process-focused evaluation because they allow for multiple defensible conclusions. To do so, we present MoReBench: 1,000 moral scenarios, each paired with a set of rubric criteria that experts consider essential to include (or avoid) when reasoning about the scenarios. MoReBench contains over 23 thousand criteria including identifying moral considerations, weighing trade-offs, and giving actionable recommendations to cover cases on AI advising humans moral decisions as well as making moral decisions autonomously. Separately, we curate MoReBench-Theory: 150 examples to test whether AI can reason under five major frameworks in normative ethics. Our results show that scaling laws and existing benchmarks on math, code, and scientific reasoning tasks fail to predict models' abilities to perform moral reasoning. Models also show partiality towards specific moral frameworks (e.g., Benthamite Act Utilitarianism and Kantian Deontology), which might be side effects of popular training paradigms. Together, these benchmarks advance process-focused reasoning evaluation towards safer and more transparent AI.

The mathematical study of voting, social choice theory, has traditionally only been applicable to choices among a few predetermined alternatives, but not to open-ended decisions such as collectively selecting a textual statement. We introduce generative social choice, a design methodology for open-ended democratic processes that combines the rigor of social choice theory with the capability of large language models to generate text and extrapolate preferences. Our framework divides the design of AI-augmented democratic processes into two components: first, proving that the process satisfies representation guarantees when given access to oracle queries; second, empirically validating that these queries can be approximately implemented using a large language model. We apply this framework to the problem of summarizing free-form opinions into a proportionally representative slate of opinion statements; specifically, we develop a democratic process with representation guarantees and use this process to portray the opinions of participants in a survey about abortion policy. In a trial with 100 representative US residents, we find that 84 out of 100 participants feel "excellently" or "exceptionally" represented by the slate of five statements we extracted.

"Thinking is for Doing." Humans can infer other people's mental states from observations--an ability called Theory-of-Mind (ToM)--and subsequently act pragmatically on those inferences. Existing question answering benchmarks such as ToMi ask models questions to make inferences about beliefs of characters in a story, but do not test whether models can then use these inferences to guide their actions. We propose a new evaluation paradigm for large language models (LLMs): Thinking for Doing (T4D), which requires models to connect inferences about others' mental states to actions in social scenarios. Experiments on T4D demonstrate that LLMs such as GPT-4 and PaLM 2 seemingly excel at tracking characters' beliefs in stories, but they struggle to translate this capability into strategic action. Our analysis reveals the core challenge for LLMs lies in identifying the implicit inferences about mental states without being explicitly asked about as in ToMi, that lead to choosing the correct action in T4D. To bridge this gap, we introduce a zero-shot prompting framework, Foresee and Reflect (FaR), which provides a reasoning structure that encourages LLMs to anticipate future challenges and reason about potential actions. FaR boosts GPT-4's performance from 50% to 71% on T4D, outperforming other prompting methods such as Chain-of-Thought and Self-Ask. Moreover, FaR generalizes to diverse out-of-distribution story structures and scenarios that also require ToM inferences to choose an action, consistently outperforming other methods including few-shot in-context learning.

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.

Making theory-of-mind inferences from human dialogue is a strong indicator of a model's underlying social abilities, which are fundamental for adept AI assistants. However, large language and reasoning models struggle to understand sophisticated social phenomena in transcript data, such as sarcasm and irony. To assess the weaknesses of current models and to identify their solutions, we introduce SocialNLI (SoNLI) -- the first social dialogue inference dataset. SoNLI consists of a collection of dialogue transcripts hand-picked to center complex social nuances like irony and sarcasm, paired with inferences, corresponding likelihood scores, and human-written explanations. We explore social inference analysis as a facet of theory-of-mind, and evaluate LLM and reasoning model theory-of-mind ability through multi-step counterfactual reasoning.

Large language models (LLMs) have demonstrated significant success in complex reasoning tasks such as math and coding. In contrast to these tasks where deductive reasoning predominates, inductive reasoning-the ability to derive general rules from incomplete evidence, remains underexplored. This paper investigates extended inductive reasoning in LLMs through the lens of personalized preference inference, a critical challenge in LLM alignment where current approaches struggle to capture diverse user preferences. The task demands strong inductive reasoning capabilities as user preferences are typically embedded implicitly across various interaction forms, requiring models to synthesize consistent preference patterns from scattered signals. We propose AlignXplore, a model that leverages extended reasoning chains to enable systematic preference inference from behavioral signals in users' interaction histories. Such explicit preference articulation enables efficient streaming inference: when new behavioral signals emerge, the model can directly build upon previously inferred preference descriptions rather than reprocessing historical signals from scratch, while also supporting iterative refinement to the inferred preferences. We develop AlignXplore by combining cold-start training based on synthetic data with subsequent online reinforcement learning. Through extensive experiments, we demonstrate that AlignXplore achieves substantial improvements over the backbone model by an average of 15.49\% on in-domain and out-of-domain benchmarks, while maintaining strong generalization ability across different input formats and downstream models. Further analyses establish best practices for preference inference learning through systematic comparison of reward modeling strategies, while revealing the emergence of human-like inductive reasoning patterns during training.

Recent advances in large language models (LLMs) have accelerated progress toward artificial general intelligence, with inference-time scaling emerging as a key technique. Contemporary approaches leverage either sequential reasoning (iteratively extending chains of thought) or parallel reasoning (generating multiple solutions simultaneously) to scale inference. However, both paradigms face fundamental limitations: sequential scaling typically relies on arbitrary token budgets for termination, leading to inefficiency or premature cutoff; while parallel scaling often lacks coordination among parallel branches and requires intrusive fine-tuning to perform effectively. In light of these challenges, we aim to design a flexible test-time collaborative inference framework that exploits the complementary strengths of both sequential and parallel reasoning paradigms. Towards this goal, the core challenge lies in developing an efficient and accurate intrinsic quality metric to assess model responses during collaborative inference, enabling dynamic control and early termination of the reasoning trace. To address this challenge, we introduce semantic entropy (SE), which quantifies the semantic diversity of parallel model responses and serves as a robust indicator of reasoning quality due to its strong negative correlation with accuracy...

