ICLR 2026 Papers

Recent progress in large reasoning models for challenging mathematical reasoning has been driven by reinforcement learning (RL). Incorporating long chain-of-thought (CoT) data during mid-training has also been shown to substantially improve reasoning depth. However, current approaches often utilize CoT data indiscriminately, leaving open the critical question of which data types most effectively enhance model reasoning capabilities. In this paper, we define the foundation model's reasoning potential for the first time as the inverse of the number of independent attempts required to correctly answer the question, which is strongly correlated with the final model performance. We then propose utilizing diverse data enriched with high-value reasoning patterns to expand the reasoning potential. Specifically, we abstract atomic reasoning patterns from CoT sequences, characterized by commonality and inductive capabilities, and use them to construct a core reference set enriched with valuable reasoning patterns. Furthermore, we propose a dual-granularity algorithm involving chains of reasoning patterns and token entropy, efficiently selecting high-value CoT data (CoTP) from the data pool that aligns with the core set, thereby training models to master reasoning effectively. Only 10B-token CoTP data enables the 85A6B Mixture-of-Experts (MoE) model to improve by **9.58\%** on the challenging AIME 2024 and 2025, and to raise the upper bound of downstream RL performance by **7.81\%**.

Reasoning LLMs suffer from quadratic compute growth as their context length increases, making reinforcement learning with verifiable rewards (RLVR) and test-time scaling prohibitively expensive. Prior work has tried to lighten the computational burden by shortening reasoning traces through pruning, summarization, or multi-stage training, but these methods remain bound to quadratic costs. We introduce Delethink, a thinking algorithm that realizes the Markovian Thinking Paradigm. Instead of producing one long monolithic reasoning trace, Delethink thinks in a sequence of chunks, the Delethink trace. Each chunk continues reasoning by referring only to a fixed number of prior tokens, which functions as a Markovian state sufficient for progressing reasoning, while deleting the rest. This preserves continuity without carrying the quadratic baggage. As a result, compute scales linearly and peak memory remains constant. In experiments, we show that Delethink can be applied directly to off-the-shelf reasoning models ranging from $1.5\textnormal{B}$ to $30\textnormal{B}$ parameters, with no loss in performance. Extended reasoning becomes possible under fixed memory and linear compute, while enabling efficient RL training on new tasks. On the DeepScaleR dataset, Delethink trains R1DistillQwen1.5B to the same benchmark performance as a standard long chain-of-thought (LongCoT) approach, where both models generate up to $24\textnormal{k}$ thinking tokens. The difference is efficiency. Delethink reasons $40\%$ faster with $70\%$ less memory footprint. By decoupling reasoning length from context length, the Markovian Thinking paradigm opens the door to next-generation reasoning LLMs that can scale to millions of tokens with linear compute and constant memory.

Reinforcement Learning (RL) has been shown to significantly boost reasoning capabilities of large language models (LLMs) in math, coding, and multi-hop reasoning tasks. However, RL fine-tuning requires abundant high-quality verifiable data, often obtained through human-annotated datasets and LLM-as-verifier loops. Both of these data types have considerable limitations: human-annotated datasets are small and expensive to curate, while LLM verifiers have high scoring latency and are costly to operate. In this work, we investigate the use of synthetic datasets in RL fine-tuning for multi-hop reasoning tasks. We discover that LLMs fine-tuned on synthetic data perform significantly better on popular real-world question-answering benchmarks, even though the synthetic data only contain fictional knowledge. On stratifying model performance by question difficulty, we find that synthetic data teaches LLMs to compose knowledge, which we to be a fundamental and generalizable reasoning skill. Our work thus highlights the utility of synthetic reasoning datasets in improving LLM reasoning capabilities.

