ICLR 2026 论文列表

Leveraging the intrinsic importance differences among experts, recent research has explored expert-level compression techniques to enhance the efficiency of Mixture-of-Experts (MoE) large language models (LLMs). However, existing approaches often rely on empirical heuristics to identify critical experts, while lacking a deeper understanding into the heterogeneous importance of experts and the inner workings of MoE LLMs. In this study, we report, for the first time, the discovery and systematic investigation of a distinct subset of experts that play a pivotal role in the model's forward inference. These experts are prevalent in open-source MoE LLMs, and despite their extremely limited number, pruning them results in a substantial decline in model performance (e.g., prune just three out of 6,144 causes Qwen3-30B-A3B to generate repetitive and uninformative outputs). We refer to these experts as Super Experts (SEs). Our comprehensive analysis provides progressively deeper insights into SEs: (i) SEs are characterized by rare but extreme activation outliers in the output of the down\_proj, which give rise to massive activations in the hidden states between decoder layers. Moreover, the distribution of SEs is model-specific, data-agnostic, and remains unaffected by post-training processes. (ii) By pruning SEs, we assess their significance across a variety of tasks, revealing their considerable impact on the model's overall performance, particularly in mathematical reasoning. (iii) We further investigate why compressing SEs exerts such a pronounced impact. We show that, in MoE LLMs, SEs serve as the primary source of the systematic outlier mechanism in Transformers, and that compressing them profoundly disrupts this process, ultimately causing the collapse of attention sinks. These findings advance the understanding of the internal dynamics of MoE LLMs, filling an important gap in the current knowledge. In addition, we developed an automated tool for rapid and accurate SE profiling. The code is provided in the supplementary materials.

Psychological constructs within individuals are widely believed to be interconnected. We investigated whether and how Large Language Models (LLMs) can model the correlational structure of human psychological traits from minimal quantitative inputs. We prompted various LLMs with Big Five Personality Scale responses from 816 human individuals to role-play their responses on nine other psychological scales. LLMs demonstrated remarkable accuracy in capturing human psychological structure, with the inter-scale correlation patterns from LLM-generated responses strongly aligning with those from human data (R² > 0.88). This zero-shot performance substantially exceeded predictions based on semantic similarity and approached the accuracy of machine learning algorithms trained directly on the dataset. Analysis of reasoning traces revealed that LLMs use a systematic two-stage process: First, they transform raw Big Five responses into natural language personality summaries through information selection and compression, analogous to generating sufficient statistics. Second, they generate target scale responses based on reasoning from these summaries. For information selection, LLMs identify the same key personality factors as trained algorithms, though they fail to differentiate item importance within factors. The resulting compressed summaries are not merely redundant representations but capture synergistic information—adding them to original scores enhances prediction alignment, suggesting they encode emergent, second-order patterns of trait interplay. Our findings demonstrate that LLMs can precisely predict individual participants' psychological traits from minimal data through a process of abstraction and reasoning, offering both a powerful tool for psychological simulation and valuable insights into their emergent reasoning capabilities.

Ultra-long generation by large language models (LLMs) is a widely demanded scenario, yet it remains a significant challenge due to their maximum generation length limit and overall quality degradation as sequence length increases. Previous approaches, exemplified by LongWriter, typically rely on ''teaching'', which involves supervised fine-tuning (SFT) on synthetic long-form outputs. However, this strategy heavily depends on synthetic SFT data, which is difficult and costly to construct, often lacks coherence and consistency, and tends to be overly artificial and structurally monotonous. In this work, we propose an incentivization-based approach that, starting entirely from scratch and without relying on any annotated or synthetic data, leverages reinforcement learning (RL) to foster the emergence of ultra-long, high-quality text generation capabilities in LLMs. We perform RL training starting from a base model, similar to R1-Zero, guiding it to engage in reasoning that facilitates planning and refinement during the writing process. To support this, we employ specialized reward models that steer the LLM towards improved length control, writing quality, and structural formatting. Experimental evaluations show that our LongWriter-Zero model, trained from Qwen2.5-32B, consistently outperforms traditional SFT methods on long-form writing tasks, achieving state-of-the-art results across all metrics on WritingBench and Arena-Write, and even surpassing 100B+ models such as DeepSeek R1 and Qwen3-235B.