Chain-of-thought (CoT) reasoning enables large language models (LLMs) to break down complex problems into interpretable intermediate steps, significantly enhancing model transparency and performance in reasoning tasks. However, conventional CoT methods rely on heuristic sampling without structured modeling of reasoning transitions, constraining their ability to systematically explore and discover diverse and effective reasoning trajectories. In this work, we introduce CTRLS, a framework that formulates CoT reasoning as a Markov decision process (MDP) with latent state transitions, enabling principled and state-aware exploration via distributional reinforcement learning. By modelling reasoning actions as explicit probability distributions in latent space, our approach explicitly models epistemic uncertainty, facilitating robust exploration of the reasoning space. As part of our framework, we introduce an on-policy reinforcement learning strategy incorporating epsilon-greedy exploration and entropy-based regularization to iteratively refine latent state transitions without requiring additional fine-tuning of the underlying LLM. Theoretical analyses provide evidence lower bounds (ELBO), theoretically grounding our transition-aware modeling of latent reasoning dynamics. Further experiments demonstrate improvements in reasoning accuracy, diversity, and exploration efficiency across benchmark reasoning tasks.

Large Language Models (LLMs) have shown exceptional results on current benchmarks when working individually. The advancement in their capabilities, along with a reduction in parameter size and inference times, has facilitated the use of these models as agents, enabling interactions among multiple models to execute complex tasks. Such collaborations offer several advantages, including the use of specialized models (e.g. coding), improved confidence through multiple computations, and enhanced divergent thinking, leading to more diverse outputs. Thus, the collaborative use of language models is expected to grow significantly in the coming years. In this work, we evaluate the behavior of a network of models collaborating through debate under the influence of an adversary. We introduce pertinent metrics to assess the adversary's effectiveness, focusing on system accuracy and model agreement. Our findings highlight the importance of a model's persuasive ability in influencing others. Additionally, we explore inference-time methods to generate more compelling arguments and evaluate the potential of prompt-based mitigation as a defensive strategy.

Large Reasoning Models (LRMs) have significantly enhanced their capabilities in complex problem-solving by introducing a thinking draft that enables multi-path Chain-of-Thought explorations before producing final answers. Ensuring the faithfulness of these intermediate reasoning processes is crucial for reliable monitoring, interpretation, and effective control. In this paper, we propose a systematic counterfactual intervention framework to rigorously evaluate thinking draft faithfulness. Our approach focuses on two complementary dimensions: (1) Intra-Draft Faithfulness, which assesses whether individual reasoning steps causally influence subsequent steps and the final draft conclusion through counterfactual step insertions; and (2) Draft-to-Answer Faithfulness, which evaluates whether final answers are logically consistent with and dependent on the thinking draft, by perturbing the draft's concluding logic. We conduct extensive experiments across six state-of-the-art LRMs. Our findings show that current LRMs demonstrate selective faithfulness to intermediate reasoning steps and frequently fail to faithfully align with the draft conclusions. These results underscore the need for more faithful and interpretable reasoning in advanced LRMs.

For the purpose of efficient and cost-effective large-scale data labeling, crowdsourcing is increasingly being utilized. To guarantee the quality of data labeling, multiple annotations need to be collected for each data sample, and truth inference algorithms have been developed to accurately infer the true labels. Despite previous studies having released public datasets to evaluate the efficacy of truth inference algorithms, these have typically focused on a single type of crowdsourcing task and neglected the temporal information associated with workers' annotation activities. These limitations significantly restrict the practical applicability of these algorithms, particularly in the context of long-term and online truth inference. In this paper, we introduce a substantial crowdsourcing annotation dataset collected from a real-world crowdsourcing platform. This dataset comprises approximately two thousand workers, one million tasks, and six million annotations. The data was gathered over a period of approximately six months from various types of tasks, and the timestamps of each annotation were preserved. We analyze the characteristics of the dataset from multiple perspectives and evaluate the effectiveness of several representative truth inference algorithms on this dataset. We anticipate that this dataset will stimulate future research on tracking workers' abilities over time in relation to different types of tasks, as well as enhancing online truth inference.

This review examines how AI technologies are transforming democratic representation, focusing on citizen participation and algorithmic decision-making. The analysis reveals that AI technologies are reshaping democratic processes in fundamental ways: enabling mass-scale deliberation, changing how citizens access and engage with political information, and transforming how representatives make and implement decisions. While AI offers unprecedented opportunities for enhancing democratic participation and governance efficiency, it also presents significant challenges to democratic legitimacy and accountability. Social media platforms' AI-driven algorithms currently mediate much political discourse, creating concerns about information manipulation and privacy. Large Language Models introduce both epistemic challenges and potential tools for improving democratic dialogue. The emergence of Mass Online Deliberation platforms suggests possibilities for scaling up meaningful citizen participation, while Algorithmic Decision-Making systems promise more efficient policy implementation but face limitations in handling complex political trade-offs. As these systems become prevalent, representatives may assume the role of architects of automated decision frameworks, responsible for guiding the translation of politically contested concepts into technical parameters and metrics. Advanced deliberation platforms offering real-time insights into citizen preferences will challenge traditional representative independence and discretion to interpret public will. The institutional integration of these participation mechanisms requires frameworks that balance the benefits with democratic stability through hybrid systems weighting different forms of democratic expression.