Web search is a cornerstone for deep research agents, enabling them to acquire and reason over knowledge beyond static corpora. Yet most existing systems follow rigid ReAct-style tool chains locked into fixed workflow structures, which hinders their ability to flexibly handle diverse query types and tool-use strategies. We introduce $\textbf{FlowSearcher}$, a novel web search framework built on agentic workflow synthesis. FlowSearcher decomposes queries into sub-goals, each orchestrated by a tailored workflow graph that adapts the depth and order of tool use, giving the system structural flexibility to handle diverse sub-goals ranging from simple lookups and focused navigation to multi-hop information synthesis. Complementing this, a hierarchical memory distills past workflows into structured experience, providing reusable context that improves orchestration and guides tool use on new queries. This shift from reactive tool calls to memory-driven workflow design and execution marks a principled step toward deliberative web research. Empirical results on GAIA, BrowseComp, and GPQA show that our memory-driven, training-free workflow synthesis consistently matches or exceeds the performance of RLHF-trained systems, pointing toward a new direction of agent design grounded in memory-enhanced structural planning rather than parameter fine-tuning.

Large Multimodal Models have achieved remarkable progress in integrating vision and language, enabling strong performance across perception, reasoning, and domain-specific tasks. However, their capacity to reason over multiple, visually similar inputs remains insufficiently explored. Such fine-grained comparative reasoning is central to real-world tasks, especially in mathematics and education, where learners must often distinguish between nearly identical diagrams to identify correct solutions. To address this gap, we present VisioMath, a curated benchmark of 1,800 high-quality K–12 mathematics problems in which all candidate answers are diagrams with subtle visual similarities. A comprehensive evaluation of state-of-the-art LMMs, covering both leading closed-source systems and widely adopted open-source models, reveals a consistent decline in accuracy as inter-image similarity increases. Analysis indicates that the dominant failure mode stems from image–text misalignment: rather than grounding reasoning in textual cues, models often resort to shallow positional heuristics, resulting in systematic errors. We further explore three alignment-oriented strategies, spanning training-free approaches and finetuning, and achieve substantial accuracy gains. We hope that VisioMath will serve as a rigorous benchmark and catalyst for developing LMMs toward deeper diagram understanding, precise comparative reasoning, and grounded multi-image–text integration.

Precisely evaluating video understanding models remains challenging: commonly used metrics such as BLEU, ROUGE, and BERTScore fail to capture the fineness of human judgment, while obtaining such judgments through manual evaluation is costly. Recent work has explored using large language models (LLMs) or multimodal LLMs (MLLMs) as evaluators, but their extension to video understanding remains relatively unexplored. In this work, we introduce VideoJudge, a 3B and 7B-sized MLLM judge specialized to evaluate outputs from video understanding models (\textit{i.e.}, text responses conditioned on videos). To train VideoJudge, our recipe builds on the interplay between a generator and an evaluator: the generator is prompted to produce responses conditioned on a target rating, and responses not matching the evaluator's rating are discarded. Across three out of four meta-evaluation benchmarks, VideoJudge-7B outperforms larger MLLM judge baselines such as Qwen2.5-VL-32B and Qwen2.5-VL-72B. Notably, we find that LLM judges (Qwen3) models perform worse than MLLM judges (Qwen2.5-VL) and that long chain-of-thought reasoning does not improve performance, indicating that providing video inputs is crucial for evaluation of video understanding tasks.

With the rapid development of language models, the number of small language models (SLMs) has grown significantly. Although they do not achieve state-of-the-art accuracy, they are more efficient and often excel at specific tasks. This raises a natural question: can multiple SLMs be orchestrated into a system where each contributes effectively, achieving higher accuracy than any individual model? Existing orchestration methods have primarily targeted frontier models (e.g., GPT-4) and perform suboptimally when applied to SLMs. To address this gap, we propose a three-stage approach for orchestrating SLMs. First, we introduce SLM-MUX, a multi-model architecture that effectively coordinates multiple SLMs. Building on this, we develop two optimization strategies: (i) a model selection search that identifies the most complementary SLMs from a given pool, and (ii) test-time scaling tailored to SLM-MUX. Our approach delivers strong results: Compared to existing orchestration methods, our approach achieves up to 13.4% improvement on MATH, 8.8% on GPQA, and 7.0% on GSM8K. With just two SLMs, SLM-MUX outperforms Qwen 2.5 72B on GPQA and GSM8K, and matches its performance on MATH. We further provide theoretical analyses to substantiate the advantages of our method. Additional experiments show that the core principle of SLM-MUX extends to open-ended generation tasks (e.g., HumanEval) and benefits other model classes, including frontier LLMs and domain-specific fine-tuned SLMs. In summary, we demonstrate that SLMs can be effectively orchestrated into more accurate and efficient systems through the proposed approach.

