ICLR 2026 Papers

Deep reasoning is fundamental for solving complex tasks, especially in vision-centric scenarios that demand sequential, multimodal understanding. However, existing benchmarks typically evaluate agents with fully synthetic, single-turn queries, limited visual modalities, and lack a framework to assess reasoning quality over multiple steps as required in real-world settings. To address this, we introduce Agent-X, a large-scale benchmark for evaluating vision-centric agents’ multistep and deep reasoning capabilities in real-world, multimodal settings. AgentX features 828 agentic tasks with authentic visual contexts, including images, multi-image comparisons, videos, and instructional text. These tasks span six major agentic environments: general visual reasoning, web browsing, security and surveillance, autonomous driving, sports, and math reasoning. Our benchmark requires agents to integrate tool use with explicit, stepwise decision-making in these diverse settings. In addition, we propose a fine-grained, step-level evaluation framework that assesses the correctness and logical coherence of each reasoning step and the effectiveness of tool usage throughout the task. Our results reveal that even the best-performing models, including GPT, Gemini, and Qwen families, struggle to solve multi-step vision tasks, achieving less than 50% full-chain success. These findings highlight key bottlenecks in current LMM reasoning and tool-use capabilities and identify future research directions in vision-centric agentic reasoning models

Unsupervised Reinforcement Learning with Verifiable Rewards (URLVR) offers a pathway for Large Language Models (LLMs) to improve without human supervision. Particularly, many works use model intrinsic information as rewards for URLVR, showing promising improvements, yet their potential and limitations remain unclear. In this work, we revisit URLVR through the lens of intrinsic rewards. We present a unified theoretical framework showing that intrinsic reward methods share a core mechanism: they trade uncertainty for performance by leveraging the model’s prior knowledge to sharpen output distributions. Empirical analysis confirms this tradeoff, revealing distinct failure modes and showing that collapse is not inevitable in small, domain-specific regimes such as test-time training. Beyond these findings, early intrinsic reward dynamics also provide a lightweight indicator of model-task priors, complementing $pass@k$ in assessing RL trainability. These insights highlight both the promise and pitfalls of URLVR, motivating future directions such as external rewards and hybrid supervision strategies.

Recently, significant progress has been made in developing reasoning-capable Large Language Models (LLMs) through long Chain-of-Thought (CoT) techniques. However, this long-CoT reasoning process imposes substantial memory overhead due to the large Key-Value (KV) Cache memory overhead. Post-training KV Cache quantization has emerged as a promising compression technique and has been extensively studied in short-context scenarios. However, directly applying existing methods to long-CoT LLMs causes significant performance degradation due to the following two reasons: (1) Large cumulative error: Existing methods fail to adequately leverage available memory, and they directly quantize the KV Cache during each decoding step, leading to large cumulative quantization error. (2) Short-context calibration: Due to Rotary Positional Embedding (RoPE), the use of short-context data during calibration fails to account for the distribution of less frequent channels in the Key Cache, resulting in performance loss. We propose Progressive Mixed-Precision KV Cache Quantization (PM-KVQ) for long-CoT LLMs to address the above issues in two folds: (1) To reduce cumulative error, we design a progressive quantization strategy to gradually lower the bit-width of KV Cache in each block. Then, we propose block-wise memory allocation to assign a higher bit-width to more sensitive transformer blocks. (2) To increase the calibration length without additional overhead, we propose a new calibration strategy with positional interpolation that leverages short calibration data with positional interpolation to approximate the data distribution of long-context data. Extensive experiments on 7B–70B long-CoT LLMs show that PM-KVQ improves reasoning benchmark performance by up to 8% over SOTA baselines under the same memory budget and achieves 2.73–5.18$\times$ throughput over the original 16-bit LLMs. Our code will be released soon.

With the rise of deep neural networks, especially in safety-critical applications, robustness and interpretability are crucial to ensure their trustworthiness. Recent advances in 3D-aware classifiers that map image features to volumetric representation of objects, rather than relying solely on 2D appearance, have greatly improved robustness on out-of-distribution (OOD) data. Such classifiers have not yet been studied from the perspective of interpretability. Meanwhile, current concept-based XAI methods often neglect OOD robustness. We aim to address both aspects with CAVE - Concept Aware Volumes for Explanations - a new direction that unifies interpretability and robustness in image classification. We design CAVE as a robust and inherently interpretable classifier that learns sparse concepts from 3D object representation. We further propose 3D Consistency (3D-C), a metric to measure spatial consistency of concepts. Unlike existing metrics that rely on human-annotated parts on images, 3D-C leverages ground-truth object meshes as a common surface to project and compare explanations across concept-based methods. CAVE achieves competitive classification performance while discovering consistent and meaningful concepts across images in various OOD settings.