Compressing neural networks without retraining is vital for deployment at scale. We study calibration-free compression through the lens of projection geometry: structured pruning is an axis-aligned projection, whereas model folding performs a low-rank projection via weight clustering. We formalize both as orthogonal operators and show that, within a rank distance of one, folding provably yields smaller parameter reconstruction error, and under mild smoothness assumptions, smaller functional perturbations than pruning. At scale, we evaluate >1'000 checkpoints spanning ResNet18, PreActResNet18, ViT-B/32, and CLIP ViT-B/32 on CIFAR-10 and ImageNet-1K, covering diverse training hyperparameters (optimizers, learning rates, augmentations, regularization, sharpness-aware training). We show that folding typically achieves higher post-compression accuracy, with the largest gains at moderate–high compression. The gap narrows and occasionally reverses at specific training setups. Our results position folding as a geometry-aware, calibration-free alternative to pruning that is often superior in practice and principled in theory.

We present SEED ($\textbf{Se}$mantic $\textbf{E}$valuation for Visual Brain $\textbf{D}$ecoding), a novel metric for evaluating the semantic decoding performance of visual brain decoding models. It integrates three complementary metrics, each capturing a different aspect of semantic similarity between images inspired by neuroscientific findings. Using carefully crowd-sourced human evaluation data, we demonstrate that SEED achieves the highest alignment with human evaluation, outperforming other widely used metrics. Through the evaluation of existing visual brain decoding models with SEED, we further reveal that crucial information is often lost in translation, even in the state-of-the-art models that achieve near-perfect scores on existing metrics. This finding highlights the limitations of current evaluation practices and provides guidance for future improvements in decoding models. Finally, to facilitate further research, we open-source the human evaluation data, encouraging the development of more advanced evaluation methods for brain decoding.

Time series forecasting remains a critical challenge across numerous domains, yet the effectiveness of complex models often varies unpredictably across datasets. Recent studies highlight the surprising competitiveness of simple linear models, suggesting that their robustness and interpretability warrant deeper theoretical investigation. This paper presents a systematic study of linear models for time series forecasting, with a focus on the role of characteristic roots in temporal dynamics. We begin by analyzing the noise-free setting, where we show that characteristic roots govern long-term behavior and explain how design choices such as instance normalization and channel independence affect model capabilities. We then extend our analysis to the noisy regime, revealing that models tend to produce spurious roots. This leads to the identification of a key data-scaling property: mitigating the influence of noise requires disproportionately large training data, highlighting the need for structural regularization. To address these challenges, we propose two complementary strategies for robust root restructuring. The first uses rank reduction techniques, including \textbf{Reduced-Rank Regression (RRR)} and \textbf{Direct Weight Rank Reduction (DWRR)}, to recover the low-dimensional latent dynamics. The second, a novel adaptive method called \textbf{Root Purge}, encourages the model to learn a noise-suppressing null space during training. Extensive experiments on standard benchmarks demonstrate the effectiveness of both approaches, validating our theoretical insights and achieving state-of-the-art results in several settings. Our findings underscore the potential of integrating classical theories for linear systems with modern learning techniques to build robust, interpretable, and data-efficient forecasting models. The code is publicly available at: https://github.com/Wangzzzzzzzz/Root-Purge-for-Time-Series-Forecasting.

Recently, OpenAI (2025) showed that training against a chain of thought (CoT) monitor can cause obfuscated CoTs, which contain bad behavior the monitor cannot detect. They proposed to keep CoTs monitorable by training only against output monitors that do not have access to CoT. We show that such training can still cause obfuscated CoTs via two mechanisms. First, when a model is trained to produce a safe-looking output, that model may generalize to making its CoTs look safe. Second, since later tokens are conditioned on earlier ones, safe‑looking CoTs may increase the likelihood of safe outputs, causing safe-looking CoTs to be reinforced. We introduce two mitigations to address these two issues, which achieve a Pareto improvement in terms of monitorability and task performance compared to regular training. To our knowledge, we are the first to identify and mitigate these problems. Our work implies that preserving CoT monitorability is more difficult than previously thought; we suggest practical guidelines for AI developers to maintain monitorable CoTs.

