NeurIPS 2025 Papers

How to design reinforcement learning (RL) tasks that effectively unleash the reasoning capability of large language models (LLMs) remains an open question. Existing RL tasks (e.g., math, programming, and constructing reasoning tasks) suffer from three key limitations: (1) Scalability. They rely heavily on human annotation or expensive LLM synthesis to generate sufficient training data. (2) Verifiability. LLMs' outputs are hard to verify automatically and reliably. (3) Controllable Difficulty. Most tasks lack fine-grained difficulty control, making it hard to train LLMs to develop reasoning ability from easy to hard. To address these limitations, we propose Saturn, a SAT-based RL framework that uses Boolean Satisfiability (SAT) problems to train and evaluate LLMs reasoning. Saturn enables scalable task construction, rule-based verification, and precise difficulty control. Saturn designs a curriculum learning pipeline that continuously improves LLMs' reasoning capability by constructing SAT tasks of increasing difficulty and training LLMs from easy to hard. To ensure stable training, we design a principled mechanism to control difficulty transitions. We introduce Saturn-2.6k, a dataset of 2,660 SAT problems with varying difficulty. It supports the evaluation of how LLM reasoning changes with problem difficulty. We apply Saturn to DeepSeek-R1-Distill-Qwen and obtain Saturn-1.5B and Saturn-7B. We achieve several notable results: (1) On SAT problems, Saturn-1.5B and Saturn-7B achieve average pass@3 improvements of +14.0 and +28.1, respectively. (2) On math and programming tasks, Saturn-1.5B and Saturn-7B improve average scores by +4.9 and +1.8 on benchmarks (e.g., AIME, LiveCodeBench). (3) Compared to the state-of-the-art (SOTA) approach in constructing RL tasks, Saturn achieves further improvements of +8.8\%. We release the source code, data, and models to support future research.

Industrial Anomaly Detection (IAD) is an indispensable quality control technology in modern production processes. Recently, on account of the outstanding visual comprehension and cross-domain knowledge transfer capabilities of multimodal large language models (MLLMs), existing studies have explored the application of MLLMs in the IAD domain and established some multimodal IAD datasets. However, although the latest datasets contain various fundamental IAD tasks, they formulate tasks in a general question-and-answer format lacking a rigorous reasoning process, and they are relatively limited in the diversity of scenarios, which restricts their reliability in practical applications. In this paper, we propose AnomalyCoT, a multimodal Chain-of-Thought (CoT) dataset for multi-scenario IAD tasks. It consists of 37,565 IAD samples with the CoT data and is defined by challenging composite IAD tasks. Meanwhile, the CoT data for each sample provides precise coordinates of anomaly regions, thereby improving visual comprehension of defects across different types. AnomalyCoT is constructed through a systematic pipeline and involves multiple manual operations. Based on AnomalyCoT, we conducted a comprehensive evaluation of various mainstream MLLMs and fine-tuned representative models in different ways. The final results show that Gemini-2.0-flash achieved the best performance in the direct evaluation with an accuracy rate of 59.6\%, while Llama 3.2-Vision achieves the best performance after LoRA fine-tuning with an accuracy rate of 94.0\%. Among all the fine-tuned models, the average accuracy improvement reaches 36.5\%, demonstrating the potential of integrating CoT datasets in future applications within the IAD field. The code and data are available at \url{https://github.com/Zhaolutuan/AnomalyCoT}.

This paper introduces Completion Pruning Policy Optimization (CPPO) to accelerate the training of reasoning models based on Group Relative Policy Optimization (GRPO). GRPO, while effective, incurs high training costs due to the need to sample multiple completions for each question. Our experiment and theoretical analysis reveal that the number of completions impacts model accuracy yet increases training time multiplicatively, and not all completions contribute equally to policy training---their contribution depends on their relative advantage. To address these issues, we propose CPPO, which prunes completions with low absolute advantages, significantly reducing the number needed for gradient calculation and updates. Additionally, we introduce a dynamic completion allocation strategy to maximize GPU utilization by incorporating additional questions, further enhancing training efficiency. Experiments show that CPPO achieves up to $7.98\times$ speedup on GSM8K and $3.48\times$ on Math while preserving or even enhancing the accuracy compared to the original GRPO. We release our code at https://github.com/lzhxmu/CPPO.