Chain-of-Thought (CoT) training has markedly advanced the reasoning capabilities of large language models (LLMs), yet the mechanisms by which CoT training enhances generalization remain inadequately understood. In this work, we demonstrate that compositional generalization is fundamental: models systematically combine simpler learned skills during CoT training to address novel and more complex problems. Through a theoretical and structural analysis, we formalize this process: 1) Theoretically, the information-theoretic generalization bounds through distributional divergence can be decomposed into in-distribution (ID) and out-of-distribution (OOD) components. Specifically, the non-CoT models fail on OOD tasks due to unseen compositional patterns, whereas CoT-trained models achieve strong generalization by composing previously learned skills. In addition, controlled experiments and real-world validation confirm that CoT training accelerates convergence and enhances generalization from ID to both ID and OOD scenarios while maintaining robust performance even with tolerable noise. 2) Structurally, CoT training internalizes reasoning into a two-stage compositional circuit, where the number of stages corresponds to the explicit reasoning steps during training. Notably, CoT-trained models resolve intermediate results at shallower layers compared to non-CoT counterparts, freeing up deeper layers to specialize in subsequent reasoning steps. A key insight is that CoT training teaches models how to think—by fostering compositional reasoning—rather than merely what to think, through the provision of correct answers alone. This paper offers valuable insights for designing CoT strategies to enhance LLMs' reasoning robustness.

While Large Language Models (LLMs) have demonstrated impressive capabilities, their output quality remains inconsistent across various application scenarios, making it difficult to identify trustworthy responses, especially in complex tasks requiring multi-step reasoning. In this paper, we propose a **Tok**en-level **U**ncertainty estimation framework for **R**easoning (**TokUR**) that enables LLMs to self-assess and self-improve their responses in mathematical reasoning. Specifically, we introduce low-rank random weight perturbation during LLM decoding to generate predictive distributions for token-level uncertainty estimation, and we aggregate these uncertainty quantities to capture the semantic uncertainty of generated responses. Experiments on mathematical reasoning datasets of varying difficulty demonstrate that TokUR exhibits a strong correlation with answer correctness and model robustness, and the uncertainty signals produced by TokUR can be leveraged to enhance the model’s reasoning performance at test time. These results highlight the effectiveness of TokUR as a principled and scalable approach for improving the reliability and interpretability of LLMs in challenging reasoning tasks.

Despite impressive capabilities, LLMs' successes often rely on pattern-matching behaviors, yet these are also linked to OOD generalization failures in compositional tasks. However, behavioral studies commonly employ task setups that allow multiple generalization sources (e.g., algebraic invariances, structural repetition), obscuring a precise and testable account of how well LLMs perform generalization through pattern matching and their limitations. To address this ambiguity, we first formalize pattern matching as functional equivalence, i.e., identifying pairs of subsequences of inputs that consistently lead to identical results when the rest of the input is held constant. Then, we systematically study how decoder-only Transformer and Mamba behave in controlled tasks with compositional structures that isolate this mechanism. Our formalism yields predictive and quantitative insights: (1) Instance-wise success of pattern matching is well predicted by the number of contexts witnessing the relevant functional equivalence. We prove a tight sample complexity bound of learning a two-hop structure by identifying the exponent of the data scaling law for perfect in-domain generalization. Our empirical results align with the theoretical prediction, under 20× parameter scaling and across architectures. (3) Path ambiguity is a structural barrier: when a variable influences the output via multiple paths, models fail to form unified intermediate state representations, impairing accuracy and interpretability. (4) Chain-of-Thought reduces data requirements yet does not resolve path ambiguity. Hence, we provide a predictive, falsifiable boundary for pattern matching and a foundational diagnostic for disentangling mixed generalization mechanisms.

Multi-modal Large Language Models (MLLMs) represent a significant advancement in artificial intelligence. Among the growing capabilities exhibited by MLLMs, abilities to understand and reason in real-world environments stand out as particularly vital as a fundamental prerequisite for a wide array of real-world applications. The current methods for evaluating MLLMs often fall short in their ability to comprehensively assess these crucial capabilities. However, being able to reason on complex environment-scale spaces, for example, room spaces, building spaces, and even urban spaces, and to predict the future and plan actions, is essential for humans and various autonomous agents to survive in the real physical world. To address these gaps, we propose a visual-question-answering benchmark, **SpaCE-Eval** (**Spa**tial Reasoning, **C**ommonsense Knowledge and **E**nvironment Interaction) in the real world, designed to evaluate some of MLLM’s most important reasoning abilities in real-world environments. As the name suggests, it challenges the models to reason on complex spatial scenarios, invoke commonsense knowledge of the physical world, and interact with the environment. The dataset consists of all new diagrams purposefully produced by humans, where diagram-question pairs are meticulously refined and selected through a rigorous pipeline. Additionally, with the benchmark, we evaluate a selection of leading MLLMs, both proprietary and open source. The results suggest that a significant enhancement of MLLMs in reasoning in the real physical world is necessary to realise more advanced general artificial intelligence.

