NeurIPS 2025 Papers

Probabilistic reasoning is a key aspect of both human and artificial intelligence that allows for handling uncertainty and ambiguity in decision-making. In this paper, we introduce a new numerical reasoning task under uncertainty for large language models, focusing on estimating the privacy risk of user-generated documents containing privacy-sensitive information. We propose BRANCH, a new LLM methodology that estimates the $k$-privacy value of a text—the size of the population matching the given information. BRANCH factorizes a joint probability distribution of personal information as random variables. The probability of each factor in a population is estimated separately using a Bayesian network and combined to compute the final $k$-value. Our experiments show that this method successfully estimates the $k$-value 73% of the time, a 13% increase compared to o3-mini with chain-of-thought reasoning. We also find that LLM uncertainty is a good indicator for accuracy, as high variance predictions are 37.47% less accurate on average.

Improving Multi-modal Large Language Models (MLLMs) in the post-training stage typically relies on supervised fine-tuning (SFT) or reinforcement learning (RL), which require expensive and manually annotated multi-modal data--an ultimately unsustainable resource. This limitation has motivated a growing interest in unsupervised paradigms as a third stage of post-training after SFT and RL. While recent efforts have explored this direction, their methods are complex and difficult to iterate. To address this, we propose MM-UPT, a simple yet effective framework for unsupervised post-training of MLLMs, enabling continual self-improvement without any external supervision. The training method of MM-UPT builds upon GRPO, replacing traditional reward signals with a self-rewarding mechanism based on majority voting over multiple sampled responses. Our experiments demonstrate that such training method effectively improves the reasoning ability of Qwen2.5-VL-7B (e.g., 66.3\%$\rightarrow$72.9\% on MathVista, 62.9\%$\rightarrow$68.7\% on We-Math), using standard dataset without ground truth labels. To further explore scalability, we extend our framework to a data self-generation setting, designing two strategies that prompt the MLLM to synthesize new training samples on its own. Additional experiments show that combining these synthetic data with the unsupervised training method can also boost performance, highlighting a promising approach for scalable self-improvement. Overall, MM-UPT offers a new paradigm for autonomous enhancement of MLLMs, serving as a critical third step after initial SFT and RL in the absence of external supervision. Our code is available at \url{https://github.com/waltonfuture/MM-UPT}.

Recent studies empirically reveal that large reasoning models (LRMs) can automatically allocate more reasoning strengths (\ie the number of reasoning tokens) for harder problems, exhibiting difficulty-awareness for better task performance. While this automatic reasoning strength allocation phenomenon has been widely observed, its underlying mechanism remains largely unexplored. To this end, we provide explanations for this phenomenon from the perspective of model activations. \textbf{We find evidence that LRMs pre-plan the reasoning strengths in their activations even before generation, with this reasoning strength causally controlled by the magnitude of a pre-allocated directional vector.} Specifically, we show that the number of reasoning tokens is predictable solely based on the question activations using linear probes, indicating that LRMs estimate the required reasoning strength in advance. We then uncover that LRMs encode this reasoning strength through a pre-allocated directional vector embedded in the activations of the model, where the vector’s magnitude modulates the reasoning strength. Subtracting this vector can lead to reduced reasoning token number and performance, while adding this vector can lead to increased reasoning token number and even improved performance. We further reveal that this direction vector consistently yields positive reasoning length prediction, and it modifies the logits of end-of-reasoning token \texttt{</think>} to affect the reasoning length. Finally, we demonstrate two potential applications of our findings: overthinking behavior detection and enabling efficient reasoning on simple problems. Our work provides new insights into the internal mechanisms of reasoning in LRMs and offers practical tools for controlling their reasoning behaviors. Our code is available at \url{https://anonymous.4open.science/r/LRM-plans-CoT-7E04}.

Inference-time computation has emerged as a promising scaling axis for improving large language model reasoning. However, despite yielding impressive performance, the optimal allocation of inference-time computation remains poorly understood. A central question is whether to prioritize sequential scaling (e.g., longer chains of thought) or parallel scaling (e.g., majority voting across multiple short chains of thought). In this work, we seek to illuminate the landscape of test-time scaling by demonstrating the existence of reasoning settings where sequential scaling offers an exponential advantage over parallel scaling. These settings are based on graph connectivity problems in challenging distributions of graphs. We validate our theoretical findings with comprehensive experiments across a range of language models, including models trained from scratch for graph connectivity with different chain of thought strategies as well as large reasoning models.

