ICML 2026 Papers

Large language models (LLMs) are increasingly applied in diverse real-world applications, each governed by bespoke behavioral and safety specifications (spec) custom-tailored by users or organizations. These specifications, categorized into safety-spec and behavioral-spec, vary across scenarios and evolve with changing preferences and requirements. We formalize this challenge as specification alignment, focusing on LLMs' ability to follow dynamic, scenario-specific spec from both behavioral and safety perspectives. To address this challenge, we introduce SpecBench, a unified benchmark for measuring specification alignment, covering 5 scenarios, 103 spec, and 1,500 prompts. Experiments on 15 reasoning and 18 instruct models with several Test-Time Deliberation (TTD) methods, including Self-Refine, TPO, and MoreThink, show that SpecBench effectively reveals alignment gaps and that test-time deliberation improves specification alignment. Based on previous TTD methods, we further propose Align3, a lightweight method with hierarchical reflection and revision to reason over specification boundaries, advancing the safety-helpfulness trade-off frontier with minimal overhead. These results highlight test-time deliberation as an effective strategy for reasoning over the real-world specification boundaries. Our code and resources are available at https://github.com/zzzhr97/SpecBench.

Hardware-related silent data corruptions during gradient aggregation pose significant challenges to fault-tolerant distributed training, often leading to slow or failed convergence. To address this, we first mathematically formulate these errors as gradient inconsistency and theoretically analyze how they result in accumulated model divergence. Guided by this analysis, we introduce PAFT, a fault-tolerant distributed training system designed with dynamic and asynchronous parameter synchronization. PAFT comprises two core components: PAFT-Sync, which mitigates divergence via periodic synchronization, and PAFT-Dyn, which minimizes overhead through dynamic training overlap and frequency scheduling. Furthermore, the system’s synchronization mechanism is optimized to support standard optimizers, including SGD, SGD momentum, and Adam. We implement PAFT on PyTorch Distributed, and experimental results training ResNet, GPT-2, and LLaMA-2 on 4$\sim$32 GPUs demonstrate that it efficiently defends against aggregation errors while maintaining training performance.

Reinforcement learning (RL) has emerged as a key mechanism for transforming LLMs into robust reasoners. While supervised fine-tuning (SFT) often limits models to the distribution of observed reasoning traces, RL post-training significantly improves performance on out-of-distribution (OOD) tasks that require unfamiliar recombinations of familiar steps. We argue that this improvement is driven by **compositional generalization**, which we formalize through a **Hierarchical Latent Selection Model**. In this framework, reasoning traces are generated by a cascade of discrete latent selection variables corresponding to reusable atomic modules, including both skills (local operations) and routing mechanisms (how intermediate information is selected, reused, and composed). We theoretically show that RL’s exploratory nature provides sufficient coverage to identify latent structure and enable compositional generalization. We design controlled experiments to validate this theory. Our results demonstrate that RL can extract atomic modules from compound traces and recombine them to solve new configurations. Moreover, we find that training on compound traces can yield stronger generalization than training on isolated atomic modules. Finally, we investigate relations between SFT and RL and identify an effective protocol in which SFT ensures coverage of all atomic modules, while RL focuses on novel compositions beyond the SFT support to encourage exploration.

Language models, as multi-task learners, acquire a wide range of abilities during training. A fundamental question is how much task-specific data is needed to learn a given task. Answering this for natural language is difficult: tasks are hard to delineate and can confound one another. To rigorously investigate the relationship between data frequency and learnability, we turn to a controlled setting using formal languages induced from probabilistic finite automata. These serve as a methodological testbed to demonstrate that standard correlational evaluation practices are inherently flawed. To enable causal analysis, we introduce the binning semiring, an algebraic object that lets us control how often a targeted property occurs in a sampled corpus. We formulate the experimental pipeline as a causal graphical model and derive decomposed Kullback--Leibler divergence metrics to measure the learnability of specific sub-tasks. Our experiments show that evaluating learnability without causal intervention leads to incorrect conclusions due to confounders in correlational analysis, and serve as a warning about correlational pitfalls in natural-language settings.

