ICML 2026 Papers

Inference time optimization techniques, such as repeated sampling, have significantly advanced the reasoning capabilities of Large Language Models (LLMs). However, the critical role of model uncertainty remains largely underexplored in these optimization strategies. In this paper, we investigate the dynamics of confidence along reasoning trajectories and for first time reveal a surprising and unique pattern: correct answer traces tend to exhibit confidence improvement over time (positive confidence gain), while incorrect traces show attenuated or declining confidence as reasoning proceeds. Based on this observation, we propose Confidence Dynamic Gain (CDG) based voting, which incorporates how the confidence trajectory of the response evolves along the reasoning chain. Experiments across four open-source architectures (DeepSeek-R1, gpt-oss, Gemma-3, Qwen-QwQ) on the AIME24/25, HMMT25, and BRUMO25 benchmarks demonstrate that CDG yields a significant performance boost over baselines. These results demonstrate that our method provides a robust discriminative signal for improving answer selection in LLM reasoning. We also provide theoretical insights for this phenomenon. Code will be released at https://github.com/Accenture/CDG.git.

Prompt learning for vision-language models (VLMs) often suffers from performance degradation when adapting to downstream tasks with noisy labels. Existing methods that rely on filtering or reconstructing supervision can propagate errors, leading to sharp performance drops. We observe that pre-trained embeddings are resilient to label noise, offering stable references despite limited adaptation. Based on this insight, we propose Evidence-Prompt, a framework built on the evidence prior that enhances prompt learning by integrating stable pre-trained knowledge. We treat prompt learning as a Bayesian reasoning task, where credibility is derived from both supervision-agnostic and supervision-conditioned evidence. This framework effectively combines these sources to infer robust training targets under noisy conditions, enabling stable learning even with high noise levels. Extensive experiments on eight benchmarks with both synthetic and real-world noisy labels demonstrate that our method flattens the accuracy–noise curve and consistently outperforms SOTA methods, with notable gains on OxfordPets dataset at a 75\% noise rate (+36.6\% under Asym and +14.4\% under Sym). Additionally, transferability experiments reveal that incorporating our evidence prior into other SOTA methods results in accuracy improvements ranging from 2.6\% to 15.66\%.

Diffusion models have achieved state-of-the-art performance in generating images, audio, and video, but their adaptation to text remains challenging due to its discrete nature. Prior approaches either apply Gaussian diffusion in continuous latent spaces, which inherits semantic structure but struggles with token decoding, or operate in categorical simplex space, which respect discreteness but disregard semantic relation between tokens. In this paper, we propose Smoothing Diffusion on Token Embeddings (Smoothie), a novel diffusion method that combines the strengths of both approaches by progressively smoothing token embeddings based on semantic similarity. This technique enables gradual information removal while maintaining a natural decoding process. Experimental results on several sequence-to-sequence and unconditional generation tasks demonstrate that Smoothie outperforms existing diffusion-based models in generation quality. Furthermore, ablation studies show that our proposed diffusion space yields better performance than both the standard embedding space and the categorical simplex.

This work investigates the resilience of contemporary large language models (LLMs) against frequent character-level perturbations. We examine three types of character-level perturbations including introducing numerous typos within words, shuffling the characters in each word, and inserting a large number of invisible characters into the text. Surprisingly, even under severe perturbation, such as shuffling nearly all words character-wise to produce text that is almost unreadable to humans, or inserting invisible characters which are several times more than the visible ones as noise, many LLMs still maintain notable performance. We explore the underlying causes of this robustness and find that LLMs exhibit remarkable resilience to chaotic segmentation and fragmented tokenization. Furthermore, we examine the mechanisms by which LLMs remove perturbations to correctly comprehend text, including both implicit and explicit mechanisms for character-level perturbation. We hope that our findings on the low-level robustness of LLMs will unveil their inherent architectural strengths, reveal the potential risks of their misuse, and inform the reliable deployment of LLMs across diverse application scenarios.