We introduce Reasoning Gym, a library of reasoning environments for reinforcement learning with verifiable rewards (RLVR). It provides over 100 tasks spanning multiple domains including algebra, arithmetic, computation, cognition, geometry, graph theory, logic, and various common games. Its key innovation is the ability to generate virtually infinite training data with adjustable complexity, unlike most previous reasoning datasets, which are typically fixed. This procedural generation approach allows for continuous evaluation across varying difficulty levels and task configurations. Our experimental results demonstrate the efficacy of Reasoning Gym in both evaluating and reinforcement learning of reasoning models.

We introduce MIRAGE, a new benchmark for multimodal expert-level reasoning and decision-making in consultative interaction settings. Designed for the domain of agriculture, MIRAGE captures the full complexity of expert consultations by combining natural user queries, expert-authored responses, and image-based context, offering a high-fidelity benchmark for evaluating models on grounded reasoning, clarification strategies, and long-form generation in a real-world, knowledge-intensive domain. Grounded in over 35,000 real user-expert interactions, and curated through a carefully designed multi-step pipeline, MIRAGE spans diverse crop health, pest diagnosis, and crop management scenarios. The benchmark includes more than 7,000 unique biological entities, covering plant species, pests, and diseases, making it one of the most taxonomically diverse benchmarks available for vision-language models in real-world expert-guided domains. Unlike existing benchmarks that rely on well-specified user inputs, MIRAGE features underspecified, context-rich scenarios, requiring models to infer latent knowledge gaps and either proactively guide the interaction or respond. Our benchmark comprises two core components. The Single-turn Challenge to reason over a single user turn and image set, identify relevant entities, infer causal explanations, and generate actionable recommendations; and a Multi-Turn challenge for dialogue state tracking, goal-driven generation, and expert-level conversational decision-making. We evaluate more than 20 closed and open-source frontier vision-language models (VLMs), using three reasoning language models as evaluators, highlighting the significant challenges posed by MIRAGE in both single-turn and multi-turn interaction settings. Even the advanced GPT4.1 and GPT4o models achieve 44.6% and 40.9% accuracy, respectively, indicating significant room for improvement.

We propose two simple, principled and practical algorithms that enjoy provable scaling laws for the test-time compute of large language models (LLMs). The first one is a two-stage knockout-style algorithm: given an input problem, it first generates multiple candidate solutions, and then aggregate them via a knockout tournament for the final output. Assuming that the LLM can generate a correct solution with non-zero probability and do better than a random guess in comparing a pair of correct and incorrect solutions, we prove theoretically that the failure probability of this algorithm decays to zero exponentially or by a power law (depending on the specific way of scaling) as its test-time compute grows. The second one is a two-stage league-style algorithm, where each candidate is evaluated by its average win rate against multiple opponents, rather than eliminated upon loss to a single opponent. Under analogous but more robust assumptions, we prove that its failure probability also decays to zero exponentially with more test-time compute. Both algorithms require a black-box LLM and nothing else (e.g., no verifier or reward model) for a minimalistic implementation, which makes them appealing for practical applications and easy to adapt for different tasks. Through extensive experiments with diverse models and datasets, we validate the proposed theories and demonstrate the outstanding scaling properties of both algorithms.

This paper presents a comprehensive theoretical analysis of the learnability of neuro-symbolic (NeSy) tasks within hybrid systems. We characterize the learnability of NeSy tasks by their derived constraint satisfaction problems (DCSPs), demonstrating that a task is learnable if and only if its corresponding DCSP admits a unique solution. Under mild assumptions, we establish the sample complexity for learnable tasks and show that, for general tasks, the asymptotic expected concept error is controlled by the degree of disagreement among DCSP solutions. Our findings unify the characterization of learnability and the phenomenon of reasoning shortcuts, providing theoretical guarantees and actionable guidance for the principled design of NeSy systems.