Recent advances in multimodal Reward Models (RMs) have shown significant promise in delivering reward signals to align vision models with human preferences. However, current RMs are generally restricted to providing direct responses or engaging in shallow reasoning processes with limited depth, often leading to inaccurate reward signals. We posit that incorporating explicit long chains of thought (CoT) into the reward reasoning process can significantly strengthen their reliability and robustness. Furthermore, we believe that once RMs internalize CoT reasoning, their direct response accuracy can also be improved through implicit reasoning capabilities. To this end, this paper proposes UnifiedReward-Think, the first unified multimodal CoT-based reward model, capable of multi-dimensional, step-by-step long-chain reasoning for both visual understanding and generation reward tasks. Specifically, we adopt an exploration-driven reinforcement fine-tuning approach to elicit and incentivize the model's latent complex reasoning ability: (1) We first use a small amount of image generation preference data to distill the reasoning process of GPT-4o, which is then used for the model's cold start to learn the format and structure of CoT reasoning. (2) Subsequently, by leveraging the model's prior knowledge and generalization capabilities, we prepare large-scale unified multimodal preference data to elicit the model's reasoning process across various vision tasks. During this phase, correct reasoning outputs are retained for rejection sampling to refine the model (3) while incorrect predicted samples are finally used for Group Relative Policy Optimization (GRPO) based reinforcement fine-tuning, enabling the model to explore diverse reasoning paths and optimize for correct and robust solutions. Extensive experiments confirm that incorporating long CoT reasoning significantly enhances the accuracy of reward signals. Notably, after mastering CoT reasoning, the model exhibits implicit reasoning capabilities, allowing it to surpass existing baselines even without explicit reasoning traces.

We study a novel language model architecture that is capable of scaling test-time computation by implicitly reasoning in latent space. Our model works by iterating a recurrent block, thereby unrolling to arbitrary depth at test-time. This stands in contrast to mainstream reasoning models that scale up compute by producing more tokens. Unlike approaches based on chain-of-thought, our approach does not require any specialized training data, can work with small context windows, and can capture types of reasoning that are not easily represented in words. We train a proof-of-concept model from scratch with 3.5 billion parameters and 800 billion tokens. We show that this model can effortlessly use varying levels of compute, significantly improving with additional compute especially on reasoning tasks, such as math and coding. Further, this architecture naturally reduces compute costs via zero-shot per-token adaptive compute, KV-cache sharing and speculative decoding.

Multimodal large language models (MLLMs) face an inherent trade-off between faithfulness and creativity, as different tasks require varying degrees of associative reasoning. However, existing methods lack the flexibility to modulate this reasoning strength, limiting MLLMs' adaptability across factual and creative scenarios. To bridge this gap, we propose equipping MLLMs with mechanisms that enable flexible control over associative reasoning. We begin by investigating the internal mechanisms underlying associative behavior in MLLMs and find that: (1) middle layers play a pivotal role in shaping model’s associative tendencies, (2) modifying representations in these layers effectively regulates associative reasoning strength, and (3) hallucinations can be exploited to derive steering vectors that guide this modulation. Building on these findings, we introduce Flexible Association Control (FlexAC), a lightweight and training-free framework for modulating associative behavior in MLLMs. FlexAC first induces hallucination-guided intermediate representations to encode associative directions. Then, it selects high-association instances to construct effective associative steering vectors, whose strengths are adaptively calibrated to balance creative guidance with output stability. Finally, recognizing the multi-dimensional nature of associative reasoning, FlexAC incorporates task-specific associative vectors derived from a forward pass on a few target-domain samples, enabling models to follow diverse associative directions and better adapt to creative tasks. Notably, our method achieves up to a 5.8× improvement in creativity on Creation-MMBench and a 29\% reduction in hallucination rate on CHAIR, surpassing existing baselines and demonstrating its effectiveness in enabling flexible control over associative reasoning in MLLMs. Our code is available at https://github.com/ylhz/FlexAC.

Recent studies have demonstrated the efficacy of using Reinforcement Learning (RL) in building reasoning models that articulate chains of thoughts prior to producing final answers. However, despite ongoing advances that aim at enabling reasoning for vision-language tasks, existing open-source visual reasoning models typically generate reasoning content with pure natural language, lacking explicit integration of visual information. This limits their ability to produce clearly articulated and visually grounded reasoning chains. To this end, we propose Grounded Reasoning with Images and Texts (GRIT), a novel method for training MLLMs to think with images. GRIT introduces a grounded reasoning paradigm, in which models generate reasoning chains that interleave natural language and explicit bounding box coordinates. These coordinates point to regions of the input image that the model consults during its reasoning process. Additionally, GRIT is equipped with a reinforcement learning approach, GRPO-GR, built upon the GRPO algorithm. GRPO-GR employs robust rewards focused on the final answer accuracy and format of the grounded reasoning output, which eliminates the need for data with reasoning chain annotations or explicit bounding box labels. As a result, GRIT achieves exceptional data efficiency, requiring as few as 20 image-question-answer triplets from existing datasets. Comprehensive evaluations demonstrate that GRIT effectively trains MLLMs to produce coherent and visually grounded reasoning chains, showing a successful unification of reasoning and grounding abilities. All code, data, and checkpoints will be released.