Compression methods, including quantization, distillation, and pruning, improve the computational efficiency of large reasoning models (LRMs). However, existing studies either fail to sufficiently compare all three compression methods on LRMs or lack in-depth interpretation analysis. In this paper, we investigate how the reasoning capabilities of LRMs are compromised during compression, through performance benchmarking and mechanistic interpretation. To uncover the effects of compression on reasoning performance, we benchmark quantized, distilled, and pruned DeepSeek-R1 models on four reasoning datasets (AIME 2024, FOLIO, Temporal Sequences, and MuSiQue). To precisely locate compression effects on model weights, we adapt difference of means and attribution patching techniques, focusing on the activation of every linear component in compressed LRMs, to interpret fine-grained causal relationships between weights and various reasoning capabilities. This fine-grained interpretation addresses a fundamental question of compression: which weights are the most important for reasoning? Overall, we find dynamically quantized 2.51-bit R1 reaches close-to-R1 performance. With empirical verification, we present three main findings that generalize across both Llama and Qwen: (1) Weight count has a greater impact on LRMs' knowledge memorization than reasoning, highlighting the risks of pruning and distillation; (2) The MLP up projection in the final layer of distilled LRMs is one of the most important components, offering a new perspective on locating critical weights - a fundamental problem in model compression; and (3) Current quantization methods overly compress the final-layer modules and MLP gate projections, so protecting just 2% of all weights that are excessively compressed can raise average accuracy by 6.57%, greatly surpassing the state-of-the-art.

Spatio-temporal reasoning is a remarkable capability of Vision Language Models (VLMs), but the underlying mechanisms of such abilities remain largely opaque. We postulate that visual/geometrical and textual representations of spatial structure must be combined at some point in VLM computations. We search for such confluence, and ask whether the identified representation can causally explain aspects of input-output model behavior through a linear model. We show empirically that VLMs encode object locations by linearly binding \textit{spatial IDs to textual activations, then perform reasoning via language tokens. Through rigorous causal interventions we demonstrate that these IDs, which are ubiquitous across the model, can systematically mediate model beliefs at intermediate VLM layers. Additionally, we find that spatial IDs serve as a diagnostic tool for identifying limitations and bottlenecks in existing VLMs. We extend our analysis to video VLMs and identify an analogous linear temporal ID mechanism. By characterizing our proposed spatiotemporal ID mechanism, we elucidate a previously underexplored internal reasoning process in VLMs, toward improved interpretability and the principled design of more aligned and capable models.

Although Large Reasoning Models (LRMs) have progressed in solving complex problems, their chain-of-thought (CoT) reasoning often contains harmful content that can persist even when the final responses appear safe. We show that this issue still remains in existing methods which overlook the unique significance of safe reasoning, undermining their trustworthiness and posing potential risks in applications if unsafe reasoning is accessible for and exploited by malicious users. We therefore shift our focus to aligning the safety of reasoning itself in this paper and explore process supervision as the solution. However, simply rewarding safe reasoning proves inadequate due to low rollout diversity and limited training signals. To tackle this challenge, we first delve into the characteristics of safe reasoning and uncover several critical insights that 1) safe reasoning is often consolidated by a few critical steps of _safety triggers_; 2) _compliance cues_ strongly correlate with unsafe continuations; and 3) corrective interventions reliably steer unsafe trajectories towards safer traces. Motivated by these, we propose **Intervened Preference Optimization (IPO)**, an alignment method that enforces safe reasoning by substituting compliance steps with safety triggers and constructing pairs for preference learning with strong signals. Experiments on jailbreak and adversarial safety benchmarks demonstrate that IPO remarkably improves overall safety regarding both reasoning and responses, outperforming SFT-based and RL-based baselines with a relative reduction of over 30\% in harmfulness, while preserving excellent performance across diverse reasoning tasks. The results highlight the importance of explicit alignment for reasoning and provide a practical path to safer LRMs.