Multi-agent LLM systems can improve reasoning and tool use, yet recent evidence shows their gains are often unstable and sensitive to interaction design. A promising direction is to train collaboration, but team post-training introduces a moving-target effect: when agents interact through a shared context, updating one agent shifts the context distribution faced by the others, which can regress coordination under naive sequential updates. We propose TeamTR, a trust-region framework for fine-tuning heterogeneous LLM teams that explicitly controls this occupancy shift. TeamTR evaluates each agent update on rollouts from the intermediate team induced by partially applied updates, and enforces per-agent trust regions via a token-decomposed reverse KL that is directly monitorable from those rollouts. This yields population-level per-update and per-stage improvement lower bounds whose functional form applies to any realized update order, and motivates a practical certificate proxy computed from logged surrogates and KL terms. We instantiate TeamTR for router-based text handoff with sequence-level returns and bounded group-normalized advantages, and show empirically that it mitigates coordination regressions, improves training stability across heterogeneous teams, and supports modular component replacement via a trust-region alignment step.

Large Reasoning Models (LRMs) increasingly rely on reasoning traces with complex internal structures. However, existing work lacks a unified answer to three fundamental questions: (1) what defines high-quality reasoning, (2) how to reliably evaluate long, implicitly structured reasoning traces, and (3) how to use such evaluation signals for reasoning optimization. To address these challenges, we provide a unified perspective. (1) We introduce the ME$^2$ principle to characterize reasoning quality along macro- and micro-level concerning efficiency and effectiveness. (2) Built on this principle, we model reasoning traces as directed acyclic graphs (DAGs) and develop a DAG-based pairwise evaluation method, capturing complex reasoning structures. (3) Based on this method, we construct the TRM-Preference dataset and train a Thinking Reward Model (TRM) to evaluate reasoning quality at scale. Experiments show that thinking rewards serve as an effective optimization signal. At test time, selecting better reasoning leads to better outcomes (up to 19.3\% gain), and during RL training, thinking rewards enhance reasoning and performance (up to 3.9\% gain) across diverse tasks. Code and data are available at https://github.com/Simplified-Reasoning/TRM.

Recent advances in Large Language Models (LLMs) have underscored the potential of Reinforcement Learning (RL) to facilitate the emergence of reasoning capabilities. Despite the encouraging results, a fundamental dilemma persists as RL improvement relies on learning from high-quality samples, yet the exploration for such samples remains bounded by the inherent limitations of LLMs. This, in effect, creates an undesirable cycle in which what cannot be explored cannot be learned. In this work, we propose Rubric-Scaffolded Reinforcement Learning (RuscaRL), a novel instructional scaffolding framework designed to break the exploration bottleneck for open-ended reasoning. Specifically, RuscaRL introduces checklist-style rubrics as (1) explicit scaffolding for exploration during rollout generation, where different rubrics are provided as external guidance within task instructions to steer diverse high-quality responses. This guidance is gradually decayed over time, encouraging the model to internalize the underlying reasoning patterns; (2) verifiable rewards for exploitation during model training, where we can obtain robust LLM-as-a-Judge scores using rubrics as references, enabling effective RL on open-ended reasoning tasks. Extensive experiments demonstrate the superiority of the proposed RuscaRL across various benchmarks, effectively expanding reasoning boundaries under the Best-of-N evaluation.

To schedule LLM inference, the \textit{shortest job first} (SJF) principle is favorable by prioritizing requests with short output lengths to avoid head-of-line (HOL) blocking. Existing methods usually predict a single output length for each request to facilitate scheduling. We argue that such a \textit{point estimate} does not match the \textit{stochastic} decoding process of LLM inference, where output length is \textit{uncertain} by nature and determined by when the end-of-sequence (EOS) token is sampled. Hence, the output length of each request should be fitted with a distribution rather than a single value. With an in-depth analysis of empirical data and the stochastic decoding process, we observe that output length follows a heavy-tailed distribution and can be fitted with the log-t distribution. On this basis, we propose a simple metric called Tail Inflated Expectation (TIE) to replace the output length in SJF scheduling, which adjusts the expectation of a log-t distribution with its tail probabilities to account for the risk that a request generates long outputs. To evaluate our TIE scheduler, we compare it with three strong baselines, and the results show that TIE reduces the per-token latency by $2.31\times$ for online inference and improves throughput by $1.42\times$ for offline data generation.