Decision-making models for individuals, particularly in high-stakes scenarios like vaccine uptake, often diverge from population optimal predictions. This gap arises from the uniqueness of the individual decision-making process, shaped by numerical attributes (e.g., cost, time) and linguistic influences (e.g., personal preferences and constraints). Developing upon Utility Theory and leveraging the textual-reasoning capabilities of Large Language Models (LLMs), this paper proposes an Adaptive Textual-symbolic Human-centric Reasoning framework (ATHENA) to address the optimal information integration. ATHENA uniquely integrates two stages: First, it discovers robust, group-level symbolic utility functions via LLM-augmented symbolic discovery; Second, it implements individual-level semantic adaptation, creating personalized semantic templates guided by the optimal utility to model personalized choices. Validated on real-world travel mode and vaccine choice tasks, ATHENA consistently outperforms utility-based, machine learning, and other LLM-based models, lifting F1 score by at least 6.5\% over the strongest cutting-edge models. Further, ablation studies confirm that both stages of ATHENA are critical and complementary, as removing either clearly degrades overall predictive performance. By organically integrating symbolic utility modeling and semantic adaptation, ATHENA provides a new scheme for modeling human-centric decisions. The project page can be found at https://yibozh.github.io/Athena.

Existing benchmarks for evaluating mathematical reasoning in large language models (LLMs) rely primarily on competition problems, formal proofs, or artificially challenging questions---failing to capture the nature of mathematics encountered in actual research environments. We introduce \textsc{RealMath}, a novel benchmark derived directly from research papers and mathematical forums that assesses LLMs' abilities on authentic mathematical tasks. Our approach addresses three critical challenges: sourcing diverse research-level content, enabling reliable automated evaluation through verifiable statements, and designing a continually refreshable dataset to mitigate contamination risks. Experimental results across multiple LLMs reveal surprising capabilities in handling research mathematics compared to competition problems, suggesting current models may already serve as valuable assistants for working mathematicians despite limitations on highly challenging problems. The code and dataset for \textsc{RealMath} are publicly available.

Data diversity is crucial for training a strong language model. Yet metrics of diversity often diverge from this goal, measuring variations in heuristic features—like n-grams or embeddings—that are detached from how the model actually performs on a target task. This motivates us to ask: *Can we redefine data diversity—beyond measuring variations in heuristic features—in a way that better predicts model generalization?* Through large-scale empirical analyses spanning over 300 training runs, carefully controlled for data scale and quality, we show that data diversity can be a strong predictor of generalization in LLM reasoning—as measured by average model performance on unseen out-of-distribution benchmarks. We introduce **G-Vendi**, a metric that quantifies diversity via the entropy of model-induced loss gradients. G-Vendi scales to million-sample datasets and yet consistently outperforms heuristic alternatives, achieving strong correlation ($\text{Spearman's } \rho \approx 0.9$) with out-of-distribution (OOD) performance across both natural language inference (NLI) and math reasoning tasks. Building on this insight, we present **Prismatic Synthesis**, a framework for generating diverse synthetic data by targeting underrepresented regions in gradient space. Experimental results show that Prismatic Synthesis consistently improves model performance as we scale synthetic data—not just on in-distribution test but across unseen, out-of-distribution benchmarks—significantly outperforming state-of-the-art models in both domains. For example, PrismMath-7B, our model distilled from a 32B LLM without human verification, outperforms R1-Distill-Qwen-7B—trained on proprietary data generated by 671B R1—on 6 out of 7 challenging math benchmarks.

Abductive Learning (ABL) integrates machine learning with logical reasoning in a loop: a learning model predicts symbolic concept labels from raw inputs, which are revised through abduction using domain knowledge and then fed back for retraining. However, due to the nondeterminism of abduction, the training process often suffers from instability, especially when the knowledge base is large and complex, resulting in a prohibitively large abduction space. While prior works focus on improving candidate selection within this space, they typically treat the knowledge base as a static black box. In this work, we propose Curriculum Abductive Learning (C-ABL), a method that explicitly leverages the internal structure of the knowledge base to address the ABL training challenges. C-ABL partitions the knowledge base into a sequence of sub-bases, progressively introduced during training. This reduces the abduction space throughout training and enables the model to incorporate logic in a stepwise, smooth way. Experiments across multiple tasks show that C-ABL outperforms previous ABL implementations, significantly improves training stability, convergence speed, and final accuracy, especially under complex knowledge setting.

