ICLR 2026 Papers

Neural operators offer powerful approaches for solving parametric partial differential equations, but extending them to spherical domains remains challenging due to the need to preserve intrinsic geometry while avoiding distortions that break rotational consistency. Existing spherical operators rely on rotational equivariance but often lack the flexibility for real-world complexity. We propose a generalized operator-design framework based on \textbf{designable Green’s function} and its harmonic expansion, establishing a solid operator-theoretic foundation for spherical learning. Based on this, we propose an absolute and relative position-dependent Green’s function that enables flexible balance of equivariance and invariance for real-world modeling. The resulting operator, \textit{Green's-function Spherical Neural Operator} (GSNO) with a novel spectral learning method, can adapt to non-equivariant systems while retaining spherical geometry, spectral efficiency and grid invariance. To exploit GSNO, we develop SHNet, a hierarchical architecture that combines multi-scale spectral modeling with spherical up-down sampling, enhancing global feature representation. Evaluations on diffusion MRI, shallow water dynamics, and global weather forecasting, GSNO and SHNet consistently outperform state-of-the-art methods. The theoretical and experimental results position GSNO as a principled and generalized framework for spherical operator learning, bridging rigorous theory with real-world complexity. The code is available at: \url{https://github.com/haot2025/GSNO}.

Error correcting codes (ECCs) are a fundamental technique for ensuring reliable communication over noisy channels. Recent advances in deep learning have enabled transformer-based decoders to achieve state-of-the-art performance on short codes; however, their computational complexity remains significantly higher than that of classical decoders due to the attention mechanism. To address this challenge, we propose EfficientMPT, an efficient message-passing transformer that significantly reduces computational complexity while preserving decoding performance. A key feature of EfficientMPT is the Efficient Error Correcting (EEC) attention mechanism, which replaces expensive matrix multiplications with lightweight vector-based element-wise operations. Unlike standard attention, EEC attention relies only on query-key interaction using global query vector, efficiently encode global contextual information for ECC decoding. Furthermore, EfficientMPT can serve as a foundation model, capable of decoding various code classes and long codes by fine-tuning. In particular, EfficientMPT achieves 85% and 91% of significant memory reduction and 47% and 57% of FLOPs reduction compared to ECCT for $(648,540)$ and $(1056,880)$ standard LDPC code, respectively.

Masked diffusion models (MDMs) offer a compelling alternative to autoregres- sive models (ARMs) for discrete text generation because they enable parallel token sampling, rather than sequential, left-to-right generation. This means po- tentially much faster inference. However, effective parallel sampling faces two competing requirements: (i) simultaneously updated tokens must be conditionally independent, and (ii) updates should prioritise high-confidence predictions. These goals conflict because high-confidence predictions often cluster and depend on each other, opportunities for parallel updates. We present PUNT, a model-agnostic sampler that reconciles this trade-off. Our method identifies token dependencies and removes lower-confidence tokens from conflicting groups. This produces sets of indices for unmasking that satisfy both independence and confidence criteria. Our approach ensures improved parallel unmasking through approximate conditional independence testing. Our experiments show that PUNT delivers a superior trade-off between accuracy and compute when compared to other strong training-free baselines, especially for generation of longer sequences. On the IFEval benchmark, it achieves up to 16% higher accuracy over baseline methods, including sequential generation (one-by- one). These gains hold across different values of hyperparameters, mitigating the need for brittle hyperparameter tuning. Moreover, we observe that PUNT induces an emergent hierarchical generation strategy, where the model first establishes high-level paragraph structure before local refinement, suggesting a planning-like generation process that contributes to strong alignment performance.

Interpreting clinical electroencephalography (EEG) is a laborious, subjective process, and existing computational models are limited to narrow classification tasks rather than holistic interpretation. A key bottleneck for applying powerful Large Vision-Language Models (LVLMs) to this domain is the scarcity of datasets pairing EEG visualizations with fine-grained, expert-level annotations. We address this by introducing CerebraGloss, an instruction-tuned LVLM for nuanced EEG interpretation. We first introduce a novel, automated data generation pipeline, featuring a bespoke YOLO-based waveform detector, to programmatically create a large-scale corpus of EEG-text instruction data. Using this data, we develop CerebraGloss, the first model of its kind capable of unified, generative analysis—performing tasks from detailed waveform description to multi-turn, context-aware dialogue. To evaluate this new capability, we construct and release CerebraGloss-Bench, a comprehensive benchmark for open-ended EEG interpretation. CerebraGloss demonstrates strong performance, surpassing leading LVLMs, including proprietary models like GPT-5, on this benchmark and achieving a new state-of-the-art on the TUSZ seizure detection task. Models, benchmark and tools are available at https://github.com/iewug/CerebraGloss.