Decentralized Learning (DL) enables users to collaboratively train models without sharing raw data by iteratively averaging local updates with neighbors in a network graph. This setting is increasingly popular for its scalability and its ability to keep data local under user control. Strong privacy guarantees in DL are typically achieved through Differential Privacy (DP), with results showing that DL can even amplify privacy by disseminating noise across peer-to-peer communications. Yet in practice, the observed privacy-utility trade-off often appears worse than in centralized training, which may be due to limitations in current DP accounting methods for DL. In this paper, we show that recent advances in centralized DP accounting based on Matrix Factorization (MF) for analyzing temporal noise correlations can also be leveraged in DL. By generalizing existing MF results, we show how to cast both standard DL algorithms and common trust models into a unified formulation. This yields tighter privacy accounting for existing DP-DL algorithms and provides a principled way to develop new ones. To demonstrate the approach, we introduce MAFALDA-SGD, a gossip-based DL algorithm with user-level correlated noise that outperforms existing methods on synthetic and real-world graphs.

Recent advances in text-to-image (T2I) diffusion models have seen rapid and widespread adoption. However, their powerful generative capabilities raise concerns about potential misuse for synthesizing harmful, private, or copyrighted content. To mitigate such risks, concept erasure techniques have emerged as a promising solution. Prior works have primarily focused on fine-tuning the denoising component (e.g., the U-Net backbone). However, recent causal tracing studies suggest that visual attribute information is localized in the early self-attention layers of the text encoder, indicating a potential alternative for concept erasing. Building on this insight, we conduct preliminary experiments and find that directly fine-tuning early layers can suppress target concepts but often degrades the generation quality of non-target concepts. To overcome this limitation, we propose High-Level Representation Misdirection (HiRM), which misdirects high-level semantic representations of target concepts in the text encoder toward designated vectors such as random directions or semantically defined directions (e.g., super-categories), while updating only early layers that contain causal states of visual attributes. Our decoupling strategy enables precise concept removal with minimal impact on unrelated concepts, as demonstrated by strong results on UnlearnCanvas and NSFW benchmarks across diverse targets (e.g., objects, styles, nudity). HiRM also preserves generative utility at low training cost and transfers effectively to state-of-the-art architectures such as Flux without additional training.

Given the prohibitive cost of pre-training large language models, it is essential to leverage smaller proxy models to optimize recipes before scaling up. However, this approach becomes challenging for reasoning capabilities, which exhibit \textit{emergent} behavior that only appears reliably at larger model sizes, often exceeding 7B parameters. To address this, we introduce \tsc{rBridge}, showing that small proxies ($\leq$1B) can effectively predict large-model reasoning by aligning more closely with \textbf{(1)} the pre-training objective and \textbf{(2)} the target task. \tsc{rBridge} achieves this by weighting negative log-likelihood with task alignment, using reasoning traces from frontier models as gold labels. In our experiments, \tsc{rBridge} \textbf{(i)} reduces dataset ranking costs by over 100$\times$ relative to the best baseline, \textbf{(ii)} achieves the strongest correlation across six reasoning benchmarks at 1B to 32B scale, and \textbf{(iii)} transfers predictive relationships across pre-training recipes at 1B to 7B scale. These findings indicate that \tsc{rBridge} offers a practical path for exploring reasoning-oriented pre-training at lower cost.

Most existing Time Series Foundation Models (TSFMs) use channel independent modeling and focus on capturing and generalizing temporal dependencies, while neglecting the correlations among channels or overlook the different aspects of correlations. However, these correlations play a vital role in Multivariate time series forecasting. To address this, we propose a Correlation-aware Adapter (**CoRA**), a lightweight plug-and-play method that requires only fine-tuning with TSFMs and is able to capture different types of correlations, so as to improve forecast performance. Specifically, to reduce complexity, we innovatively decompose the correlation matrix into low-rank Time-Varying and Time-Invariant components. For the Time-Varying component, we further design learnable polynomials to learn dynamic correlations by capturing trends or periodic patterns. To learn positive and negative correlations that appear only among some variables, we introduce a novel dual contrastive learning method that identifies correlations through projection layers, regulated by a Heterogeneous-Partial contrastive loss during training, without introducing additional complexity in the inference stage. Extensive experiments on 10 real-world datasets demonstrate that CoRA improves the state-of-the-art TSFMs in average forecast performance.

Sets represent a fundamental abstraction across many types of data. To handle the unordered nature of set-structured data, models such as DeepSets and PointNet rely on fixed, non-learnable pooling operations (e.g., sum or max) -- a design choice that can hinder the transferability of learned embeddings and limits model expressivity. More recently, learnable aggregation functions have been proposed as more expressive alternatives. In this work, we advance this line of research by introducing the Neuralized Kolmogorov Mean (NKM) -- a novel, trainable framework for learning a generalized measure of central tendency through an invertible neural function. We further propose quasi-arithmetic neural networks (QUANNs), which incorporate the NKM as a learnable aggregation function. We provide a theoretical analysis showing that, QUANNs are universal approximators for a broad class of common set-function decompositions and, thanks to their invertible neural components, learn more structured latent representations. Empirically, QUANNs outperform state-of-the-art baselines across diverse benchmarks, while learning embeddings that transfer effectively even to tasks that do not involve sets.