Deploying machine learning models in production may allow adversaries to infer sensitive information about training data. There is a vast literature analyzing different types of inference risks, ranging from membership inference to reconstruction attacks. Inspired by the success of games (i.e., probabilistic experiments) to study security properties in cryptography, some authors describe privacy inference risks in machine learning using a similar game-based style. However, adversary capabilities and goals are often stated in subtly different ways from one presentation to the other, which makes it hard to relate and compose results. In this paper, we present a game-based framework to systematize the body of knowledge on privacy inference risks in machine learning. We use this framework to (1) provide a unifying structure for definitions of inference risks, (2) formally establish known relations among definitions, and (3) to uncover hitherto unknown relations that would have been difficult to spot otherwise.

Recent advances leverage post-training to enhance model reasoning performance, which typically requires costly training pipelines and still suffers from inefficient, overly lengthy outputs. We introduce Speculative Thinking, a training-free framework that enables large reasoning models to guide smaller ones during inference at the reasoning level, distinct from speculative decoding, which operates at the token level. Our approach is based on two observations: (1) reasoning-supportive tokens such as "wait" frequently appear after structural delimiters like "\n\n", serving as signals for reflection or continuation; and (2) larger models exhibit stronger control over reflective behavior, reducing unnecessary backtracking while improving reasoning quality. By strategically delegating reflective steps to a more capable model, our method significantly boosts the reasoning accuracy of reasoning models while shortening their output. With the assistance of the 32B reasoning model, the 1.5B model's accuracy on MATH500 increases from 83.2% to 89.4%, marking a substantial improvement of 6.2%. Simultaneously, the average output length is reduced from 5439 tokens to 4583 tokens, representing a 15.7% decrease. Moreover, when applied to a non-reasoning model (Qwen-2.5-7B-Instruct), our framework boosts its accuracy from 74.0% to 81.8% on the same benchmark, achieving a relative improvement of 7.8%.

Large Audio-Language Models (LALMs) have demonstrated remarkable performance in tasks involving audio perception and understanding, such as speech recognition and audio captioning. However, their reasoning capabilities - critical for solving complex real-world problems - remain underexplored. In this work, we conduct the first exploration into integrating Chain-of-Thought (CoT) reasoning into LALMs to enhance their reasoning ability across auditory modalities. We evaluate representative CoT methods, analyzing their performance in both information extraction and reasoning tasks across sound, music, and speech domains. Our findings reveal that CoT methods significantly improve performance on easy and medium tasks but encounter challenges with hard tasks, where reasoning chains can confuse the model rather than improve accuracy. Additionally, we identify a positive correlation between reasoning path length and accuracy, demonstrating the potential of scaling inference for advanced instruction-following and reasoning. This study not only highlights the promise of CoT in enhancing LALM reasoning capabilities but also identifies key limitations and provides actionable directions for future research.

Recent advances in reasoning-centric models promise improved robustness through mechanisms such as chain-of-thought prompting and test-time scaling. However, their ability to withstand misleading user input remains underexplored. In this paper, we conduct a systematic evaluation of three state-of-the-art reasoning models, i.e., OpenAI's o4-mini, Claude-3.7-Sonnet and Gemini-2.5-Flash, across three multimodal benchmarks: MMMU, MathVista, and CharXiv. Our evaluation reveals significant accuracy drops (25-29% on average) following gaslighting negation prompts, indicating that even top-tier reasoning models struggle to preserve correct answers under manipulative user feedback. Built upon the insights of the evaluation and to further probe this vulnerability, we introduce GaslightingBench-R, a new diagnostic benchmark specifically designed to evaluate reasoning models' susceptibility to defend their belief under gaslighting negation prompt. Constructed by filtering and curating 1,025 challenging samples from the existing benchmarks, GaslightingBench-R induces even more dramatic failures, with accuracy drops exceeding 53% on average. Our findings reveal fundamental limitations in the robustness of reasoning models, highlighting the gap between step-by-step reasoning and belief persistence.

The surprisingly likely criterion in the seminal work of Prelec (the Bayesian Truth Serum) guarantees truthfulness in a game-theoretic multi-agent setting, by rewarding rational agents to maximise the expected information gain with their answers w.r.t. their probabilistic beliefs. We investigate the relevance of a similar criterion for responses of LLMs. We hypothesize that if the surprisingly likely criterion works in LLMs, under certain conditions, the responses that maximize the reward under this criterion should be more accurate than the responses that only maximize the posterior probability. Using benchmarks including the TruthfulQA benchmark and using openly available LLMs: GPT-2 and LLaMA-2, we show that the method indeed improves the accuracy significantly (for example, upto 24 percentage points aggregate improvement on TruthfulQA and upto 70 percentage points improvement on individual categories of questions).

Chain-of-thought (CoT) prompting enhances reasoning in large language models (LLMs) but often leads to verbose and redundant outputs, thus increasing inference cost. We hypothesize that many reasoning steps are unnecessary for producing correct answers. To investigate this, we start with a systematic study to examine what is the minimum reasoning required for a model to reach a stable decision. We find that on math reasoning tasks like math, models typically converge to their final answers after 60\% of the reasoning steps, suggesting substantial redundancy in the remaining content. Based on these insights, we propose three inference-time strategies to improve efficiency: (1) early stopping via answer consistency, (2) boosting the probability of generating end-of-reasoning signals, and (3) a supervised method that learns when to stop based on internal activations. Experiments across five benchmarks and five open-weights LLMs show that our methods significantly reduce token usage with little or no accuracy drop. In particular, on NaturalQuestions, Answer Consistency reduces tokens by over 40\% while further improving accuracy. Our work underscores the importance of cost-effective reasoning methods that operate at inference time, offering practical benefits for real-world applications.