Large Language Models (LLMs) often struggle with challenging, multi-step reasoning problems due to a fundamental learning gap -- Reinforcement Learning with Verifiable Rewards (RLVR) suffers from sparse rewards when correct solutions are rarely sampled, while Supervised Fine-Tuning (SFT) tends to overfit to long demonstrations through rigid token mimicry. To bridge this gap, we introduce Supervised Reinforcement Learning (SRL), a framework that reformulates problem-solving as a sequence of logical actions. SRL trains the model to learn from each action, where the model first generates an internal reasoning monologue and then commits to an action. The model receives dense rewards based on the similarity between its actions and the expert’s at each step, providing a richer signal than RLVR. More importantly, by only rewarding the action, SRL allows the model flexibility in its self-generated thought process, promoting stronger reasoning abilities than SFT. On challenging mathematical reasoning benchmarks, SRL significantly outperforms both methods. Furthermore, a curriculum that cold-start with SRL before refining with RLVR achieves the strongest results. SRL also generalizes effectively to agentic software engineering tasks, establishing it as a robust framework for various reasoning tasks.

Monocular 3D reconstruction methods and vision-language models (VLMs) demonstrate impressive results on standard benchmarks, yet their true understanding of geometric properties remains unclear. We introduce GIQ, a comprehensive benchmark specifically designed to evaluate the geometric reasoning capabilities of vision and vision-language foundation models. GIQ comprises synthetic and real-world images and corresponding 3D meshes of diverse polyhedra—including Platonic, Archimedean, Johnson, and Catalan solids, as well as stellations and compound shapes—covering varying levels of complexity and symmetry. Through systematic experiments involving monocular 3D reconstruction, 3D symmetry detection, mental rotation tests, and zero-shot shape classification tasks, we reveal significant shortcomings in current models. State-of-the-art reconstruction algorithms trained on extensive 3D datasets struggle to reconstruct even basic geometric forms accurately. While foundation models effectively detect specific 3D symmetry elements via non-linear probing, they falter significantly in tasks requiring detailed geometric differentiation, such as mental rotation. Moreover, advanced vision-language assistants exhibit remarkably low accuracy on complex polyhedra, systematically misinterpreting basic properties like face geometry, convexity, and compound structures. GIQ is publicly available at toomanymatts.github.io/giq-benchmark/, providing a structured platform to benchmark critical gaps in geometric intelligence and facilitate future progress in robust, geometry-aware representation learning.

DeepSeek-R1-Zero has successfully demonstrated the emergence of reasoning capabilities in LLMs purely through Reinforcement Learning (RL). Inspired by this breakthrough, we explore how RL can be utilized to enhance the reasoning capability of MLLMs. However, direct training with RL struggles to activate complex reasoning capabilities such as questioning and reflection in MLLMs, due to the absence of substantial high-quality multimodal reasoning data. To address this issue, we propose the reasoning MLLM, Vision-R1, to improve multimodal reasoning capability. Specifically, we first construct a high-quality multimodal CoT dataset without human annotations by leveraging an existing MLLM and DeepSeek-R1 through modality bridging and data filtering to obtain a 200K multimodal CoT dataset, Vision-R1-cold dataset. It serves as cold-start initialization data for Vision-R1. To mitigate the optimization challenges caused by overthinking after cold start, we propose Progressive Thinking Suppression Training (PTST) strategy and employ Group Relative Policy Optimization (GRPO) with the hard formatting result reward function to gradually refine the model's ability to learn correct and complex reasoning processes on the multimodal math dataset. Comprehensive experiments show our model achieves an average improvement of $\sim$6\% across various multimodal math reasoning benchmarks using only a 10K multimodal math data during RL training. Vision-R1-7B achieves a 73.5\% accuracy on the widely used MathVista benchmark, which is only 0.4\% lower than the leading reasoning model, OpenAI O1. Scaling up the amount of multimodal math data in the RL training, Vision-R1-32B and Vison-R1-72B achieves 76.4\% and 78.2\% MathVista benchmark scores, respectively.

