ICML 2026 论文列表

Current approaches to enhance Large Language Model (LLM) reasoning, such as Chain-of-Thought and "Wait" prompts, primarily encourage models to think more, yet often fail to guide them toward Truth. While Representation Editing (RepE) offers a intrinsic control, its application to dynamic reasoning trajectories remains underexplored. In this work, we bridge this gap by investigating the geometry of truth within unfolding reasoning chains. We uncover three critical insights: (1) Truth is encoded at the sentence level and is entangled with latent reasoning patterns; (2) Effective intervention follows an Uncertainty Principle and a Decay Effect, requiring localization to early, high-entropy forks; (3) Naive steering vectors suffer from noise, risking collateral damage to correct trajectories. Based on these findings, we propose DynaSteer, a dynamic RepE framework. DynaSteer employs pattern clustering to disentangle reasoning manifolds and utilizes Fisher-LDA to project purified truth. By dynamically monitoring lookahead entropy, it selectively steers and rolls back trajectories only when necessary. Comprehensive experimental results on several MATH benchmark verify the effectiveness of DynaSteer, and experiments on out-of-domain coding tasks further confirm its generalization ability. Our code is publicly available at https://github.com/tianlwang/DynaSteer.

As a multimodal extension of Chain-of-Thought (CoT), Thinking with Images (TWI) has emerged as a promising avenue to enhance the reasoning capability of Multi-modal Large Language Models (MLLMs), which generates interleaved CoT by incorporating visual cues into the textual reasoning process. However, the success of existing TWI methods heavily relies on the assumption that interleaved CoTs are faultless, which is easily violated due to the complexity of multimodal understanding. In this paper, we reveal and study a highly-practical yet under-explored problem in TWI, termed Noisy Thinking (NT). Specifically, NT refers to the imperfect visual cues mining and answer reasoning process. As the saying goes, ``One mistake leads to another'', erroneous interleaved CoT would cause error accumulation, thus significantly degrading the performance. To solve NT, we propose a novel method dubbed Reliable Thinking with Images (RTWI). In brief, RTWI estimates the reliability of visual cues and textual CoT in a unified text-centric manner and then employs robust filtering and voting modules to prevent NT from contaminating final answer. Extensive experiments on seven benchmarks verify the effectiveness of RTWI against NT.

Autoregressive Large Language Models (LLMs) often fail in complex reasoning because early-stage errors remain uncorrectable in subsequent steps—a limitation fundamentally rooted in the inherent irreversibility of the Transformer architecture. In this paper, we propose HEdit, a lightweight reasoning enhancement paradigm that equips models with a "hindsight-like" capability for dynamic error correction during generation. Our core insight involves deconstructing reasoning failures into two pivotal stages: latent representational biases emerging at logical anchors, and the subsequent eruption of explicit cognitive dissonance at trigger points. Based on these observations, the HEdit framework detects internal inconsistency signals at trigger points in real-time, actively backtracks to critical anchors, and utilizes a lightweight trainable editor to precisely refine their Key-Value (KV) caches. This mechanism effectively breaks the unidirectional constraints of autoregressive inference. Empirical results demonstrate that HEdit significantly enhances the performance of various models on mathematical reasoning tasks—with average accuracy improvements ranging from 2.2\% to 10.8\%—while maintaining extremely low overhead (add parameters $<0.5\%$). HEdit provides a dynamic, pluggable and lightweight solution, making it particularly beneficial for users in low-resource environments.

Chain-of-Thought (CoT) prompting enables multi-step reasoning in large language models, yet long-horizon generation remains brittle under distribution shift and context interference: irrelevant cues persist, small deviations compound into inference drift, and late-stage corrections can destabilize the trajectory. We recast autoregressive decoding as a perturbed long-horizon dynamical system and introduce an *inference-time stabilization operator* that targets *trajectory-level* reliability rather than token-level fluency. Specifically, we propose *ODE-guided language models*, which augment a base Transformer with a persistent continuous-time *thought state* whose dynamics are explicitly designed to be dissipative, enabling stable evidence accumulation with controlled forgetting. Instantiating this framework, *Thinking in Flow* (TiF) equips the model with a lightweight Neural ODE controller and injects its output through post-norm residual updates to achieve numerically stable, low-intrusion steering. A demand--supply (uncertainty--capacity) gate determines *when* intervention is warranted, while a direction gate determines *how* to steer in representation space, yielding selective, do-no-harm corrections instead of persistent bias. We establish well-posedness, dissipativity, and incremental stability of the controlled thought dynamics, implying bounded interventions over arbitrarily long contexts, and empirically demonstrate improved robustness to distractions and semantic perturbations, while matching or improving accuracy on mathematical reasoning benchmarks across both the Llama and Qwen model families; we further observe gains on non-mathematical BBH reasoning tasks when training TiF on Llama.