Large Reasoning Models (LRMs) have achieved impressive performance on challenging tasks, yet their deep reasoning often incurs substantial computational costs. To achieve efficient reasoning, existing reinforcement learning methods still struggle to construct short reasoning path during the rollout stage, limiting effective learning. Inspired by Evidence Accumulation Models, we find that LRMs have accumulated sufficient information early in reasoning, making further reasoning steps redundant. Based on this insight, we propose Just-Enough Thinking (JET), which trains models to proactively terminate unnecessary reasoning. JET performs trajectory truncation during rollout to expose the model to short, distributionally consistent reasoning paths. Besides, it uses a quality-controlled length reward to better encourage concise reasoning while maintaining correctness. Extensive experiments demonstrate that JET significantly improves reasoning efficiency without sacrificing accuracy. In particular, JET delivers a 4.6% accuracy improvement while reducing the output length by 46.3% on the Olympiad benchmark using DeepSeek-R1-Distill-Qwen-1.5B. Our code is available in the GitHub.

While large reasoning models have shown remarkable ability to generate long chains-of-thought (CoTs) in English, we still lack understanding of how these long-form reasoning abilities transfer to the vast majority of the world’s languages. In this work, we systematically investigate four key stages of model development–scaling, pretraining, post-training, and inference–to understand how long CoT capabilities extend beyond English. We compare two reasoning settings across nine non-English target languages: En-CoT, where models process target-language inputs, but reason in English; and Target-CoT, where models both process inputs and generate long CoTs in the target language. We find that scaling reasoning model size improves multilingual task performance in En-CoT, but Target-CoT performance lags behind. This gap widens for tasks requiring long, multi-step CoTs such as mathematical reasoning. Shifting to pretraining, we find that adding a specialized reasoning stage enhances En-CoT performance but degrades Target-CoT, whereas broad multilingual pretraining improves both modes simultaneously. Given the scarcity of high-quality reasoning traces in languages other than English, we explore synthetic data curation approaches for post-training. We demonstrate that fine-tuning on reasoning traces automatically translated from gold English traces outperforms fine-tuning on target-language traces distilled from large reasoning models. Finally, we report disparities in inference efficiency between languages and uncover language-specific failure modes in CoTs. We release models, datasets, and code to foster further research.

Large Language Models (LLMs) excel at problem solving by generating chain of thoughts in natural language, but such verbal thinking is computationally costly and prone to overthinking. Recent work instead proposes a latent thinking architecture Huginn-3.5B, which represents intermediate reasoning steps as sequence of latent representations. However, latent thoughts lack interpretability and are difficult to supervise, raising concerns about the correctness and reliability of its latent thinking processes. In this paper, we provide a systematic study of how Huginn-3.5B thinks in the latent space and how external supervision signals can improve its latent thinking processes. We show that latent thoughts leading to correct versus incorrect answers exhibit highly distinguishable patterns, and that a latent classifier can reliably predict answer correctness directly from latent thoughts. Leveraging these insights, we propose Latent Thinking Optimization (LTO), a probabilistic algorithm that employs the latent classifier as a Latent Reward Model (LRM) to optimize the latent thinking processes. Extensive experiments across diverse reasoning tasks demonstrate that LRM is highly effective in detecting incorrect latent thinking patterns, and LTO can significantly improve the latent thinking processes. Furthermore, we show that LRM can generalize across diverse domains, and LTO can be seamlessly applied to general LLMs to improve their thinking processes. In contrast to verbal thinking, our method demonstrates that reward modeling and scaling test-time thinking with supervision can be performed directly in the latent space, highlighting its potential as a general, efficient, and domain-agnostic approach to improving the thinking processes of LLMs.