Recently, sophisticated deep learning-based approaches have been developed for generating efficient initial guesses to accelerate the convergence of density functional theory (DFT) calculations. While the actual initial guesses are often density matrices (DM), quantities that can convert into density matrices also qualify as alternative forms of initial guesses. Hence, existing works mostly rely on the prediction of the Hamiltonian matrix for obtaining high-quality initial guesses. However, the Hamiltonian matrix is both numerically difficult to predict and intrinsically non-transferable, hindering the application of such models in real scenarios. In light of this, we propose a method that constructs DFT initial guesses by predicting the electron density in a compact auxiliary basis representation using E(3)-equivariant neural networks. Trained exclusively on small molecules with up to 20 atoms, our model achieves an average 33.3% reduction in SCF iterations for molecules three times larger (up to 60 atoms). This result is particularly significant given that baseline Hamiltonian-based methods fail to generalize, often increasing the iteration count by over 80\% or failing to converge entirely on these larger systems. Furthermore, we demonstrate that this acceleration is robustly scalable: the model successfully accelerates calculations for systems with up to 900 atoms (polymers and polypeptides) without retraining. To the best of our knowledge, this work represents the first and robust candidate for a universally transferable DFT acceleration method. We are also releasing the SCFbench dataset and its accompanying code to facilitate future research in this promising direction.

Standard discrete diffusion models treat all unobserved states the same way, typically mapping them to an absorbing [MASK] token. This creates an "information void" where global semantic information that may be inferred for the masked tokens from the unmasked tokens is not directly passed from one denoising step to another. We introduce **Continuously Augmented Discrete Diffusion (CADD)**, a framework that augments the discrete state space with a paired diffusion in a continuous latent space. This yields graded, gradually corrupted states in which masked tokens are represented by noisy yet informative latent vectors rather than information voids. At each reverse step, CADD uses the continuous latent as a semantic hint to guide discrete denoising. The design is clean and compatible with existing discrete diffusion training. At sampling time, the strength and estimator of the continuous latent vector enables a controlled trade-off between mode-coverage (diversity-oriented) and mode-seeking (context-localization-oriented). Empirically, we demonstrate CADD improves generative quality over mask-based diffusion across text generation, image synthesis, and code modeling, with consistent gains on both qualitative and quantitative metrics against strong discrete baselines.

Effective specification-aware part retrieval within complex CAD assemblies is essential for automated engineering tasks. However, using LLMs/VLMs for this task is challenging: the metadata sequences often exceed token budgets, and fine-tuning high-performing proprietary models (e.g., GPT, Gemini) is unavailable. Therefore, we need a framework that delivers engineering value by handling long, non-natural-language metadata associated with real 3D assemblies. We propose an inference-time adaptation framework that combines corrected Error Notebooks with RAG to substantially improve VLM-based part retrieval. Each Error Notebook is built by correcting initial CoTs through reflective refinement, and then filtering each trajectory using a grammar-constraint (GC) verifier to ensure structural well-formedness. The resulting notebook forms a high-quality repository of specification-CoT-answer triplets, from which RAG retrieves specification-relevant exemplars to condition the model’s inference. We additionally contribute a CAD dataset with preference annotations. Experiments with proprietary models (GPT-4o, Gemini, etc) show large gains, with GPT-4o (Omni) achieving up to +23.4 absolute accuracy points on the human-preference benchmark. The proposed GC verifier can further produce +4.5 accuracy points. Our approach also surpasses other training-free baselines (standard few-shot learning, self-consistency) and yields substantial improvements for open-source VLMs (Qwen2-VL-2B-Instruct, Aya-Vision-8B). Under the cross-model GC setting, where the Error Notebook is constructed using GPT-4o (Omni), the 2B model inference achieves performance that comes within roughly 4 points of GPT-4o mini.