Example-based guidance is widely used to improve mathematical reasoning at inference time, yet its effectiveness is highly unstable across problems and models—even when the guidance is correct and problem-relevant. We show that this instability arises from a previously underexplored gap between *strategy usage*—whether a reasoning strategy appears in successful solutions—and *strategy executability*—whether the strategy remains effective when instantiated as guidance for a target model. Through a controlled analysis of paired human-written and model-generated solutions, we identify a systematic dissociation between usage and executability: human- and model-derived strategies differ in structured, domain-dependent ways, leading to complementary strengths and consistent source-dependent reversals under guidance. Building on this diagnosis, we propose *Selective Strategy Retrieval* (SSR), a test-time framework that explicitly models executability by selectively retrieving and combining strategies using empirical, multi-route, source-aware signals. Across multiple mathematical reasoning benchmarks, SSR yields reliable and consistent improvements over direct solving, in-context learning, and single-source guidance, improving accuracy by up to $+13$ points on AIME25 and $+5$ points on Apex for compact reasoning models. Code and benchmark are publicly available at: https://github.com/lwd17/strategy-execute-pipeline.

Large Language Models (LLMs) employing Chain-of-Thought reasoning achieve strong performance but suffer from excessive token consumption that inflates inference costs. Existing efficiency methods—such as explicit length penalties, difficulty estimators, or multi-stage curricula—either degrade reasoning quality or require complex training pipelines. We introduce **Batched Contextual Reinforcement (BCR)**, a minimalist, single-stage training paradigm that unlocks efficient reasoning through a simple structural modification: training the model to solve N problems simultaneously within a shared context window, rewarded purely by per-instance accuracy. This formulation creates an implicit token budget that yields several key findings: (1) We identify a novel _task-scaling law_: as the number of concurrent problems N increases at inference time, per-problem token usage decreases monotonically---a phenomenon that arises purely at inference, holds for models both before and after training, and is unrelated to accuracy or the training procedure. BCR makes this regime practical by degrading accuracy far more gracefully than baselines as N grows, establishing N as a controllable throughput dimension. (2) BCR challenges the traditional accuracy-efficiency trade-off by demonstrating a "free lunch" phenomenon at standard single-problem (N=1) inference. Across both 1.5B and 4B model families, BCR reduces token usage by 15.8\% to 62.6\% while consistently maintaining or improving accuracy across five major mathematical benchmarks (e.g., +13.3\% on AIME25 for the 4B model). (3) Qualitative analyses reveal emergent self-regulated efficiency, where models autonomously eliminate redundant metacognitive loops without explicit length supervision. (4) Crucially, we empirically demonstrate that implicit budget constraints successfully circumvent the adversarial gradients and catastrophic optimization collapse inherent to explicit length penalties, offering a highly stable, constraint-based alternative for length control. These results establish BCR as a highly practical framework, demonstrating how simple structural training incentives can unlock latent high-density reasoning modes in LLMs.

Incorporating code into training corpora has become a widely acknowledged practice in the development of modern foundation language models (LMs). Compared with a general Internet corpus, code offers high-quality, well-structured signals that substantially augment the coding proficiency of models. Beyond programming skills, prior research has suggested that code data may also contribute to non-coding capabilities. Nevertheless, through a series of rigorous controlled experiments, we demonstrate that the influence of code on other domains, particularly reasoning, remains limited. Our principal findings are as follows: (1) Code corpus yields substantial gains in programming-related abilities but only competed with knowledge-intensive tasks. (2) We identify a core subset that functions as cognitive scaffolding for mathematical reasoning, especially for complex problem-solving scenarios. (3) Formal reasoning provides more pronounced improvements in challenging mathematical reasoning tasks, while natural language–based reasoning proves more effective for simpler reasoning problems. Finally, by probing the internal mechanisms of LMs, we reveal how training data modulates routing patterns, thereby shaping emergent model behavior. As a central driver of model capability, our findings disentangle domain-specific data into finer-grained, cross-domain ability dimensions and underscore promising directions for future data optimization.

Despite their strong performance on reasoning tasks, Large reasoning models (LRMs) often suffer from overthinking, producing unnecessarily long outputs and incurring high end-to-end latency, a significant limitation to their real-world deployment. To address overthinking, early-exit mechanisms have been proposed to terminate reasoning before typical completion, showing that this approach can effectively shorten generation length with minimal impact on accuracy. However, their reliance on probing mechanisms introduces a detection overhead that limits their end-to-end latency gains and compromises their generalizability across diverse problems. Inspired by the use of hidden states in speculative decoding, we propose **SpecExit**, a novel framework that predicts both future tokens and an early-exit signal directly from a lightweight draft model without probing overhead. Our method offers significant improvements, achieving up to 66\% generation length reduction and 2.5$\times$ end-to-end speedup compared with the speculative decoding baseline, without compromising accuracy. Our method leverages the inherent signals from hidden states to provide effective early-exit signals, suggesting broader use of hidden states for efficient reasoning. Our code is available at: https://anonymous.4open.science/r/SpecExit-B802.