Unlearning in large language models (LLMs) is critical for regulatory compliance and for building ethical generative AI systems that avoid producing private, toxic, illegal, or copyrighted content. Despite rapid progress, in this work, we show that \textit{almost all} existing unlearning methods fail to achieve true forgetting in practice. Specifically, while evaluations of these `unlearned' models under deterministic (greedy) decoding often suggest successful knowledge removal using standard benchmarks, we show that sensitive information reliably resurfaces when models are sampled with standard probabilistic decoding. To rigorously capture this vulnerability, we introduce \texttt{leak@$k$}, a new meta-evaluation metric that quantifies the likelihood of forgotten knowledge reappearing when generating $k$ samples from the model under realistic decoding strategies. Using three widely adopted benchmarks, TOFU, MUSE, and WMDP, we conduct the first large-scale, systematic study of unlearning reliability using \texttt{leak@$k$} metric. Our findings demonstrate that knowledge leakage persists across methods and tasks, underscoring that current state-of-the-art (SOTA) unlearning techniques provide only limited forgetting. We propose an algorithm, termed Robust Unlearning under LEak@$k$ metric (\texttt{RULE}) to address this concern. We demonstrate that \texttt{RULE} provides an unlearned model for TOFU benchmark with no information leakage for a large number of generation samples. On the MUSE benchmark, \texttt{RULE} outperforms SOTA unlearning methods under the \texttt{leak@$k$} metric across most sampling budgets $k$. Codes are available at \url{https://github.com/OptimAI-Lab/Leak-k}.

Speculative decoding (SD) addresses the high inference costs of LLMs by having lightweight drafters generate candidates for large verifiers to validate in parallel. Existing draft-verify methods use binary decisions: accept or fully recompute. Yet we find that many rejected tokens can be verified correctly by a slim submodel derived from the full verifier via intra-model routing, instead of the full verifier. This motivates our slim-verifier to handle tokens requiring moderate verification resources, reducing expensive large-model calls. We propose **V**erification via **I**ntr**a**-Model Routing for **S**peculative **D**ecoding (VIA-SD), a multi-tier framework using a routed slim-verifier. Draft tokens are processed hierarchically: direct acceptance for high-confidence cases, slim-verifier regeneration for medium-confidence cases, and full-model verification for uncertain cases. Across four representative tasks and multiple model families, VIA-SD reduces rejection rates by 0.10–0.22 and delivers 10–20% speedups over strong SD baselines, while achieving 2.5–3× acceleration over non-drafting decoding. Moreover, VIA-SD is compatible with existing SD frameworks without modifying their training procedures. Our results suggest multi-tier SD as a general paradigm for scalable and efficient LLM inference. Project page: https://zju-xyc.github.io/VIA-SD-Project-Page/

Diffusion Large Language Models (dLLMs) have emerged as a promising non-autoregressive generative paradigm. Given the prohibitive computational cost of full fine-tuning, Parameter-Efficient Fine-Tuning (PEFT) has become the standard approach. However, existing PEFT methods (e.g., LoRA), originally tailored for autoregressive models, rely on static parameters that are agnostic to the noise level. Consequently, they ignore the intrinsic dynamics of the diffusion process, where input distributions and generation difficulty shift significantly along the denoising trajectory, rendering them suboptimal for dLLMs. To address this, we propose **N**oise-**a**ware Low-**R**ank **A**daptation (NaRA), which introduces a low-rank core matrix generated by a lightweight, globally shared hypernetwork conditioned on the noise level. This design enables the update matrices to vary continuously along the diffusion process while keeping parameter and latency overhead negligible. We provide a theoretical justification for the proposed NaRA framework and empirically demonstrate consistent improvements over noise-agnostic baselines across commonsense reasoning, mathematical reasoning, and code generation benchmarks. Our code is available at [https://github.com/generaldi/NaRA](https://github.com/generaldi/NaRA).