The remarkable success of multimodal large language models (MLLMs) has driven advances in multimodal embeddings, yet existing models remain inherently discriminative, limiting their ability to benefit from reasoning-driven generation paradigm. In this work, we pioneer the exploration of generative embeddings, unifying embedding tasks within a generative paradigm. We propose UME-R1, a universal multimodal embedding framework consisting of a two-stage training strategy: a cold-start supervised fine-tuning equips the model with reasoning capabilities and enables it to generate both discriminative and generative embeddings; a subsequent reinforcement learning enhances reasoning and further optimizes generative embedding quality. This pioneering work reveals four key insights: 1) generative embeddings unlock substantial performance gains over conventional discriminative embeddings by leveraging the powerful generative reasoning capabilities of MLLMs; 2) discriminative and generative embeddings are complementary, whose combined oracle performance far exceeding that of either alone; 3) RL can effectively enhance generative embeddings, establishing a scalable optimization paradigm.; 4) repeated sampling at inference boosts downstream task coverage (pass@k), highlighting the inference-time scalability potential of generative embeddings. Evaluated on the MMEB-V2 benchmark across 78 tasks spanning video, image, and visual documents, UME-R1 significantly outperforms conventional discriminative embedding models and offers a foundation for more interpretable, reasoning-driven generative multimodal embeddings.

Recent advances in large language models (LLMs) test-time computing have introduced the capability to perform intermediate chain-of-thought (CoT) reasoning (thinking) before generating answers. While increasing the thinking budget yields smooth performance improvements at inference time, the relationship between LLM capability, query complexity, and optimal budget allocation remains poorly understood for achieving compute-optimal inference. To address this challenge, we utilize $\textit{self-consistency}$, the agreement among multiple reasoning paths, as a proxy for thinking necessity. We first identify that lower self-consistency indicates when queries require extended thinking to reach correct answers. Building on this insight, we introduce $\texttt{Sonata}$ (Self-Consistency-Guided Adapter for Thinking Allocation), a lightweight approach that adaptively allocates thinking budgets to optimize the performance-efficiency tradeoff. $\texttt{Sonata}$ includes an adapter trained offline on a calibration dataset to predict self-consistency directly from the last layer hidden representations during the query prefilling stage. This prediction then guides on-the-fly budget allocation before thinking. The adapter is general, transferable across diverse tasks once trained, and introduces $<1$$\textperthousand$ computational overhead during inference. Notably, Sonata is compatible with existing CoT compression methods, enabling further efficiency gains when managing thinking budgets across queries. Extensive experiments on multiple models (Qwen3-8B, Qwen3-32B, GPT-OSS-120B, Qwen3-235B-A22B) and benchmarks~(AIME25, GSM8K, MATH500, GPQA, LiveCodeBench) demonstrate that $\texttt{Sonata}$ achieves $20\\%$ to $60\\%$ reduction in thinking tokens while maintaining the same accuracy, or up to $2\\%$ improvement in accuracy with the same token cost.

Recent advances in multimodal large reasoning models (MLRMs) have substantially improved their ability to solve complex textual and visual tasks. However, these models tend to *overthink* on simple problems, producing unnecessarily lengthy reasoning traces, while *under-exploring* on challenging ones, leading to missed solutions. To address this imbalance, we propose **ARES**, a unified open-source framework for *adaptive reasoning* that dynamically allocates exploration effort based on task difficulty. Our approach is motivated by two key empirical findings: (i) while single-token entropy is noisy, *high window-entropy (HWE) tokens* (token-level entropies averaged under a sliding window) can reliably capture reasoning-critical moments; and (ii) reducing HWE usage benefits easy problems, while increasing it is essential for solving hard ones. Building on these insights, ARES introduces a two-stage training pipeline. In the *Adaptive Cold-Start* stage, we curate multimodal and textual data paired with reasoning traces of length proportional to problem difficulty, equipping the model with initial difficulty awareness. In the second stage, we develop *Adaptive Entropy Policy Optimization (AEPO)*, which uses HWE tokens as exploration triggers to decide *when to explore*, and a hierarchical entropy reward with dynamic KL control to decide *how much to explore*. Extensive experiments demonstrate that ARES achieves state-of-the-art performance and reasoning efficiency across diverse mathematical, logical, and multimodal benchmarks, while closing the gap to leading commercial systems under significantly lower inference costs. The anonymous code repository is available at https://anonymous.4open.science/r/ARES-60728M.