Flow-based generative models provide strong unconditional priors for inverse problems, but guiding their dynamics for conditional generation remains challenging. Recent work casts training-free conditional generation in flow models as an optimal control problem; however, solving the resulting trajectory optimisation is computationally and memory intensive, requiring differentiation through the flow dynamics or adjoint solves. We propose MPC-Flow, a model predictive control framework that formulates inverse problem solving with flow-based generative models as a sequence of control sub-problems, enabling practical optimal control-based guidance at inference time. We provide theoretical analysis linking MPC-Flow to the underlying optimal control objective and show how different algorithmic choices yield a spectrum of guidance algorithms, including regimes that avoid backpropagation through the generative model trajectory. We evaluate MPC-Flow on benchmark image restoration tasks, spanning linear and non-linear settings such as in-painting, deblurring, and super-resolution, and demonstrate strong performance and scalability to massive state-of-the-art architectures via training-free guidance of FLUX.2 (32B) in a quantised setting on consumer hardware.

Relational reasoning is the ability to infer relations that jointly bind multiple entities, attributes, or variables. While this capability is essential for scientific reasoning, most existing evaluations of relational reasoning in large language models focus on structured inputs such as tables, graphs, or synthetic relational tasks, and do not isolate the sources of difficulty that arise from higher-arity relational binding. We study this problem through the lens of *Relational Complexity (RC)*, defined as the minimum number of independent entities or operands that must be simultaneously bound to apply a relation. RC provides a principled way to vary reasoning difficulty independently of confounders such as input size, vocabulary, and representational choices. Building on RC, we introduce REL, a generative benchmark framework spanning algebra, chemistry, and biology that varies RC within each domain. Evaluating frontier LLMs, we observe a consistent and monotonic degradation in performance as RC increases, even when the total number of entities is held fixed. This failure mode persists under increased test-time compute and with in-context learning, suggesting a limitation tied to the arity of the required relational binding rather than insufficient inference steps or exposure to examples. Our results identify a well-defined regime of higher-arity reasoning in which current models struggle and motivate revisiting reasoning benchmarks through the lens of relational complexity.

Supervised fine-tuning (SFT) on a small, high-quality set of long reasoning traces is an effective approach for eliciting strong reasoning capabilities in Large Language Models (LLMs). However, existing methods for curating high-quality SFT data rely heavily on strong reasoning models to filter examples based on diversity and difficulty, making the curation process costly while often yielding suboptimal data quality. In this work, we show that diverse and challenging reasoning examples can be identified using only the initial reasoning tokens. Specifically, we demonstrate that difficult problems can be reliably detected based on the loss of the first 100 reasoning tokens evaluated at a randomly perturbed checkpoint of the pretrained model. We further show that examples exhibiting similar loss patterns over their first 1k reasoning tokens across a small number of perturbed checkpoints extrapolating along the fine-tuning trajectory provably induce similar gradients. We validate our approach through extensive experiments on fine-tuning Qwen2.5-7B and Llama3.1-8B models on the M23K medical reasoning and OpenThoughts-Math datasets. Our method outperforms existing baselines by up to 1.7% while being 91% more token efficient.

While the ecosystem of Lean and Mathlib has enjoyed celebrated success in formal mathematical reasoning with the help of large language models (LLMs), the absence of many folklore lemmas in Mathlib remains a persistent barrier that limits Lean's usability as an everyday tool for mathematicians like LaTeX or Maple. To address this, we introduce MathlibLemma, a modular LLM-based pipeline for automated folklore-lemma mining: the discovery, formalization, and proving of reusable intermediate facts that mathematicians often take for granted but that are not always present in formal libraries. At its core, MathlibLemma proactively mines the missing connective tissue of mathematics. The pipeline produces a verified library of folklore-style lemmas, including 1,506 Lean-checked proofs that pass a proof-bypass screen; a small curated pilot subset has also been merged into Mathlib, providing external evidence that selected outputs can meet expert library standards. Leveraging this pipeline, we further construct the MathlibLemma benchmark, a suite of 4,028 non-trivial type-checked Lean statements spanning a broad range of mathematical domains. By transforming the role of LLMs from passive consumers to active contributors, this work takes a step toward AI-assisted expansion of formal mathematical libraries.