While energy-based models have recently proven to be a powerful framework for learning to reason with neural networks, their practical application is still limited by computational cost. That is, existing methods for energy-based iterative reasoning suffer from computational bottlenecks by relying on expensive optimization routines during training and especially during inference. Furthermore, these routines may not always converge to minimal energy states, potentially leading to suboptimal reasoning. To address these limitations, we propose a novel and efficient algorithm for energy-based iterative reasoning based on a difference-of-convex (DC) functions approach. Our algorithm achieves a significant speedup compared to prior methods while offering theoretical convergence guarantees ensuring locally minimal energy states. In addition, we achieve state-of-the-art or superior performance on continuous reasoning tasks, as demonstrated by our experiments on multiple benchmark datasets from continuous algorithmic reasoning. As such, our method offers a leap in computational efficiency, enabling faster inference with theoretical guarantees, and hence unlocking the potential of energy-based models for iterative reasoning applications.

We present **DIPO**, a novel framework for the controllable generation of articulated 3D objects from a pair of images: one depicting the object in a resting state and the other in an articulated state. Compared to the single-image approach, our dual-image input imposes only a modest overhead for data collection, but at the same time provides important motion information, which is a reliable guide for predicting kinematic relationships between parts. Specifically, we propose a dual-image diffusion model that captures relationships between the image pair to generate part layouts and joint parameters. In addition, we introduce a Chain-of-Thought (CoT) based **graph reasoner** that explicitly infers part connectivity relationships. To further improve robustness and generalization on complex articulated objects, we develop a fully automated dataset expansion pipeline, name **LEGO-Art**, that enriches the diversity and complexity of PartNet-Mobility dataset. We propose **PM-X**, a large-scale dataset of complex articulated 3D objects, accompanied by rendered images, URDF annotations, and textual descriptions. Extensive experiments demonstrate that DIPO significantly outperforms existing baselines in both the resting state and the articulated state, while the proposed PM-X dataset further enhances generalization to diverse and structurally complex articulated objects. Our code and dataset are available at https://github.com/RQ-Wu/DIPO.

In this work, we introduce CAD-Coder, a novel framework that reformulates text-to-CAD as the generation of CadQuery scripts—a Python-based, parametric CAD language. This representation enables direct geometric validation, a richer modeling vocabulary, and seamless integration with existing LLMs. To further enhance code validity and geometric fidelity, we propose a two-stage learning pipeline: (1) supervised fine-tuning on paired text–CadQuery data, and (2) reinforcement learning with Group Reward Policy Optimization (GRPO), guided by a CAD-specific reward comprising both a geometric reward (Chamfer Distance) and a format reward. We also introduce a chain-of-thought (CoT) planning process to improve model reasoning, and construct a large-scale, high-quality dataset of 110K text–CadQuery–3D model triplets and 1.5K CoT samples via an automated pipeline. Extensive experiments demonstrate that CAD-Coder enables LLMs to generate diverse, valid, and complex CAD models directly from natural language, advancing the state of the art of text-to-CAD generation and geometric reasoning.

Most video-anomaly research stops at frame-wise detection, offering little insight into why an event is abnormal, typically outputting only frame-wise anomaly scores without spatial or semantic context. Recent video anomaly localization and video anomaly understanding methods improve explainability but remain data-dependent and task-specific. We propose a unified reasoning framework that bridges the gap between temporal detection, spatial localization, and textual explanation. Our approach is built upon a chained test-time reasoning process that sequentially connects these tasks, enabling holistic zero-shot anomaly analysis without any additional training. Specifically, our approach leverages intra-task reasoning to refine temporal detections and inter-task chaining for spatial and semantic understanding, yielding improved interpretability and generalization in a fully zero-shot manner. Without any additional data or gradients, our method achieves state-of-the-art zero-shot performance across multiple video anomaly detection, localization, and explanation benchmarks. The results demonstrate that careful prompt design with task-wise chaining can unlock the reasoning power of foundation models, enabling practical, interpretable video anomaly analysis in a fully zero-shot manner. Project Page: https://rathgrith.github.io/Unified_Frame_VAA/.