Speculative decoding is widely used in accelerating large language model (LLM) inference. In this work, we focus on the online draft model selection problem in speculative decoding. We design an algorithm that provably competes with the best draft model in hindsight for each query in terms of either the token acceptance probability or expected acceptance length. In particular, we show that we can accurately evaluate all draft models, instead of only the chosen model without incurring additional queries to the target model, which allows us to improve exponentially over the existing bandit-based approach as the number of draft models increases. Our approach is generically applicable with any speculative decoding methods (single draft, multi-drafts and draft-trees). Moreover, we design system-efficient versions of online learners and demonstrate that the overhead in computation and latency can be substantially reduced. We conduct extensive experiments on open-source LLMs and diverse datasets, demonstrating that our methods substantially outperform the state-of-the-art EAGLE3 and the BanditSpec baseline in a variety of domains where specialized domain-expert drafters are available, especially when long reasoning chains are required.

Regret Matching (RM) and its variants are widely employed to learn a Nash equilibrium (NE) in large-scale games. However, most existing research only establishes a theoretical convergence rate of $O(1/\sqrt{T})$ for these algorithms in learning an NE. Recent studies have shown that smooth RM$^+$ variants, the advanced variants of RM, can achieve an improved convergence rate of $O(1/T)$. Despite this improvement, smooth RM$^+$ variants lose the parameter-free property, i.e., no parameters that need to be tuned, a highly desirable feature in practical applications. In this paper, we propose a novel smooth RM$^+$ variant called Monotone Increasing Smooth Predictive Regret Matching$^+$ (MI-SPRM$^+$), which retains the parameter-free property while still achieving a theoretical convergence rate of $O(1/T)$. To achieve these properties, MI-SPRM$^+$ employs a technology called Adaptive Regret Domain (ARD), which ensures that the lower bound for the 1-norm of accumulated regrets increases monotonically by adjusting the decision space at each iteration. This design is motivated by the observation that the range of step-sizes supporting the $O(1/T)$ convergence rate in existing smooth RM$^+$ variants is contingent on the lower bound for the 1-norm of accumulated regrets. Experimental results confirm that MI-SPRM$^+$ empirically attains an $O(1/T)$ convergence rate.

Image captioning is a fundamental task that bridges the visual and linguistic domains, playing a critical role in pre-training Large Vision-Language Models (LVLMs). Current state-of-the-art captioning models are typically trained with Supervised Fine-Tuning (SFT), a paradigm that relies on expensive, non-scalable data annotated by humans or proprietary models. This approach often leads to models that memorize specific ground-truth answers, limiting their generality and ability to generate diverse, creative descriptions. To overcome the limitation of SFT, we propose applying the Reinforcement Learning with Verifiable Rewards (RLVR) paradigm to the open-ended task of image captioning. A primary challenge, however, is designing an objective reward function for the inherently subjective nature of what constitutes a "good" caption. We introduce Captioning Reinforce- ment Learning (CapRL), a novel training framework that redefines caption quality through its utility: a high-quality caption should enable a non-visual language model to accurately answer questions about the corresponding image. CapRL employs a decoupled two-stage pipeline where an LVLM generates a caption, and the objective reward is derived from the accuracy of a separate, vision-free LLM answering Multiple-Choice Questions based solely on that caption. As the first study to apply RLVR to the subjective image captioning task, we demonstrate that CapRL significantly enhances multiple settings. Pretraining on the CapRL- 5M caption dataset annotated by CapRL-3B results in substantial gains across 12 benchmarks. Moreover, within the Prism Framework for caption quality evaluation, CapRL achieves performance comparable to Qwen2.5-VL-72B, while exceeding the baseline by an average margin of 8.4%. Results validate that our CapRL effec- tively trains models to produce a more general and accurate image descriptions, moving beyond the limitations of traditional SFT-based image captioning models.

Existing expert merging strategies for Sparse Mixture of Experts (SMoE) typically rely on input-dependent or input-independent averaging of expert parameters, but often lack a principled weighting mechanism. In this work, we reinterpret expert merging through the lens of game theory, revealing cooperative and competitive dynamics among experts. Based on this perspective, we introduce Nash Merging of Experts (NAMEx), a novel framework that incorporates Nash Bargaining into the merging process, enabling more balanced and efficient collaboration among experts. Additionally, we incorporate complex momentum into NAMEx to accelerate expert propagation with theoretical guarantees for convergence. Extensive experiments across language modeling, text classification, image classification, and zero-shot robustness under data corruption show that NAMEx consistently outperforms competing methods while integrating seamlessly with popular MoE architectures. Finally, we demonstrate NAMEx’s scalability by applying it to large-scale systems, including Qwen1.5-MoE (14B) and DeepSeek-MoE (16B), where it proves effective in both zero-shot and fine-tuning settings.