Computer-Aided Design (CAD) is pivotal in industrial manufacturing, with orthographic projection reasoning foundational to its entire workflow—encompassing design, manufacturing, and simulation. However, prevailing deep-learning approaches employ standard 3D reconstruction pipelines as an alternative, which often introduce imprecise dimensions and limit the parametric editability required for CAD workflows. Recently, some researchers adopt vision–language models (VLMs), particularly supervised fine-tuning (SFT), to tackle CAD-related challenges. SFT shows promise but often devolves into pattern memorization, resulting in poor out-of-distribution (OOD) performance on complex reasoning tasks. To tackle these limitations, we introduce CReFT-CAD, a two-stage fine-tuning paradigm: first, a curriculum-driven reinforcement learning stage with difficulty-aware rewards to steadily build reasoning abilities; second, supervised post-tuning to refine instruction following and semantic extraction. Complementing this, we release TriView2CAD, the first large-scale, open-source benchmark for orthographic projection reasoning, comprising 200,000 synthetic and 3,000 real-world orthographic projections with precise dimensional annotations and six interoperable data modalities. Benchmarking leading VLMs on orthographic projection reasoning, we show that CReFT-CAD significantly improves reasoning accuracy and OOD generalizability in real-world scenarios, providing valuable insights to advance CAD reasoning research. The code and adopted datasets are available at \url{https://github.com/KeNiu042/CReFT-CAD}.

We present Audio Flamingo 3 (AF3), a fully open state-of-the-art (SOTA) large audio-language model that advances reasoning and understanding across speech, sound, and music. AF3 introduces: (i) AF-Whisper, a unified audio encoder trained using a novel strategy for joint representation learning across all 3 modalities of speech, sound, and music; (ii) flexible, on-demand thinking, allowing the model to do chain-of-thought-type reasoning before answering; (iii) multi-turn, multi-audio chat; (iv) long audio understanding and reasoning (including speech) up to 10 minutes; and (v) voice-to-voice interaction. To enable these capabilities, we propose several large-scale training datasets curated using novel strategies, including AudioSkills-XL, LongAudio-XL, AF-Think, and AF-Chat, and train AF3 with a novel five-stage curriculum-based training strategy. Trained on only open-source audio data, AF3 achieves new SOTA results on over 20+ (long) audio understanding and reasoning benchmarks, surpassing both open-weight and closed-source models trained on much larger datasets.

Clinical reasoning in medicine is a hypothesis-driven process where physicians refine diagnoses from limited information through targeted history, physical examination, and diagnostic investigations. In contrast, current medical benchmarks for large language models (LLMs) primarily assess knowledge recall through single-turn questions, where complete clinical information is provided upfront. To address this gap, we introduce VivaBench, a multi-turn benchmark that evaluates sequential clinical reasoning in LLM agents. Our dataset consists of 1762 physician-curated clinical vignettes structured as interactive scenarios that simulate a $ \textit{viva voce}$ (oral) examination in medical training, requiring agents to actively probe for relevant findings, select appropriate investigations, and synthesize information across multiple steps to reach a diagnosis. While current LLMs demonstrate competence in diagnosing conditions from well-described clinical presentations, their performance degrades significantly when required to navigate iterative diagnostic reasoning under uncertainty in our evaluation. Our analysis identified several failure modes that mirror common cognitive errors in clinical practice, including: (1) fixation on initial hypotheses, (2) inappropriate investigation ordering, (3) premature diagnostic closure, and (4) failing to screen for critical conditions. These patterns reveal fundamental limitations in how current LLMs reason and make decisions under uncertainty. Through VivaBench, we provide a standardized benchmark for evaluating conversational medical AI systems for real-world clinical decision support. Beyond medical applications, we contribute to the larger corpus of research on agentic AI by demonstrating how sequential reasoning trajectories can diverge in complex decision-making environments.

Continual Test-Time Adaptation (CTTA) aims to quickly fine-tune the model during the test phase so that it can adapt to multiple unknown downstream domain distributions without pre-acquiring downstream domain data. To this end, existing advanced CTTA methods mainly reduce the catastrophic forgetting of historical knowledge caused by irregular switching of downstream domain data by restoring the initial model or reusing historical models. However, these methods are usually accompanied by serious insufficient learning of new knowledge and interference from potentially harmful historical knowledge, resulting in severe performance degradation. To this end, we propose a class-aware domain Knowledge Fusion and Fission method for continual test-time adaptation, called KFF, which adaptively expands and merges class-aware domain knowledge in old and new domains according to the test-time data from different domains, where discriminative historical knowledge can be dynamically accumulated. Specifically, considering the huge domain gap within streaming data, a domain Knowledge FIssion (KFI) module is designed to adaptively separate new domain knowledge from a paired class-aware domain prompt pool, alleviating the impact of negative knowledge brought by old domains that are distinct from the current domain. Besides, to avoid the cumulative computation and storage overheads from continuously fissioning new knowledge, a domain Knowledge FUsion (KFU) module is further designed to merge the fissioned new knowledge into the existing knowledge pool with minimal cost, where a greedy knowledge dynamic merging strategy is designed to improve the compatibility of new and old knowledge while keeping the computational efficiency.