Attention patterns play a crucial role in both training and inference of large language models (LLMs). Prior works have identified individual patterns—such as retrieval heads, sink heads, and diagonal traces—but these observations remain fragmented and lack a unifying explanation. To bridge this gap, we provide a unifying framework to explain the existence of diverse attention patterns by analyzing their underlying mathematical formulations with a temporal continuous perspective. Our work can both deepen the understanding of attention behavior and guide inference acceleration approaches. Specifically, this framework characterizes attention patterns as either predictable patterns, characterized by clear regularities, or unpredictable ones that appear random. Our analysis further reveals that the distinction between them can be explained by variations in query self-similarity across the temporal dimension. Focusing on the predictable patterns, we further provide a detailed mathematical analysis of three representative predictable patterns in terms of the joint effect of queries, keys, and Rotary Positional Embeddings. To validate the framework, we apply it to KV cache compression and LLM pruning tasks. In these experiments, a simple metric inspired by our theory consistently improves performance over baseline methods.

Recent works have proven tokenisation to be NP-complete. However, their proofs' constructions rely on tokenisation being applied to inputs with alphabets of unbounded cardinality, which does not accurately reflect the real world. Indeed, since practical applications of tokenisers involve fixed-size alphabets (e.g., Unicode or bytes), the implications of such a statement may be challenged. In this work, we examine the computational complexity of tokenisation over bounded alphabets, considering two variants of this problem: bottom-up tokenisation and direct tokenisation, where we must, respectively, select a sequence of merge operations (in bottom-up tokenisation) or a vocabulary (in direct tokenisation) whose application compresses a dataset to at most $\delta$ symbols. When alphabets are bounded to have only 2 characters, we do not only prove that bottom-up and direct tokenisation are NP-complete, but also that there is no polynomial-time approximation scheme for either of these problems (unless P = NP). Furthermore, even when alphabets are bounded to contain a single character, we can still prove the NP-completeness of direct tokenisation. Although the single-character case is not practical on its own, proving hardness results for an $n$-ary alphabet allows us to prove the same results for alphabets of any larger size. We thus conclude that direct tokenisation over any alphabet is NP-complete, and that both bottom-up and direct tokenisation do not admit polynomial-time approximation schemes for any alphabet of size 2 or larger.

In this paper, we revisit stochastic gradient descent (SGD) with AdaGrad-type preconditioning. Our contributions are twofold. First, we develop a unified convergence analysis of SGD with adaptive preconditioning under anisotropic or matrix smoothness and noise assumptions. This allows us to recover state-of-the-art convergence results for several popular adaptive gradient methods, including AdaGrad-Norm, AdaGrad, and ASGO/One-sided Shampoo. In addition, we establish the fundamental connection between two recently proposed algorithms, Scion and DASGO, and provide the first theoretical guarantees for the latter. Second, we show that the convergence of methods like AdaGrad and DASGO can be provably accelerated beyond the best-known rates using Nesterov momentum. Consequently, we obtain the first theoretical justification that AdaGrad-type algorithms can simultaneously benefit from both diagonal preconditioning and momentum, which may provide an ultimate explanation for the practical efficiency of Adam.

Large language models (LLMs) are reshaping the recommender system paradigm by enabling users to express preferences and receive recommendations through conversations. Yet, aligning LLMs to the recommendation task remains challenging: pretrained LLMs often generate out-of-catalog items, violate required output formats, and their ranking quality degrades sharply toward the end of the generated list. To this end, we propose ConvRec-R1, a two-stage framework for end-to-end training of LLM-based conversational recommender systems. In Stage 1, we construct a behavioral-cloning dataset with a Remap-Reflect-Adjust pipeline, which produces high-quality, catalog-grounded demonstrations from powerful blackbox LLMs to warm-start the RL training. In Stage 2, we propose Rank-GRPO, a principled extension of group relative policy optimization (GRPO) tailored to tasks with rank-style outputs. Rank-GRPO treats each rank in the recommendation list as the unit instead of token (too fine-grained) or sequence (too coarse), redefining rewards to remove non-causal credit assignment and introducing a rank-level importance ratio based on the geometric mean of rank-wise token probabilities to stabilize policy updates. Experiments on the public Reddit-v2 dataset show that ConvRec-R1 converges faster and achieves higher Recall and NDCG than GRPO-style baselines. Code and datasets are released at https://anonymous.4open.science/r/ConvRec-R1-5615.