Large language models (LLMs) have shown strong empirical gains as self-evolving agents for CUDA kernel generation, driven by feedback-conditioned planning across generations. However, how planning decisions attribute and combine heterogeneous feedback signals remains opaque. Standard end-to-end ablations fail to resolve this question, as iterative planning amplifies early perturbations and conflates feedback effects with trajectory-dependent drift. We introduce \texttt{CUDAnalyst}, a unified analysis layer for controlled, generation-level attribution of planning decisions to feedback components via trajectory freezing and selective feedback injection. \texttt{CUDAnalyst} enables stable generation-level evaluation and principled coalitional-style attribution of feedback effects and interactions. Our results show that explicit planning is beneficial only when feedback is aligned, that effective planning emerges from structured multi-feedback interactions, and that high-level plans from stronger reasoning models can partially transfer to weaker ones. These trends hold across reference backbones, representative workloads, and reference induction regimes, indicating that the identified feedback-to-plan structure is robust within the controlled axes studied.

Large language models (LLMs) are trained at significant computational and data cost, making them valuable intellectual property (IP). Existing IP verification methods primarily rely either on invasive watermarking that degrades model utility, or on superficial behavioral signatures disrupted by fine-tuning and model merging. This apparent trade-off between model utility and IP protection has constrained practical deployment. We challenge this trade-off and propose CircuitPrint, a non-invasive IP fingerprinting framework that enables robust verification through standard model queries by leveraging stable internal computational circuits of LLMs. We show that these circuits function as a persistent computational backbone across model derivatives, allowing them to serve as stable fingerprints for distinguishing LLMs. Building on this stability, CircuitPrint constructs IP signatures by identifying mechanistically essential supernodes that causally produce specific predictions within these circuits. Specifically, trigger queries are synthesized to replicate the internal suppression of these supernodes, thereby inducing distinctive and observable output shifts. Experimental results demonstrate that CircuitPrint substantially outperforms existing baselines while remaining robust under aggressive fine-tuning and model merging, effectively resolving this trade-off without altering model parameters.

While many-shot ICL achieves remarkable performance, prior studies of its scaling behavior have mainly focused on non-reasoning tasks. In this work, we study many-shot ICL on reasoning tasks, with a particular focus on many-shot chain-of-thought in-context learning (CoT-ICL). Analyzing across non-reasoning and reasoning tasks and across non-reasoning and reasoning-oriented LLMs, we identify several distinctive properties of many-shot CoT-ICL. We further interpret these findings by viewing many-shot CoT-ICL as in-context test-time learning rather than scaled pattern matching, and suggest two principles: (i) demonstrations should be easy for the target model to understand, and (ii) they should be ordered to support a smooth conceptual progression. Guided by the principle, we propose Curvilinear Demonstration Selection (CDS), a simple ordering method that yields up to a 5.42 percentage-point gain on a math task with 64 demonstrations. Overall, our results reframe the long context window from a retrieval buffer into a structured curriculum for in-context test-time learning.

Diffusion large language models (dLLMs) offer capabilities beyond those of autoregressive (AR) LLMs, such as parallel decoding and random-order generation. However, realizing these benefits in practice is non-trivial, as dLLMs inherently face an *accuracy-parallelism trade-off*. Despite increasing interest, existing methods typically focus on only one-side of the coin, targeting either efficiency or accuracy. To address this limitation, we propose d3LLM (*Pseudo-Distilled Diffusion Large Language Model*), striking a balance between accuracy and parallelism: (i) during training, we introduce *pseudo-trajectory distillation* to teach the model which tokens can be decoded confidently at early steps, thereby improving parallelism; (ii) during inference, we employ *entropy-based multi-block decoding* with a KV-cache refresh mechanism to achieve high parallelism while maintaining accuracy. To better evaluate dLLMs, we also introduce AUP (*Accuracy Under Parallelism*), a new metric that jointly measures accuracy and parallelism. Experiments demonstrate that our d3LLM achieves up to $10\times$ speedup over vanilla LLaDA/Dream, and $5\times$ speedup over AR models without much accuracy drop. Our code is available at https://github.com/hao-ai-lab/d3LLM.