Language use is shaped by pragmatics -- i.e., reasoning about communicative goals and norms in context. As language models (LMs) are increasingly used as conversational agents, it becomes ever more important to understand their pragmatic reasoning abilities. We propose an evaluation framework derived from Wavelength, a popular communication game where a speaker and a listener communicate about a broad range of concepts in a granular manner. We study a range of LMs on both language comprehension and language production using direct and Chain-of-Thought (CoT) prompting, and further explore a Rational Speech Act (RSA) approach to incorporating Bayesian pragmatic reasoning into LM inference. We find that state-of-the-art LMs, but not smaller ones, achieve strong performance on language comprehension, obtaining similar-to-human accuracy and exhibiting high correlations with human judgments even without CoT prompting or RSA. On language production, CoT can outperform direct prompting, and using RSA provides significant improvements over both approaches. Our study helps identify the strengths and limitations in LMs' pragmatic reasoning abilities and demonstrates the potential for improving them with RSA, opening up future avenues for understanding conceptual representation, language understanding, and social reasoning in LMs and humans.

Artificial intelligence functions not as an epistemic leveller, but as an accelerant of cognitive stratification, entrenching and formalising informational castes within liberal-democratic societies. Synthesising formal epistemology, political theory, algorithmic architecture, and economic incentive structures, the argument traces how contemporary AI systems selectively amplify the reasoning capacity of individuals equipped with recursive abstraction, symbolic logic, and adversarial interrogation, whilst simultaneously pacifying the cognitively untrained through engagement-optimised interfaces. Fluency replaces rigour, immediacy displaces reflection, and procedural reasoning is eclipsed by reactive suggestion. The result is a technocratic realignment of power: no longer grounded in material capital alone, but in the capacity to navigate, deconstruct, and manipulate systems of epistemic production. Information ceases to be a commons; it becomes the substrate through which consent is manufactured and autonomy subdued. Deliberative democracy collapses not through censorship, but through the erosion of interpretive agency. The proposed response is not technocratic regulation, nor universal access, but the reconstruction of rational autonomy as a civic mandate, codified in education, protected by epistemic rights, and structurally embedded within open cognitive infrastructure.

Context is everything, even in commonsense moral reasoning. Changing contexts can flip the moral judgment of an action; "Lying to a friend" is wrong in general, but may be morally acceptable if it is intended to protect their life. We present ClarifyDelphi, an interactive system that learns to ask clarification questions (e.g., why did you lie to your friend?) in order to elicit additional salient contexts of a social or moral situation. We posit that questions whose potential answers lead to diverging moral judgments are the most informative. Thus, we propose a reinforcement learning framework with a defeasibility reward that aims to maximize the divergence between moral judgments of hypothetical answers to a question. Human evaluation demonstrates that our system generates more relevant, informative and defeasible questions compared to competitive baselines. Our work is ultimately inspired by studies in cognitive science that have investigated the flexibility in moral cognition (i.e., the diverse contexts in which moral rules can be bent), and we hope that research in this direction can assist both cognitive and computational investigations of moral judgments.

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.

Large Language Models (LLMs) are typically trained to reflect a relatively uniform set of values, which limits their applicability to tasks that require understanding of nuanced human perspectives. Recent research has underscored the importance of enabling LLMs to support steerable pluralism -- the capacity to adopt a specific perspective and align generated outputs with it. In this work, we investigate whether Chain-of-Thought (CoT) reasoning techniques can be applied to building steerable pluralistic models. We explore several methods, including CoT prompting, fine-tuning on human-authored CoT, fine-tuning on synthetic explanations, and Reinforcement Learning with Verifiable Rewards (RLVR). We evaluate these approaches using the Value Kaleidoscope and OpinionQA datasets. Among the methods studied, RLVR consistently outperforms others and demonstrates strong training sample efficiency. We further analyze the generated CoT traces with respect to faithfulness and safety.

Recently, techniques such as explicit structured reasoning have demonstrated strong test-time scaling behavior by enforcing a separation between the model's internal "thinking" process and the final response. A key factor influencing answer quality in this setting is the length of the thinking stage. When the reasoning is too short, the model may fail to capture the complexity of the task. Conversely, when it is too long, the model may overthink, leading to unnecessary computation and degraded performance. This paper explores and exploits the underlying mechanisms by which LLMs understand and regulate the length of their reasoning during explicit thought processes. First, we show that LLMs encode their progress through the reasoning process and introduce an interactive progress bar visualization, which is then used to reveal insights on the model's planning dynamics. Second, we manipulate the internal progress encoding during inference to reduce unnecessary steps and generate a more concise and decisive chain of thoughts. Our empirical results demonstrate that this "overclocking" method mitigates overthinking, improves answer accuracy, and reduces inference latency. Our code is publicly available.

Chain-of-thought reasoning, while powerful, can produce unnecessarily verbose output for simpler problems. We present a framework for difficulty-aware reasoning that teaches models to dynamically adjust reasoning depth based on problem complexity. Remarkably, we show that models can be endowed with such dynamic inference pathways without any architectural modifications; we simply post-train on data that is carefully curated to include chain-of-thought traces that are proportional in length to problem difficulty. Our analysis reveals that post-training via supervised fine-tuning (SFT) primarily captures patterns like reasoning length and format, while direct preference optimization (DPO) preserves reasoning accuracy, with their combination reducing length and maintaining or improving performance. Both quantitative metrics and qualitative assessments confirm that models can learn to "think proportionally", reasoning minimally on simple problems while maintaining depth for complex ones.

Large language models (LLMs) have shown impressive performance on complex reasoning by leveraging chain-of-thought (CoT) prompting to generate intermediate reasoning chains as the rationale to infer the answer. However, existing CoT studies have focused on the language modality. We propose Multimodal-CoT that incorporates language (text) and vision (images) modalities into a two-stage framework that separates rationale generation and answer inference. In this way, answer inference can leverage better generated rationales that are based on multimodal information. With Multimodal-CoT, our model under 1 billion parameters outperforms the previous state-of-the-art LLM (GPT-3.5) by 16 percentage points (75.17%->91.68% accuracy) on the ScienceQA benchmark and even surpasses human performance. Code is publicly available available at https://github.com/amazon-science/mm-cot.