Inductive Knowledge Graph Reasoning (KGR) aims to discover facts in open-domain KGs containing unknown entities and relations, which poses a challenge for KGR models in comprehending uncertain KG components. Existing studies have proposed Knowledge Graph Foundation Models (KGFMs) that learn structural invariances across KGs to handle this uncertainty. Recently, Large Language Models (LLMs) have demonstrated strong capabilities for open-domain knowledge reasoning. As a result, the latest research has focused on LLM-based KGFMs that integrate LLM knowledge with KG context for inductive KGR. However, the intrinsic knowledge of LLMs may be overshadowed by sparse KG context, leading to LLM knowledge distortion, which can cause irreversible damage to model reasoning. Moreover, existing LLM-based KGR methods still struggle to fully constrain generative hallucinations in LLMs, severely limiting the credibility of reasoning results. To address these limitations, we propose a Knowledge Reasoning Language Model (KRLM) that achieves unified coordination between LLM knowledge and KG context throughout the KGR process. Specifically, we design a Knowledge Reasoning Language (KRL) instruction format and a KRL tokenizer to align LLM knowledge with KG representations. Then, we propose a KRL attention layer that coordinates intrinsic LLM knowledge with additional KG context through a dynamic knowledge memory mechanism. Finally, a structure-aware next-entity predictor is proposed, which strictly constrains the reasoning results within a trustworthy knowledge domain. Extensive experimental results on 25 real-world inductive KGR datasets demonstrate the significant superiority of the proposed KRLM in both zero-shot reasoning and fine-tuning scenarios.

Large language models (LLMs), despite possessing latent safety understanding from their vast pretraining data, remain vulnerable to generating harmful content and exhibit issues such as over-refusal and utility degradation after safety alignment. Current safety alignment methods often result in superficial refusal shortcuts or rely on intensive supervision for reasoning-based approaches, failing to fully leverage the model's intrinsic safety self-awareness. We propose \textbf{AlphaAlign}, a simple yet effective pure reinforcement learning (RL) framework with verifiable safety reward designed to incentivize this latent safety awareness through proactive safety reasoning. AlphaAlign employs a dual-reward system: a verifiable safety reward encourages correctly formatted and explicitly justified refusals for harmful queries while penalizing over-refusals, and a normalized helpfulness reward guides high-quality responses to benign inputs. This allows the model to develop proactive safety reasoning capabilities without depending on supervised safety-specific reasoning data. AlphaAlign demonstrates three key advantages: (1) Simplicity and efficiency, requiring only binary prompt safety labels and minimal RL steps for substantial improvements. (2) Breaking the safety-utility trade-off, by enhancing refusal of harmful content and reducing over-refusals, while simultaneously maintaining or even improving general task performance and robustness to unseen jailbreaks. (3) Deep alignment, fostering proactive safety reasoning that generates explicit safety rationales rather than relying on shallow refusal patterns. Our codes are available at \url{https://anonymous.4open.science/r/AlphaAlign-D5B0}

Reasoning models often exhibit overthinking, characterized by redundant reasoning steps. We identify \emph{internal bias} elicited by the input question as a key trigger of such behavior. Upon encountering a problem, the model immediately forms a preliminary guess about the answer, which we term an internal bias since it may not be explicitly generated, and it arises without systematic reasoning. When this guess conflicts with its subsequent reasoning, the model tends to engage in excessive reflection, resulting in wasted computation. We validate the association between internal bias and overthinking across multiple models and diverse reasoning tasks. To demonstrate the causal relationship more rigorously, we conduct two counterfactual interventions, showing that removing the input question after the model reduces the redundant reasoning across various complex reasoning tasks, and manually injecting bias affects overthinking accordingly. Further interpretability experiments suggest that excessive attention to the input question serves as a key mechanism through which internal bias influences subsequent reasoning trajectories. Finally, we evaluated several methods aimed at mitigating overthinking, yet the influence of internal bias persisted under all conditions.