Simulating society with large language models (LLMs), we argue, requires more than generating plausible behavior; it demands cognitively grounded reasoning that is structured, revisable, and traceable. LLM-based agents are increasingly used to emulate individual and group behavior, primarily through prompting and supervised fine-tuning. Yet current simulations remain grounded in a behaviorist “demographics in, behavior out” paradigm, focusing on surface-level plausibility. As a result, they often lack internal coherence, causal reasoning, and belief traceability—making them unreliable for modeling how people reason, deliberate, and respond to interventions. To address this, we present a conceptual modeling paradigm, Generative Minds (GenMinds), which draws from cognitive science to support structured belief representations in generative agents. To evaluate such agents, we introduce the RECAP (REconstructing CAusal Paths) framework, a benchmark designed to assess reasoning fidelity via causal traceability, demographic grounding, and intervention consistency. These contributions advance a broader shift: from surface-level mimicry to generative agents that simulate thought—not just language—for social simulations.

Training language models on long sequence data is a demanding requirement for enhancing the model's capability on complex tasks, e.g., long-chain reasoning. However, as the sequence length scales up, the memory cost for storing activation values becomes huge during the Backpropagation (BP) process, even with the application of gradient checkpointing technique. To tackle this challenge, we propose a *memory-efficient* and *exact* BP method called **StreamBP**, which performs a linear decomposition of the chain rule along the sequence dimension in a layer-wise manner, significantly reducing the memory cost of activation values and logits. The proposed method is applicable to common objectives such as SFT, GRPO, and DPO. From an implementation perspective, StreamBP achieves less computational FLOPs and faster BP speed by leveraging the causal structure of the language model. Compared to gradient checkpointing, StreamBP scales up the maximum sequence length of BP by $2.8-5.5 \times$ larger, while using comparable or even less BP time. Note that StreamBP's sequence length scaling ability can be directly transferred to batch size scaling for accelerating training. We further develop a communication-efficient distributed StreamBP to effectively support multi-GPU training and broaden its applicability. Our code can be easily integrated into the training pipeline of any transformer models and is available at https://github.com/Ledzy/StreamBP.

Despite recent progress in large-scale reinforcement learning (RL) for reasoning, the training recipe for building high-performing reasoning models remains elusive. Key implementation details of frontier models, such as DeepSeek-R1, including data curation strategies and RL training recipe, are often omitted. Moreover, recent research indicates distillation remains more effective than RL for smaller models. In this work, we demonstrate that large-scale RL can significantly enhance the reasoning capabilities of strong, small- and mid-sized models, achieving results that surpass those of state-of-the-art distillation-based models. We systematically study the RL training process through extensive ablations and propose a simple yet effective approach: first training on math-only prompts, then on code-only prompts. Notably, we find that math-only RL not only significantly enhances the performance of strong distilled models on math benchmarks (e.g., +14.6\% / +17.2\% on AIME 2025 for the 7B / 14B models), but also code reasoning tasks (e.g., +6.8\% / +5.8\% on LiveCodeBench for the 7B / 14B models). In addition, extended code-only RL further improves code benchmark performance while causing minimal degradation in math results. We develop a robust data curation pipeline to collect challenging prompts with high-quality, verifiable answers and test cases to enable verification-based RL across both domains. The dataset will be released to support open research. Finally, we identify key experimental insights, including curriculum learning with progressively increasing response lengths and the stabilizing effect of on-policy parameter updates. We find that RL not only elicits the foundational reasoning capabilities acquired during pretraining and supervised fine-tuning (SFT), but also pushes the limits of the model’s reasoning ability, enabling it to solve problems that were previously unsolvable.