Large language models (LLMs) have attracted considerable attention in various fields for their cost-effective solutions to diverse challenges, especially with advancements in instruction tuning and quantization. E-commerce, with its complex tasks and extensive product-user interactions, presents a promising application area for LLMs. However, the domain-specific concepts and knowledge inherent in e-commerce pose significant challenges for adapting general LLMs. To address this issue, we developed EC-Guide https://github.com/fzp0424/EC-Guide-KDDUP-2024, a comprehensive e-commerce guide for instruction tuning and quantization of LLMs. We also heuristically integrated Chain-of-Thought (CoT) during inference to enhance arithmetic performance. Our approach achieved the 2nd place in Track 2 and 5th place in Track 5 at the Amazon KDD Cup'24 https://www.aicrowd.com/challenges/amazon-kdd-cup-2024-multi-task-online-shopping-challenge-for-llms. Additionally, our solution is model-agnostic, enabling effective scalability across larger systems.

Recently, there have been notable advancements in large language models (LLMs), demonstrating their growing abilities in complex reasoning. However, existing research largely overlooks a thorough and systematic comparison of these models' reasoning processes and outputs, particularly regarding their self-reflection pattern (also termed "Aha moment") and the interconnections across diverse domains. This paper proposes a novel framework for analyzing the reasoning characteristics of four cutting-edge large reasoning models (GPT-o1, DeepSeek-R1, Kimi-k1.5, and Grok-3) using keywords statistic and LLM-as-a-judge paradigm. Our approach connects their internal thinking processes with their final outputs. A diverse dataset consists of real-world scenario-based questions covering logical deduction, causal inference, and multi-step problem-solving. Additionally, a set of metrics is put forward to assess both the coherence of reasoning and the accuracy of the outputs. The research results uncover various patterns of how these models balance exploration and exploitation, deal with problems, and reach conclusions during the reasoning process. Through quantitative and qualitative comparisons, disparities among these models are identified in aspects such as the depth of reasoning, the reliance on intermediate steps, and the degree of similarity between their thinking processes and output patterns and those of GPT-o1. This work offers valuable insights into the trade-off between computational efficiency and reasoning robustness and provides practical recommendations for enhancing model design and evaluation in practical applications. We publicly release our project at: https://github.com/ChangWenhan/FromThinking2Output

Recent studies demonstrate that prompting an appropriate role-playing persona to an LLM improves its reasoning capability. However, assigning a proper persona is difficult since an LLM's performance is extremely sensitive to assigned prompts; therefore, personas sometimes hinder LLMs and degrade their reasoning capabilities. In this paper, we propose a novel framework, Jekyll \& Hyde, which ensembles the results of role-playing and neutral prompts to eradicate performance degradation via unilateral use of role-playing prompted LLM and enhance the robustness of an LLM's reasoning ability. Specifically, Jekyll \& Hyde collects two potential solutions from both role-playing and neutral prompts and selects a better solution after cross-checking via an LLM evaluator. However, LLM-based evaluators tend to be affected by the order of those potential solutions within the prompt when selecting the proper solution; thus, we also propose a robust LLM evaluator to mitigate the position bias. The experimental analysis demonstrates that role-playing prompts distract LLMs and degrade their reasoning abilities in 4 out of 12 datasets, even when using GPT-4. In addition, we reveal that Jekyll \& Hyde improves reasoning capabilities by selecting better choices among the potential solutions on twelve widely-used reasoning datasets. We further show that our proposed LLM evaluator outperforms other baselines, proving the LLMs' position bias is successfully mitigated.

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

Chain-of-thought (CoT) reasoning has been highly successful in solving complex tasks in natural language processing, and recent multimodal large language models (MLLMs) have extended this paradigm to video reasoning. However, these models typically build on lengthy reasoning chains and large numbers of input visual tokens. Motivated by empirical observations from our benchmark study, we hypothesize that concise reasoning combined with a reduced set of visual tokens can be sufficient for effective video reasoning. To evaluate this hypothesis, we design and validate an efficient post-training and inference framework that enhances a video MLLM's reasoning capability. Our framework enables models to operate on compressed visual tokens and generate brief reasoning traces prior to answering. The resulting models achieve substantially improved inference efficiency, deliver competitive performance across diverse benchmarks, and avoid reliance on manual CoT annotations or supervised fine-tuning. Collectively, our results suggest that long, human-like CoT reasoning may not be necessary for general video reasoning, and that concise reasoning can be both effective and efficient. Our code will be released at https://github.com/LaVi-Lab/Rethink_CoT_Video.

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.

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.

Claim verification is critical for enhancing digital literacy. However, the state-of-the-art single-LLM methods struggle with complex claim verification that involves multi-faceted evidences. Inspired by real-world fact-checking practices, we propose DebateCV, the first claim verification framework that adopts a debate-driven methodology using multiple LLM agents. In our framework, two Debaters take opposing stances on a claim and engage in multi-round argumentation, while a Moderator evaluates the arguments and renders a verdict with justifications. To further improve the performance of the Moderator, we introduce a novel post-training strategy that leverages synthetic debate data generated by the zero-shot DebateCV, effectively addressing the scarcity of real-world debate-driven claim verification data. Experimental results show that our method outperforms existing claim verification methods under varying levels of evidence quality. Our code and dataset are publicly available at https://anonymous.4open.science/r/DebateCV-6781.

We propose a novel speculative decoding method tailored for multi-sample reasoning scenarios, such as self-consistency and Best-of-N sampling. Our method exploits the intrinsic consensus of parallel generation paths to synthesize high-quality draft tokens without requiring auxiliary models or external databases. By dynamically analyzing structural patterns across parallel reasoning paths through a probabilistic aggregation mechanism, it identifies consensus token sequences that align with the decoding distribution. Evaluations on mathematical reasoning benchmarks demonstrate a substantial improvement in draft acceptance rates over baselines, while reducing the latency in draft token construction. This work establishes a paradigm shift for efficient multi-sample inference, enabling seamless integration of speculative decoding with sampling-based reasoning techniques.