Logical consistency, the requirement that statements remain non-contradictory under logical rules, is fundamental for trustworthy reasoning, yet current LLMs often fail to maintain it even on simple inference tasks. Existing benchmarks for LLM logical consistency are not scalable, not diverse, and not challenging, with state-of-the-art models already surpassing 95% accuracy. LogiConBench is the first benchmark that (1) generates unlimited logical rule combinations with precise labels, (2) provides controllable-depth graphs with explicit reasoning paths, and (3) remains challenging for state-of-the-art LLMs. To achieve this, LogiConBench automatically generates logical graphs where nodes represent symbolic propositions and edges denote reasoning relations. From these graphs, it samples lists of propositions, extracts reasoning paths, determines all consistent label lists, and translates them into diverse natural language expressions. While we release a 280K-sample corpus in this work, the framework can be scaled to generate unlimited data. To strengthen its evaluative significance, we evaluate 14 frontier LLMs on two tasks with varying difficulty levels, and find that the Enumerative task remains extremely challenging, with the best exact accuracy as only 34%. Our code and data are available at https://anonymous.4open.science/r/LogiConBench-11D1/.

Large language models trained with reinforcement learning on verifiable rewards often inflate response length—trading brevity for accuracy. While longer reasoning can help on hard problems, many extra tokens are filler: verbose text making little progress. We introduce GFPO (Group Filtered Policy Optimization), which curbs this length explosion by sampling larger groups per problem and only training on responses filtered by (1) length and (2) token efficiency (reward per token). By sampling more during training time, GFPO teaches models to think less at inference time. On Phi-4-reasoning, GFPO cuts GRPO’s length inflation by up to 85\% across STEM and coding benchmarks (AIME 24/25, GPQA, Omni-MATH, LiveCodeBench) while preserving accuracy. We find that GFPO also outperforms Dr. GRPO in both accuracy and length reduction and generalizes across model sizes and families. We further propose Adaptive Difficulty GFPO, which allocates more training exploration to harder problems, yielding better efficiency-accuracy trade-offs on challenging questions. With only a 7\% increase in training time, GFPO reduces end-to-end latency by $\sim$30\%, cutting response time on hard queries by 90 seconds. GFPO trades modest training-time increases for lasting gains in inference—an effective recipe for efficient reasoning.

Existing research of 3D LLMs still struggles to achieve efficient and explainable reasoning, primarily due to the under-exploration of the mechanism of human-like scene-object grounded reasoning. This paper bridges the gap by presenting a novel framework. We first introduce a Chain-of-Thought reasoning framework in 3D scenes (SceneCOT), decoupling a complex reasoning task into simpler and manageable problems, and building corresponding visual clues based on multimodal expert modules. To enable such a framework, we build the first large-scale 3D scene Chain-of-Thought reasoning dataset, SceneCOT, including more than 190k high-quality data instances. Extensive experiments across various complex 3D scene reasoning benchmarks demonstrate that our new framework achieves state-of-the-art with clear interpretability. To our knowledge, this is the first attempt to successfully implement the COT technique for achieving human-like step-by-step reasoning for 3D scene understanding, where we show great potential in extending it to a wider range of 3D scene understanding scenarios.

Powerful large language models (LLMs) from different providers have been expensively trained and finetuned to specialize across varying domains. In this work, we introduce a new kind of Conductor model trained with reinforcement learning to automatically discover powerful coordination strategies among LLMs. Our Conductor learns not only to design targeted communication topologies for effective agent-to-agent collaboration, but also to prompt engineer focused instructions to the LLMs to maximally leverage their individual capabilities. We show that, by learning optimal coordination strategies over pools of powerful worker LLMs, a 7B Conductor achieves significant performance gains beyond any individual worker, attaining state-of-the-art results in challenging reasoning benchmarks, such as LiveCodeBench and GPQA. By training with randomized agent pools, our conductor effectively adapts to arbitrary sets of open- and closed-source agents, meeting any user requirements. Furthermore, allowing the Conductor to select itself as a worker gives rise to recursive topologies, elevating performance with a new form of dynamic test-time scaling through online iterative adaptation. More broadly, ours is among the early work demonstrating language model coordination can be unlocked through RL, where powerful coordination strategies emerge naturally in LLMs through pure end-to-end reward maximization.