Realistic 3D indoor scene synthesis is vital for embodied AI and digital content creation. It can be naturally divided into two subtasks: object generation and layout generation. While recent generative models have significantly advanced object-level quality and controllability, layout generation remains challenging due to limited datasets. Existing methods either overfit to these datasets or rely on predefined constraints to optimize numerical layout that sacrifice flexibility. As a result, they fail to generate scenes that are both open-vocabulary and aligned with fine-grained user instructions. We introduce DirectLayout, a framework that directly generates numerical 3D layouts from text descriptions using generalizable spatial reasoning of large language models (LLMs). DirectLayout decomposes the generation into three stages: producing a Bird's-Eye View (BEV) layout, lifting it into 3D space, and refining object placements. To enable explicit spatial reasoning and help the model grasp basic principles of object placement, we employ Chain-of-Thought (CoT) Activation based on the 3D-Front dataset. Additionally, we design CoT-Grounded Generative Layout Reward to enhance generalization and spatial planning. During inference, DirectLayout addresses asset-layout mismatches via Iterative Asset-Layout Alignment through in-context learning. Extensive experiments demonstrate that DirectLayout achieves impressive semantic consistency, generalization and physical plausibility.

Building robust and general reasoning ability is a central goal in the development of large language models (LLMs). Recent efforts increasingly turn to code as a rich training source, given its inherent logical structure and diverse reasoning paradigms—such as divide-and-conquer, topological ordering, and enumeration. However, reasoning in code is often expressed implicitly and entangled with syntactic or implementation noise, making direct training on raw code suboptimal. To address this, we introduce TraceMind, a large-scale corpus of 2.6 million samples that transforms code execution into explicit, step-by-step chain-of-thought style rationales, which we call Chain of Execution (CoE). The corpus spans domains including mathematics, classical algorithms and algorithmic competition, and is enriched with variable-tracing questions and code rewritings to enhance logical granularity and code diversity. We evaluate Tracepile using three training setups—continue-pretraining, instruction tuning after pretraining, and two-stage finetuning. Experiments across four base models (LLaMA 3, LLaMA 3.1, Qwen-2.5, and Qwen-2.5 Coder) and 20 benchmarks covering math, code, logic, and algorithms demonstrate consistent improvements. Notably, Tracepile boosts LLaMA3-8B by 9.2\% on average across nine math datasets and delivers clear gains on LiveCodeBench, CRUX, and Zebra Logic under two-stage finetuning.

Selecting an appropriate reasoning method for a given query remains a key challenge in language model generation. Existing approaches typically generate multiple candidate responses and use an aggregation strategy to select the output answer, often assuming that more candidate answers yield higher accuracy. We revisit this assumption through a rigorous theoretical analysis, deriving accuracy bounds for standard aggregation methods under fixed generation distributions and candidate sizes. Building on these insights, we introduce EPIC, an Ensemble Planning with Contrastive learning framework to learn a shared representation space that captures both model reasoning abilities and query-method compatibility. EPIC incorporates our probability bounds as a regularizer in a utility-driven optimization that balances accuracy and computational cost. Experiments on diverse mathematical reasoning tasks show that EPIC consistently selects optimal reasoning methods, improving accuracy while reducing computational overhead. Our code can be found at https://github.com/nguyenngocbaocmt02/EPIC.

Large Language Models (LLMs) are now integral across various domains and have demonstrated impressive performance. Progress, however, rests on the premise that benchmark scores are both accurate and reproducible. We demonstrate that the reproducibility of LLM performance is fragile: changing system configuration, such as evaluation batch size, GPU count, and GPU version, can introduce significant differences in the generated responses. This issue is especially pronounced in reasoning models, where minor rounding differences in early tokens can cascade into divergent chains of thought, ultimately affecting accuracy. For instance, under bfloat16 precision with greedy decoding, a reasoning model like DeepSeek-R1-Distill-Qwen-7B can exhibit up to 9\% variation in accuracy and 9,000 tokens difference in response length due to differences in GPU count, type, and evaluation batch size. We trace the root cause of this variability to the non-associative nature of floating-point arithmetic under limited numerical precision. This work presents the first systematic investigation into how numerical precision affects reproducibility in LLM inference. Through carefully controlled experiments across various hardware, software, and precision settings, we quantify when and how model outputs diverge. Our analysis reveals that floating-point precision—while critical for reproducibility—is often neglected in evaluation practices. Inspired by this, we develop a lightweight inference pipeline, dubbed LayerCast, that stores weights in 16-bit precision but performs all computations in FP32, balancing memory efficiency with numerical stability. Code is available at https://github.com/nanomaoli/llm_reproducibility.