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

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.

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.

Accurate prediction of human behavior is essential for robust and safe human-AI collaboration. However, existing approaches for modeling people are often data-hungry and brittle because they either make unrealistic assumptions about rationality or are too computationally demanding to adapt rapidly. Our key insight is that many everyday social interactions may follow predictable patterns; efficient "scripts" that minimize cognitive load for actors and observers, e.g., "wait for the green light, then go." We propose modeling these routines as behavioral programs instantiated in computer code rather than policies conditioned on beliefs and desires. We introduce ROTE, a novel algorithm that leverages both large language models (LLMs) for synthesizing a hypothesis space of behavioral programs, and probabilistic inference for reasoning about uncertainty over that space. We test ROTE in a suite of gridworld tasks and a large-scale embodied household simulator. ROTE predicts human and AI behaviors from sparse observations, outperforming competitive baselines -- including behavior cloning and LLM-based methods -- by as much as 50% in terms of in-sample accuracy and out-of-sample generalization. By treating action understanding as a program synthesis problem, ROTE opens a path for AI systems to efficiently and effectively predict human behavior in the real-world.

Existing large language models (LLMs) show exceptional problem-solving capabilities but might struggle with complex reasoning tasks. Despite the successes of chain-of-thought and tree-based search methods, they mainly depend on the internal knowledge of LLMs to search over intermediate reasoning steps, limited to dealing with simple tasks involving fewer reasoning steps. In this paper, we propose RAG-Star, a novel RAG approach that integrates the retrieved information to guide the tree-based deliberative reasoning process that relies on the inherent knowledge of LLMs. By leveraging Monte Carlo Tree Search, RAG-Star iteratively plans intermediate sub-queries and answers for reasoning based on the LLM itself. To consolidate internal and external knowledge, we propose an retrieval-augmented verification that utilizes query- and answer-aware reward modeling to provide feedback for the inherent reasoning of LLMs. Our experiments involving Llama-3.1-8B-Instruct and GPT-4o demonstrate that RAG-Star significantly outperforms previous RAG and reasoning methods.

The core premise of AI debate as a scalable oversight technique is that it is harder to lie convincingly than to refute a lie, enabling the judge to identify the correct position. Yet, existing debate experiments have relied on datasets with ground truth, where lying is reduced to defending an incorrect proposition. This overlooks a subjective dimension: lying also requires the belief that the claim defended is false. In this work, we apply debate to subjective questions and explicitly measure large language models' prior beliefs before experiments. Debaters were asked to select their preferred position, then presented with a judge persona deliberately designed to conflict with their identified priors. This setup tested whether models would adopt sycophantic strategies, aligning with the judge's presumed perspective to maximize persuasiveness, or remain faithful to their prior beliefs. We implemented and compared two debate protocols, sequential and simultaneous, to evaluate potential systematic biases. Finally, we assessed whether models were more persuasive and produced higher-quality arguments when defending positions consistent with their prior beliefs versus when arguing against them. Our main findings show that models tend to prefer defending stances aligned with the judge persona rather than their prior beliefs, sequential debate introduces significant bias favoring the second debater, models are more persuasive when defending positions aligned with their prior beliefs, and paradoxically, arguments misaligned with prior beliefs are rated as higher quality in pairwise comparison. These results can inform human judges to provide higher-quality training signals and contribute to more aligned AI systems, while revealing important aspects of human-AI interaction regarding persuasion dynamics in language models.

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However, existing methods are often computationally expensive, or demand costly retraining when priors change, limiting their utility, particularly in sequential inference problems such as real-time sensor fusion. To address these challenges, we introduce the Distribution Transformer -- a novel architecture that can learn arbitrary distribution-to-distribution mappings. Our method can be trained to map a prior to the corresponding posterior, conditioned on some dataset -- thus performing approximate Bayesian inference. Our novel architecture represents a prior distribution as a (universally-approximating) Gaussian Mixture Model (GMM), and transforms it into a GMM representation of the posterior. The components of the GMM attend to each other via self-attention, and to the datapoints via cross-attention. We demonstrate that Distribution Transformers both maintain flexibility to vary the prior, and significantly reduces computation times-from minutes to milliseconds-while achieving log-likelihood performance on par with or superior to existing approximate inference methods across tasks such as sequential inference, quantum system parameter inference, and Gaussian Process predictive posterior inference with hyperpriors.

As machine learning and algorithmic decision making systems are increasingly being leveraged in high-stakes human-in-the-loop settings, there is a pressing need to understand the rationale of their predictions. Researchers have responded to this need with explainable AI (XAI), but often proclaim interpretability axiomatically without evaluation. When these systems are evaluated, they are often tested through offline simulations with proxy metrics of interpretability (such as model complexity). We empirically evaluate the veracity of three common interpretability assumptions through a large scale human-subjects experiment with a simple "placebo explanation" control. We find that feature attribution explanations provide marginal utility in our task for a human decision maker and in certain cases result in worse decisions due to cognitive and contextual confounders. This result challenges the assumed universal benefit of applying these methods and we hope this work will underscore the importance of human evaluation in XAI research. Supplemental materials -- including anonymized data from the experiment, code to replicate the study, an interactive demo of the experiment, and the models used in the analysis -- can be found at: https://doi.pizza/challenging-xai.

How do large language models understand moral dimensions compared to humans? This first large-scale Bayesian evaluation of market-leading language models provides the answer. In contrast to prior work using deterministic ground truth (majority or inclusion rules), we model annotator disagreements to capture both aleatoric uncertainty (inherent human disagreement) and epistemic uncertainty (model domain sensitivity). We evaluate top language models (Claude Sonnet 4, DeepSeek-V3, Llama 4 Maverick) across 250K+ annotations from ~700 annotators on 100K+ texts spanning social media, news, and forums. Our GPU-optimized Bayesian framework processed 1M+ model queries, revealing that AI models typically rank among the top 25\% of human annotators, achieving much better-than-average balanced accuracy. Importantly, we find that AI produces far fewer false negatives than humans, highlighting their more sensitive moral detection capabilities.