Recent advances in the audio language modeling (ALM) domain tackle audio understanding and text-to-audio generation as separate tasks. Very few studies attempt to unify these tasks -- an essential step toward advanced multimodal reasoning. This paper introduces Unified Audio Language Model (UALM), which aims to unify audio understanding, text-to-audio generation, and multimodal reasoning in a single model. To achieve this goal, we first present UALM-Gen, a text-to-audio language model that directly predicts audio tokens and is comparable to state-of-the-art diffusion-based models. We then demonstrate, using proper data blending, training recipes, and inference techniques, that our single UALM model matches the quality of state-of-the-art specialized models in audio understanding, text-to-audio generation, and text reasoning. Furthermore, we present UALM-R1, a multimodal reasoning model that utilizes both text and audio in the intermediate thinking steps to facilitate complex generation tasks. To our knowledge, this is the first demonstration in audio research of cross-modal generative reasoning, with its effectiveness confirmed by subjective evaluations.

Despite rapid progress in Multi-modal Large Language Models and Large Audio-Language Models, existing audio benchmarks largely test semantics that can be recovered from text captions, masking deficits in fine-grained perceptual reasoning. We formalize audio 4D intelligence that is defined as reasoning over sound dynamics in time and 3D space, and introduce STAR-Bench to measure it. STAR-Bench combines a Foundational Acoustic Perception setting (six attributes under absolute and relative regimes) with a Holistic Spatio-Temporal Reasoning setting that includes segment reordering for continuous and discrete processes and spatial tasks spanning static localization, multi-source relations, and dynamic trajectories. Our data curation pipeline uses two methods to ensure high-quality samples. For foundational tasks, we use procedurally synthesized and physics-simulated audio. For holistic data, we follow a four-stage process that includes human annotation and final selection based on human performance. Unlike prior benchmarks where caption-only answering reduces accuracy slightly, STAR-Bench induces far larger drops (-31.5\% temporal, -35.2\% spatial), evidencing its focus on linguistically hard-to-describe cues. Evaluating 19 models reveals substantial gaps compared with humans and a capability hierarchy: closed-source models are bottlenecked by fine-grained perception, while open-source models lag across perception, knowledge, and reasoning. Our STAR-Bench provides critical insights and a clear path forward for developing future models with a more robust understanding of the physical world.

Large-scale reinforcement learning with verifiable rewards (RLVR) has proven effective in harnessing the potential of large language models (LLMs) for single-turn reasoning tasks. In realistic reasoning scenarios, LLMs often rely on external tools to assist in task-solving processes. However, current RL algorithms typically employ trajectory-level rollout sampling, consistently neglecting the fine-grained exploration of multi-turn tool-call steps. To bridge this gap, we propose Agentic Reinforced Policy Optimization (ARPO), a novel agentic RL algorithm tailored for training multi-turn LLM-based agents. Our preliminary experiments reveal that LLMs frequently exhibit increased uncertainty after tool-call steps, as evidenced by higher entropy in the distribution of generated tokens. Motivated by this, ARPO incorporates an entropy-based adaptive rollout mechanism, encouraging the policy model to adaptively branch sampling during high-entropy tool-call rounds, thereby promoting step-level exploration of latent tool-use behaviors. By integrating an advantage attribution estimation, ARPO enables LLMs to internalize advantage differences in stepwise tool-use interactions. Experiments across 13 challenging benchmarks demonstrate ARPO's superiority over trajectory-level RL algorithms. Remarkably, ARPO achieves improved performance using only half of the tool-use budget required by existing methods, offering a scalable solution for aligning LLM-based agents with real-time dynamic environments. Our codes are released at https://github.com/RUC-NLPIR/ARPO.

We introduce **LudoBench**, a multimodal reasoning benchmark that evaluates whether vision-enabled large language models (LMs) can acquire, integrate, and reason over heterogeneous game knowledge in mainstream analog tabletop games. Unlike prior works that emphasize deep strategic mastery, LudoBench targets an initial reasoning challenge uninitiated gamers face: *correctly comprehending a new tabletop strategy game for the first time*. We examine whether, given a visual depiction of a tabletop scene and a corresponding ruleset, a model can correctly answer grounded questions about the pictured scenario. Concretely, LudoBench tests three cumulative situated game-comprehension capabilities: (1) *Environment Perception*, (2) *Heterogeneous Rules Integration*, and (3) *Short-horizon Optimization*, to progressively stress-test the foundational reasoning required for real-world game comprehension. Evaluating frontier LMs on three diverse strategy games, we find that even the strongest models achieve only ~68% accuracy on simple environment perception tasks and fall below 10% on situated multi-step comprehension puzzles that hobbyist gamers can routinely solve. Our extensive failure analysis and knowledge-ablation experiments reveal that *models largely fail to comprehend rich cross-modal reference knowledge* and are subsequently unable to apply this knowledge to messy and unfamiliar situated environments. Our findings highlight the many steps remaining for current methods to succeed on complex multimodal reasoning in the real world.