The rapid spread of multimodal misinformation on social media has raised growing concerns, while research on video misinformation detection remains limited due to the lack of large-scale, diverse datasets. Existing methods often overfit to rigid templates and lack deep reasoning over deceptive content. To address these challenges, we introduce FakeVV, a large-scale benchmark comprising over 100,000 video-text pairs with fine-grained, interpretable annotations. In addition, we further propose Fact-R1, a novel framework that integrates deep reasoning with collaborative rule-based reinforcement learning. Fact-R1 is trained through a three-stage process: (1) misinformation long-Chain-of-Thought (CoT) instruction tuning, (2) preference alignment via Direct Preference Optimization (DPO), and (3) Group Relative Policy Optimization (GRPO) using a novel verifiable reward function. This enables Fact-R1 to exhibit emergent reasoning behaviors comparable to those observed in advanced text-based reinforcement learning systems, but in the more complex multimodal misinformation setting. Our work establishes a new paradigm for misinformation detection, bridging large-scale video understanding, reasoning-guided alignment, and interpretable verification.

Human cognition is theorized to operate in two modes: fast, intuitive System 1 thinking and slow, deliberate System 2 thinking. While current Large Reasoning Models (LRMs) excel at System 2 thinking, their inability to perform fast thinking leads to high computational overhead and latency. In this work, we enable LRMs to approximate human intelligence through dynamic thinking speed adjustment, optimizing accuracy-efficiency trade-offs. Our approach addresses two key questions: (1) how to control thinking speed in LRMs, and (2) when to adjust it for optimal performance. For the first question, we identify the steering vector that governs slow-fast thinking transitions in LRMs' representation space. Using this vector, we achieve the first representation editing-based test-time scaling effect, outperforming existing prompt-based scaling methods. For the second question, we apply real-time difficulty estimation to signal reasoning segments of varying complexity. Combining these techniques, we propose the first reasoning strategy that enables fast processing of easy steps and deeper analysis for complex reasoning. Without any training or additional cost, our plug-and-play method yields an average +1.3\% accuracy with -8.6\% token usage across leading LRMs and advanced reasoning benchmarks. All of our algorithms are implemented based on vLLM and are expected to support broader applications and inspire future research.

Recently, reasoning-based MLLMs have achieved a degree of success in generating long-form textual reasoning chains. However, they still struggle with complex tasks that necessitate dynamic and iterative focusing on and revisiting of visual regions to achieve precise grounding of textual reasoning in visual evidence. We introduce VLM-R³ (Visual Language Model with Region Recognition, Reasoning, and Refinement ), a framework that equips an MLLM with the ability to (i) decide when additional visual evidence is needed, (ii) determine where to ground within the image, and (iii) seamlessly weave the relevant sub-image content back into an interleaved chain-of-thought. The core of our method is \textbf{Region-Conditioned Reinforcement Policy Optimization (R-GRPO)}, a training paradigm that rewards the model for selecting informative regions, formulating appropriate transformations (e.g. crop, zoom), and integrating the resulting visual context into subsequent reasoning steps. To bootstrap this policy, we compile a modest but carefully curated Visuo-Lingual Interleaved Rationale (VLIR) corpus that provides step-level supervision on region selection and textual justification. Extensive experiments on MathVista, ScienceQA, and other benchmarks show that VLM-R$^3$ sets a new state of the art in zero-shot and few-shot settings, with the largest gains appearing on questions demanding subtle spatial reasoning or fine-grained visual cue extraction.

Self-Supervised Learning (SSL) for Combinatorial Optimization (CO) is an emerging paradigm for solving combinatorial problems using neural networks. In this paper, we address a central challenge of SSL for CO: solving problems with discrete constraints. We design an end-to-end differentiable framework that enables us to solve discrete constrained optimization problems with neural networks. Concretely, we leverage algorithmic techniques from the literature on convex geometry and Carathéodory's theorem to decompose neural network outputs into convex combinations of polytope corners that correspond to feasible sets. This decomposition-based approach enables self-supervised training but also ensures efficient quality-preserving rounding of the neural net output into feasible solutions. Extensive experiments in cardinality-constrained optimization show that our approach can consistently outperform neural baselines. We further provide worked-out examples of how our method can be applied beyond cardinality-constrained problems to a diverse set of combinatorial optimization tasks, including finding independent sets in graphs, and solving matroid-constrained problems.