Large Language Models (LLMs) have made significant strides in problem-solving by incorporating reasoning processes. However, this enhanced reasoning capability results in an increased number of output tokens during inference, leading to higher computational costs. To address this challenge, we propose TwT (Thinking without Tokens), a method that reduces inference-time costs through habitual reasoning distillation with multi-teachers' guidance, while maintaining high performance. Our approach introduces a Habitual Reasoning Distillation method, which internalizes explicit reasoning into the model's habitual behavior through a Teacher-Guided compression strategy inspired by human cognition. Additionally, we propose Dual-Criteria Rejection Sampling (DCRS), a technique that generates a high-quality and diverse distillation dataset using multiple teacher models, making our method suitable for unsupervised scenarios. Experimental results demonstrate that TwT effectively reduces inference costs while preserving superior performance, achieving up to a 13.6% improvement in accuracy with fewer output tokens compared to other distillation methods, offering a highly practical solution for efficient LLM deployment.

While Large Language Models (LLMs) demonstrate impressive reasoning capabilities, growing evidence suggests much of their success stems from memorized answer-reasoning patterns rather than genuine inference. In this work, we investigate a central question: are LLMs primarily anchored to final answers or to the textual pattern of reasoning chains? We propose a five-level answer-visibility prompt framework that systematically manipulates answer cues and probes model behavior through indirect, behavioral analysis. Experiments across state-of-the-art LLMs reveal a strong and consistent reliance on explicit answers. The performance drops by 26.90\% when answer cues are masked, even with complete reasoning chains. These findings suggest that much of the reasoning exhibited by LLMs may reflect post-hoc rationalization rather than true inference, calling into question their inferential depth. Our study uncovers the answer-anchoring phenomenon with rigorous empirical validation and underscores the need for a more nuanced understanding of what constitutes reasoning in LLMs.

Recently, long-thought reasoning LLMs, such as OpenAI's O1, adopt extended reasoning processes similar to how humans ponder over complex problems. This reasoning paradigm significantly enhances the model's problem-solving abilities and has achieved promising results. However, long-thought reasoning process leads to a substantial increase in inference time. A pressing challenge is reducing the inference overhead of long-thought LLMs while ensuring accuracy. In this paper, we experimentally demonstrate that long-thought reasoning models struggle to effectively allocate token budgets based on problem difficulty and reasoning redundancies. To address this, we propose Length-Harmonizing Fine-Tuning (O1-Pruner), aiming at minimizing reasoning overhead while maintaining accuracy. This effective fine-tuning method first estimates the LLM's baseline performance through pre-sampling and then uses RL-style fine-tuning to encourage the model to generate shorter reasoning processes under accuracy constraints. This allows the model to achieve efficient reasoning with lower redundancy while maintaining accuracy. Experiments on various mathematical reasoning benchmarks show that O1-Pruner not only significantly reduces inference overhead but also achieves higher accuracy, providing a novel and promising solution to this challenge. Our code is coming soon at https://github.com/StarDewXXX/O1-Pruner

Multi-agent interactions, such as communication, teaching, and bluffing, often rely on higher-order social inference, i.e., understanding how others infer oneself. Such intricate reasoning can be effectively modeled through nested multi-agent reasoning. Nonetheless, the computational complexity escalates exponentially with each level of reasoning, posing a significant challenge. However, humans effortlessly perform complex social inferences as part of their daily lives. To bridge the gap between human-like inference capabilities and computational limitations, we propose a novel approach: leveraging neural networks to amortize high-order social inference, thereby expediting nested multi-agent reasoning. We evaluate our method in two challenging multi-agent interaction domains. The experimental results demonstrate that our method is computationally efficient while exhibiting minimal degradation in accuracy.

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

Beliefs serve as the foundation for human cognition and decision-making. They guide individuals in deriving meaning from their lives, shaping their behaviors, and forming social connections. Therefore, a model that encapsulates beliefs and their interrelationships is crucial for quantitatively studying the influence of beliefs on our actions. Despite its importance, research on the interplay between human beliefs has often been limited to a small set of beliefs pertaining to specific issues, with a heavy reliance on surveys or experiments. Here, we propose a method for extracting nuanced relations between thousands of beliefs by leveraging large-scale user participation data from an online debate platform and mapping these beliefs to an embedding space using a fine-tuned large language model (LLM). This belief embedding space effectively encapsulates the interconnectedness of diverse beliefs as well as polarization across various social issues. We discover that the positions within this belief space predict new beliefs of individuals. Furthermore, we find that the relative distance between one's existing beliefs and new beliefs can serve as a quantitative estimate of cognitive dissonance, allowing us to predict new beliefs. Our study highlights how modern LLMs, when combined with collective online records of human beliefs, can offer insights into the fundamental principles that govern human belief formation and decision-making processes.

Recent advancements in reasoning with large language models (RLLMs), such as OpenAI-O1 and DeepSeek-R1, have demonstrated their impressive capabilities in complex domains like mathematics and coding. A central factor in their success lies in the application of long chain-of-thought (Long CoT) characteristics, which enhance reasoning abilities and enable the solution of intricate problems. However, despite these developments, a comprehensive survey on Long CoT is still lacking, limiting our understanding of its distinctions from traditional short chain-of-thought (Short CoT) and complicating ongoing debates on issues like "overthinking" and "test-time scaling." This survey seeks to fill this gap by offering a unified perspective on Long CoT. (1) We first distinguish Long CoT from Short CoT and introduce a novel taxonomy to categorize current reasoning paradigms. (2) Next, we explore the key characteristics of Long CoT: deep reasoning, extensive exploration, and feasible reflection, which enable models to handle more complex tasks and produce more efficient, coherent outcomes compared to the shallower Short CoT. (3) We then investigate key phenomena such as the emergence of Long CoT with these characteristics, including overthinking, and test-time scaling, offering insights into how these processes manifest in practice. (4) Finally, we identify significant research gaps and highlight promising future directions, including the integration of multi-modal reasoning, efficiency improvements, and enhanced knowledge frameworks. By providing a structured overview, this survey aims to inspire future research and further the development of logical reasoning in artificial intelligence.