Parameter-based knowledge editing updates the internal knowledge of large language models (LLMs) via localized weight modifications and has attracted significant attention. However, most existing methods overlook fundamental theoretical limitations and are rarely evaluated under realistic, practice-oriented settings. In this paper, we first present a theoretical analysis based on the dimensional Collapse Hypothesis, explaining how localized parameter edits can propagate along fragile directions in the representation space, inducing global interference and ultimately causing reasoning collapse. Building on this insight, we conduct a comprehensive empirical evaluation by systematically varying knowledge complexity, number of edits, evaluation dimensions, and baseline methods. Our results show that parameter-based editing methods consistently damage core LLM capabilities. In contrast, a simple retrieval-based baseline achieves consistently stronger performance than all parameter-editing methods across all evaluated conditions. These findings highlight that preserving the fundamental capabilities of LLMs after knowledge editing should be a central concern for future research.

Recent studies have revealed two intriguing phenomena in large language models: attention sinks and massive activations. However, the co-emergence and co-existence of these two phenomena remain poorly understood. In this work, we revisit the prevailing view that massive activations are the primary mechanism responsible for concentrating attention on sink tokens, and provide a more nuanced interpretation of their relationship. Through both theoretical analysis and empirical evidence, we demonstrate that massive activations and attention sinks jointly act to prevent excessive token mixing in self-attention. Specifically, attention sinks suppress mixing among non-sink tokens, whereas massive activations suppress mixing between sink tokens and non-sink tokens. Furthermore, our theory provides a principled explanation of how KV-biases, gating mechanisms, and normalization layers can remove massive activations while largely preserving attention sinks. We further conduct intervention analyses and find that removing the value vector of the sink token can recover attention sinks even when massive activations are entirely suppressed. Overall, this work provides a mechanistic perspective on how massive activations and attention sinks interact under normalization and self-attention layers, offering new insights into their functional roles in Transformer models.

Identifying training data of large-scale models is critical for copyright litigation, privacy auditing, and ensuring fair evaluation. However, existing works typically treat this task as an instance-wise identification without controlling the error rate of the identified set, which cannot provide statistically reliable evidence. In this work, we formalize training data identification as a set-level inference problem and propose Provable Training Data Identification (PTDI), a distribution-free approach that enables provable and strict false identification rate control. Specifically, our method computes conformal p-values for each data point using a set of known unseen data and then develops a novel Jackknife-corrected Beta boundary (JKBB) estimator to estimate the training-data proportion of the test set, which allows us to scale these p-values. By applying the Benjamini–Hochberg (BH) procedure to the scaled p-values, we select a subset of data points with provable and strict false identification control. Extensive experiments across various models and datasets demonstrate that PTDI achieves higher power than prior methods while strictly controlling the FIR.

When does learning elicit \textit{existing} knowledge, and when does it primarily teach \textit{new} capabilities? We find that the amount of generalizable information language models learn during training predicts the origins of their emergent capabilities. Minuscule amounts of information---in many cases, a few bits in a single example---can unlock large fractions of models' maximum performance when capabilities are \textit{elicited} rather than \textit{taught}. We quantify these learning regimes using excess description length (EDL), an information-theoretic measure of generalizable information learned during training. We find that elicitation and teaching exhibit distinct EDL signatures that characterize the predominant learning mechanism as information scales: elicitation requires orders of magnitude less information than teaching to comparable performance. We demonstrate that EDL provides a practical tool for quantitatively estimating the maximum amount of predictive information models can compress from data into trainable parameters during learning. These capacity limits describe optimal tradeoffs between data and parameter count that robustly predict when parameter-efficient fine-tuning methods (\textit{e.g.}, LoRA) will underperform full fine-tuning.