While large language models (LLMs) perform strongly on diverse tasks, their trustworthiness is limited by erratic behavior that is unfaithful to their internal knowledge. In particular, LLMs often fail on multiple-choice questions (MCQs) even if they encode correct answers in their hidden representations, revealing a misalignment between internal knowledge and output behavior. We investigate and mitigate this *knowledge-prediction gap* on MCQs through a three-step analysis of hidden representations. First, we quantify the prevalence and magnitude of the gap across models and datasets. Second, we provide a geometric interpretation by identifying distinct *knowledge* and *prediction* subspaces in the residual stream. Third, we introduce **KAPPA**, a lightweight inference-time intervention that aligns the two subspaces within the residual stream to reduce the knowledge-prediction gap. Our results provide a geometric and interpretable explanation of the knowledge-prediction gap in LLMs. Furthermore, KAPPA effectively reduces the gap across diverse MCQ benchmarks and models, and generalizes to free-form settings.

Supervised fine-tuning with expert demonstrations often produces models that imitate outputs without internalizing the reasoning processes needed for robust generalization. While critique-based approaches show promise, training models to generate critiques directly, such as Critique Fine-Tuning (CFT), can lead to output-format drift and degradation of general capabilities. We propose $\textbf{C}$ritique-$\textbf{G}$uided $\textbf{D}$istillation (CGD), a training framework that decouples critique consumption from critique generation. During fine-tuning, the student is trained to refine flawed responses conditioned on teacher critiques. CGD treats critiques as a $\textit{training-time-only}$ supervision signal, encouraging internalization of error-aware reasoning: critiques guide learning but are absent at inference. Across five model families, CGD consistently outperforms CFT and standard distillation on mathematical reasoning benchmarks, yielding 7\% average improvements and gains of up to +15.0\% on AMC23 and +12.2\% on MATH-500. On challenging competition problems such as AIME24 and AIME25, CGD achieves substantially higher Pass@1 and stronger performance at low Pass@k, indicating improved reasoning quality per sample. Importantly, CGD preserves general instruction-following capabilities where CFT degrades significantly ($-$21.3\% on IFEval). These results position CGD as a practical and compute-efficient intermediate training paradigm for reasoning-centric tasks without introducing architectural inference-time overhead.

Large language models (LLMs) demand substantial computational and memory resources, posing challenges for efficient deployment. Two complementary approaches have emerged to address these issues: token-adaptive layer execution, which reduces floating-point operations (FLOPs) by selectively bypassing layers, and quantization, which lowers memory footprint by reducing weight precision. However, naively integrating these techniques leads to additional accuracy degradation due to reduced redundancy in token-adaptive models. We propose QTALE (Quantization-Robust Token-Adaptive Layer Execution for LLMs), a novel framework that enables seamless integration of token-adaptive execution with quantization while preserving accuracy. Conventional token-adaptive methods reduce redundancy in two ways: (1) by limiting the diversity of training paths explored during fine-tuning, and (2) by lowering the number of parameters actively involved in inference. To overcome these limitations, QTALE introduces two key components: (1) a training strategy that ensures diverse execution paths are actively explored during fine-tuning, and (2) a post-training mechanism that allows flexible adjustment of the execution ratio at inference to reintroduce redundancy when needed. Experimental results show that QTALE enables seamless integration of token-adaptive layer execution with quantization, showing no noticeable accuracy difference, with the gap to quantization-only models kept below 0.5\% on CommonsenseQA benchmarks. By combining token-adaptive execution for FLOPs reduction and quantization for memory savings, QTALE provides an effective solution for efficient LLM deployment.