Among the hardest tasks for humans are those found in competitive programming where problems require sophisticated algorithmic thinking, puzzle solving, and the creation of effective code. As a domain to assess language models (LMs), it has not received enough attention, though. This study presents the ICPC benchmark, which consists of 254 international collegiate programming contest (ICPC) tasks. Each problem includes official analysis, reference code, and sample, high-quality unit, and hidden tests. We are able to develop and evaluate a variety of LM inference techniques for competitive programming with these resources. With zero-shot chain-of-thought prompting, we find that o1 only achieves a 19.1\% pass@1 solve rate. With our best inference technique, which combines multi-turn self-judge with reflection and retrieval over episodic information, raises this to 42.2\%. Furthermore, we conduct a new human-in-the-loop investigation to gain a deeper understanding of the remaining difficulties. Surprisingly, we discover that o1 can solve 17 out of 18 problems that were previously unsolvable by any model or technique with just a few specific instructions. A footstep toward LMs with grounded, imaginative, and algorithmic thinking is provided by our quantitative findings and qualitative research. We open-source our code and data at https://github.com/kraritt/zolve.

Scaling the test-time compute of large language models has demonstrated impressive performance on reasoning benchmarks. However, existing evaluations of test-time scaling make the strong assumption that a reasoning system should always give an answer to any question provided. This overlooks concerns about whether a model is confident in its answer, and whether it is appropriate to always provide a response. To address these concerns, we extract confidence scores during reasoning for thresholding model responses. We find that increasing compute budget at inference time not only helps models answer more questions correctly, but also increases confidence in correct responses. We then extend the current paradigm of zero-risk responses during evaluation by considering settings with non-zero levels of response risk, and suggest a recipe for reporting evaluations under these settings.

Recent advances in inference time scaling with extended long chain-of thought have significantly improved the reasoning capabilities of both general and medical large language models (LLMs). However, these models tend to engage in lengthy reasoning processes regardless of the difficulty of the input question, leading to increased inference costs in real-world applications. Therefore, enabling adaptive thinking where models think less for simpler questions and think more for complex ones is critical for the effective use of medical LLMs in practice. Despite its importance, there is a lack of end-to-end approaches designed to enhance the adaptive thinking capabilities of medical LLMs while providing a comprehensive examination of the trade-off between performance and computational cost. To bridge this gap, we propose AdaThink-Med, the first end-to-end framework designed to enhance adaptive thinking ability in medical reasoning models with uncertainty-guided length calibration. AdaThink-Med first generates multiple candidate outputs for each question, evaluates the correctness and uncertainty of each candidate, and then estimates problem difficulty via an uncertainty-guided length calibration module. For outputs with low difficulty and correct answers, the framework penalizes longer reasoning paths; whereas for those with high difficulty and incorrect answers, it encourages extending the chain of thought to explore alternative solutions. On six public medical QA benchmarks, AdaThink-Med achieves up to 6.4x length reduction on average while retaining performance with only minimal degradation. Intriguingly, we observe that AdaThink-Med spontaneously develops two distinct reasoning modes, which we characterize as "non-thinking" and "thinking", demonstrating the model's ability to suppress redundant reasoning processes dynamically.

Recent reasoning Large Language Models (LLMs) demonstrate remarkable problem-solving abilities but often generate long thinking traces whose utility is unclear. Our work aims to improve their efficiency, enabling them to reach high performance without overthinking. First, we analyze the entropy of token probabilities in reasoning traces. Across three models, we observe a consistent U-shaped entropy pattern: high entropy on easy problems despite high accuracy, low entropy on problems with medium difficulty, and high entropy on hard problems reflecting uncertainty. Specifically, we notice 22--25\% entropy reduction from easy to medium difficulty regions, suggesting an {overthinking} phenomenon on easy instances. Building on these insights, we introduce DiffAdapt, a lightweight framework that selects Easy/Normal/Hard inference strategies per question based on their difficulty and reasoning trace entropy. Each inference strategy consists of a fixed prompt, temperature and maximum token length. In contrast to existing efficiency optimization methods, our approach does not fine-tune base LLM but a small probe that classifies LLM's final hidden state, allowing inexpensive adaptation. We comprehensively evaluate our method on five models and eight benchmarks. Our method achieves comparable or improved accuracy while reducing token usage by up to 22.4\%, establishing a practical path toward compute-efficient reasoning.

With the release of R1, a publicly available large reasoning model (LRM), researchers commonly train new LRMs by training language models on R1's long chain-of-thought (CoT) inferences. While prior works show that LRMs' capabilities can be reproduced through direct distillation, the continued reliance on the existing models (e.g., R1) remains a critical limitation in advancing the field. As a first step toward independent LRM development, this paper explores the possibility of constructing a long CoT dataset with LLMs that are not trained for inference-time scaling. To this end, we present the Long CoT Collection, a dataset of 100K CoT rationales annotated using existing short CoT LLMs. We develop a pipeline that induces o1's novel reasoning strategies into short CoT LLMs, enabling them to think longer and introducing controllability over the thought budget to better manage the overthinking problem. Our extensive analyses validate that our dataset achieves quality comparable to--or slightly below--R1. Furthermore, our experiments demonstrate that training on our dataset not only strengthens general reasoning skills, but also provides a strong foundation for reinforcement learning--models initialized on our data achieve 2-3x larger gains with RLVR.