Large Reasoning Models (LRMs) suffer from sycophantic behavior, where models tend to agree with users' incorrect beliefs and follow misinformation rather than maintain independent reasoning. This behavior undermines model reliability and poses societal risks. Mitigating LRM sycophancy requires monitoring how this sycophancy emerges during the reasoning trajectory; however, current methods mainly focus on judging based on final answers and correcting them, without understanding how sycophancy develops during reasoning processes. To address this limitation, we propose MONICA, a novel Monitor-guided Calibration framework that monitors and mitigates sycophancy during model inference at the level of reasoning steps, without requiring the model to finish generating its complete answer. MONICA integrates a sycophantic monitor that provides real-time monitoring of sycophantic drift scores during response generation with a calibrator that dynamically suppresses sycophantic behavior when scores exceed predefined thresholds. Extensive experiments across 12 datasets and 3 LRMs demonstrate that our method effectively reduces sycophantic behavior in both intermediate reasoning steps and final answers, yielding robust performance improvements.

Recent large language models (LLMs) achieve strong performance in generating promising reasoning paths for complex tasks. However, despite powerful generation ability, LLMs remain weak at verifying their own answers, revealing a persistent capability asymmetry between generation and self-verification. In this work, we conduct an in-depth investigation of this asymmetry throughout training evolution and show that, even on the same task, improving generation does not lead to corresponding improvements in self-verification. Interestingly, we find that the reverse direction of this asymmetry behaves differently: learning to self-verify can effectively improve generation performance, achieving accuracy comparable to standard generation training while yielding more efficient and effective reasoning traces. Building on this observation, we further explore integrating self-verification into generation training by formulating a multi-task reinforcement learning framework, where generation and self-verification are optimized as two independent but complementary objectives. Extensive experiments across benchmarks and models demonstrate performance gains over generation-only training in both generation and verification capabilities.

Rotation-based Post-Training Quantization (PTQ) has emerged as a promising solution for mitigating activation outliers in the quantization of Large Language Models (LLMs). Global rotation methods achieve inference efficiency by fusing activation rotations into attention and FFN blocks, but suffer from limited expressivity as they are constrained to use a single learnable rotation matrix across all layers. To tackle this, layer-wise transformation methods emerged, achieving superior accuracy through localized adaptation. However, layer-wise methods cannot fuse activation rotation matrices into weights, requiring online computations and causing significant overhead. In this paper, we propose **ReSpinQuant**, a quantization framework that resolves such overhead by leveraging offline activation rotation fusion and matching basis using efficient residual subspace rotation. This design reconciles the high expressivity of layer-wise adaptation with only negligible inference overhead. Extensive experiments on W4A4 and W3A3 quantization demonstrate that ReSpinQuant achieves state-of-the-art performance, outperforming global rotation methods and matching the accuracy of computationally expensive layer-wise methods with minimal overhead.

We have witnessed remarkable advances in LLM reasoning capabilities with the advent of DeepSeek-R1. However, much of this progress has been fueled by the abundance of internet question–answer (QA) pairs—a major bottleneck going forward, since such data is limited in scale and concentrated mainly in domains like mathematics. In contrast, other sciences such as physics lack large-scale QA datasets to effectively train reasoning-capable models. In this work, we show that physics simulators can serve as a powerful alternative source of supervision for training LLMs for physical reasoning. We generate random scenes in physics engines, create synthetic question–answer pairs from simulated interactions, and train LLMs using reinforcement learning on this synthetic data. Our models exhibit zero-shot sim-to-real transfer to real-world physics benchmarks: for example, training solely on synthetic simulated data improves performance on IPhO (International Physics Olympiad) problems by 5-10 percentage points across model sizes. These results demonstrate that physics simulators can act as scalable data generators, enabling LLMs to acquire deep physical reasoning skills beyond the limitations of internet-scale QA data. Code available at: https://sim2reason.github.io/.