The deployment of Large Language Models (LLMs) with extended context windows is increasingly constrained by the linear growth of Key-Value (KV) cache memory. Vector Quantization (VQ), particularly Residual Quantization (RQ), is a promising approach for pushing KV cache storage toward the sub-1-bit regime by progressively encoding residuals with small codebooks. However, most VQ methods still rely on standard $\ell_2$ $K$-means as the core codebook-learning primitive. We identify a subtle high-dimensional issue of this primitive: Euclidean centroid averaging can induce centroid shrinkage, which weakens the angular alignment term in the $\ell_2$ distortion and makes directional preservation harder. To address this issue, we propose Gain-Shape $K$-means (GSKM), a drop-in replacement for $K$-means that improves directional fidelity while matching, and in some regimes improving, $\ell_2$ distortion. We then build Gain-Shape Residual Quantization (GSRQ) by incorporating a weighted extension of GSKM into an RQ pipeline. On LLaMA-3-8B, GSRQ substantially improves over strong KV cache quantization baselines across bit rates. At 1-bit, it improves the average accuracy across LongBench tasks from 11.34 to 33.54, a gain of 22.20 percentage points over VQLLM.

Efficient Distillation (EDistill) compresses large language models (LLMs) by structured pruning parameters and tuning lightweight modules with high training efficiency. Although these EDistilled LLMs achieve state-of-the-art (SOTA) performance on general ability benchmarks relative to similarly sized LLMs, we identify a severe degradation in their multi-step reasoning ability, which we term reasoning collapse. We systematically analyze the geometric origins of reasoning collapse and show that the SOTA EDistill method based on width-reducing projection matrices suffers from eRank collapse, in which the effective rank (eRank) of hidden representations drops. We theoretically explain how singular values of randomly initialized projection matrices become unevenly distributed, leading to eRank collapse and thus token indistinguishability. To address this issue, we propose RED (Reasoning-preserved Efficient Distillation) for LLMs, which introduces activation-aware initialization to initialize projection matrices as channel-selection matrices, thus theoretically mitigating eRank collapse. Experiments on Llama and Qwen series demonstrate that RED substantially recovers reasoning while maintaining high training efficiency and SOTA general ability.

In-context learning (ICL) excels at new tasks from minimal examples, yet we still lack a mechanistic explanation of how few-shot prompts shape a model’s function vector (FV)--a causal activation direction that drives task behavior on the ICL query. Across tasks and models, an $n$-shot FV is well-approximated by a linear combination of example-level sub-FVs, suggesting additive and composable contributions from individual demonstrations. Beyond additivity, we show that models contextualize individual examples' representations based on prior examples to adaptively reweight which demonstrations dominate the FV: attention shifts toward examples that are more informative and less ambiguous under the context. Finally, a causal decomposition separates Query–Key routing from Value updates, finding that contextualization’s most consistent contributions to FV quality arise from Query–Key alignment--particularly in ambiguous settings--while Value-mediated effects are more heterogeneous. Together, these results unify additive superposition with context-dependent attention reweighting into a mechanistic, testable account of how few-shot prompts implement tasks.

The progressive scaling of large language models (LLMs) has consistently enhanced multimodal understanding and advanced reasoning capabilities, but has substantially increased computational and hardware execution overhead. In this paper, we present S-Quant, a novel post-method that compresses only model weights. We partition each weight tensor into fixed-size blocks and assign a single seed to each block. The seed drives a hardware-friendly Linear Feedback Shift Register (LFSR) generator that dynamically produces multiple basis matrices. Each block is then reconstructed as a linear combination of these basis matrices, with block-specific coefficients, which substantially reduces the amount of stored data, increases the data-transfer efficiency between memory and compute units, and consequently speeds up memory-bound inference for large language models. Experimental results on different LLM models ranging from 7B–70B parameters show that S-Quant attains state-of-the-art performance when weights are compressed to approximately 3-bit or 4-bit. We also design a dedicated ASIC accelerator that achieves a 4× speed-up for memory-bound LLM inference.

While Large language models (LLMs) have strong abilities, they generally rely on fine-tuning to supplement downstream task-specific knowledge. Due to the prohibitive memory overhead of full fine-tuning (FT), existing parameter-efficient fine-tuning techniques, e.g., LoRA and Adapters, update parameters only in low-rank or restricted subspaces. However, they fail to approximate FT---the performative fine-tuner---and risk performance degradation in tough tasks. Therefore, we naturally raise a *Low-cost Full Fine-tuning* question: Can we approach standard full fine-tuning in theory, yet with much lower costs in practice? Our key insight is that performing selective updates at each step can, theoretically, recover FT asymptotically, while being cost-effective and ignoring no parameter direction. This motivates a new general fine-tuning paradigm (called *Think-Touch*): we first predict potentials of parameter groups (*think*) and then update only the selected (*touch*) in one step. Theoretically, we show that under a very weak sufficient condition---divergence of the cumulative coverage of the expected gradient norm---any selection strategy can converge in the full-parameter space to a stationary point at which the FT admits no further first-order improvement. Besides, we further derive the general convergence rate for our paradigm and identify a post-hoc greedy strategy that is rate-optimal. Unfortunately, this strategy cannot be directly applied in practice due to its reliance on full and accurate gradient information. Thus, we propose a bandit-based method to online approximate this ideal strategy in the long run with a rigorous regret guarantee. Extensive experimental results on various tasks demonstrate the potential of our paradigm, including much lower space overheads against FT and better performance than LoRAs.

Large language models (LLMs) must balance diversity and creativity against logical coherence in open-ended generation. Existing truncation-based samplers are effective but largely heuristic, relying mainly on probability mass and entropy while ignoring semantic geometry of the token space. We present Top-$W$, a geometry-aware truncation rule that uses Wasserstein distance—defined over token-embedding geometry—to keep the cropped distribution close to the original, while explicitly balancing retained probability mass against the entropy of the kept set. Our theory yields a simple closed-form structure for the fixed-potential subset update: depending on the mass–entropy trade-off, the optimal crop either collapses to a single token or takes the form of a one-dimensional prefix that can be found efficiently with a linear scan. We implement Top-$W$ using efficient geometry-based potentials (nearest-set or $k$-NN) and pair it with an alternating decoding routine that keeps the standard truncation-and-sampling interface unchanged. Extensive experiments on four benchmarks (GSM8K, GPQA, AlpacaEval, and MT-Bench) across three instruction-tuned models show that Top-$W$ consistently outperforms prior state-of-the-art decoding approaches achieving up to 33.7 percentage improvement. Moreover, we find that Top-$W$ not only improves accuracy-focused performance, but also boosts creativity under judge-based open-ended evaluation.

Process rewards have been widely used in deep reinforcement learning to improve training efficiency, reduce variance, and prevent reward hacking. In LLM reasoning, existing works also explore various solutions for learning effective process reward models (PRM) with or without the help of an expert policy. However, existing methods either rely on strong assumptions about the expert policies (e.g., requiring their reward functions) or suffer intrinsic limitations (e.g., entropy collapse), resulting in weak PRMs or limited generalizability. In this paper, we introduce rePIRL, an inverse RL-inspired framework that learns effective PRMs with minimal assumptions about expert policies. Specifically, we design a dual learning process that updates the policy and the PRM interchangeably. Our learning algorithm has customized techniques to address the challenges of scaling traditional inverse RL to LLMs. We theoretically show that our proposed learning framework can unify both online and offline PRM learning methods, justifying that rePIRL can learn PRMs with minimal assumptions. Empirical evaluations on standardized math and coding reasoning datasets demonstrate the effectiveness of rePIRL over existing methods. We further show the application of our trained PRM in test-time training, test-time scaling, and providing an early signal for training hard problems. Finally, we validate our training recipe and key design choices via a detailed ablation study.

We introduce a predictive model that estimates the pre-training loss of large models from model size ($N$), batch size ($B$) and number of weight updates ($K$). This is the first loss prediction model that can handle changing batch size. The model outperforms Chinchilla's loss model, a model of the test loss using the batch size and number of tokens, in terms of projecting the loss at extrapolated compute budgets (up to 1000 folds). A natural use of the model is to find optimal $N,B,K$ configurations under explicit and compound resource constraints like time, memory and compute. In our experiments, the model-selected configurations are close to ground-truth optimal. Our work advocates for loss prediction as a better alternative to heuristic-based laws, which are growing in complexity. The implementation is available on \href{https://github.com/chuningxdy/Noisy-Quadratic-System}{GitHub}.