Large language models (LLMs) have achieved remarkable success across diverse applications but remain vulnerable to jailbreak attacks, where attackers craft prompts that bypass safety alignment and elicit unsafe responses. Among existing approaches, optimization-based attacks have shown strong effectiveness, yet current methods often suffer from frequent refusals, pseudo-harmful outputs, and inefficient token-level updates. In this work, we propose TAO-Attack, a new optimization-based jailbreak method. TAO-Attack employs a two-stage loss function: the first stage suppresses refusals to ensure the model continues harmful prefixes, while the second stage penalizes pseudo-harmful outputs and encourages the model toward more harmful completions. In addition, we design a direction-priority token optimization (DPTO) strategy that improves efficiency by aligning candidates with the gradient direction before considering update magnitude. Extensive experiments on multiple LLMs demonstrate that TAO-Attack consistently outperforms state-of-the-art methods, achieving higher attack success rates and even reaching 100\% in certain scenarios.

Steering a large language model's attention towards user-specified highlighted text is a critical capability. Existing prompt highlighting methods are incompatible with modern efficient attention mechanisms like Flash Attention due to their reliance on post-hoc matrix editing. We introduce Spectral Editing Key Amplification (SEKA), a training-free steering method that tackles this by directly editing key embeddings before attention computation. SEKA learns universal relevance subspaces offline via spectral decomposition. We extend this to Adaptive SEKA (AdaSEKA), a query-adaptive variant that uses a training-free routing mechanism to dynamically combine multiple expert subspaces based on the prompt's semantic intent. Our experiments show both methods significantly outperform strong baselines on standard steering benchmarks while adding much lower latency and memory overhead, ensuring full compatibility with optimised attention.

High-quality visual representation is a long-standing pursuit in computer vision. In the context of multimodal LLMs (MLLMs), feeding higher-resolution images can produce more fine-grained visual tokens. However, it introduces additional computational and design complexity, due to multiple forward passes and post-processing of increased tokens. Before simply adopting a higher resolution, have we truly unlocked the model's full perception capability at a standard resolution? Therefore, we study an interesting problem: how to achieve fine visual perception under lower cost without larger images. We present SigLIP-HD in this work. The core is a highly simple fine-to-coarse supervision design. We enforce the coarse feature of a mid-resolution image to mimic the fine-grained feature of its high-resolution version. We build this framework on the advanced SigLIP 2 model. Our final model produces better visual tokens at exactly the same inference budget. It is validated on extensive MLLM benchmarks and consistently delivers stronger results than our baseline model, especially on OCR-related tasks.

Dataset distillation (DD) attempts to construct a compact synthetic dataset that serves as a proxy for a large real dataset under a fixed storage budget, thereby reducing the storage burden and training costs. Prior works assume the full dataset is available upfront which is distilled at once, although real datasets are collected incrementally over time in practice. To alleviate this gap, we introduce a new problem setting, *Domain Incremental Dataset Distillation*, that continually distills datasets from different domains into a single synthetic dataset. The conventional DD sequentially processes arriving datasets in order, overwriting the old knowledge with new one, causing catastrophic forgetting problem. To overcome this drawback, we propose *Asymmetric Synthetic Data Update* strategy that adjusts the per-sample update rates for synthetic dataset while balancing the stability-plasticity trade-off. Specifically, we design a bi-level optimization method based on meta learning framework to estimate the optimal update rates, that allow each sample to focus on either stability or plasticity, thereby striking a balance between the stability and plasticity. Experimental results demonstrate that our approach effectively mitigates the catastrophic forgetting and achieves superior performance of dataset distillation across continually incoming datasets compared with existing methods.

The Entropic Optimal Transport (EOT) problem and its dynamic counterpart, the Schrödinger bridge (SB) problem, play an important role in modern machine learning, linking generative modeling with optimal transport theory. While recent advances in discrete diffusion and flow models have sparked growing interest in applying SB methods to discrete domains, there is still no reliable way to evaluate how well these methods actually solve the underlying problem. We address this challenge by introducing a benchmark for SB on discrete spaces. Our construction yields pairs of probability distributions with analytically known SB solutions, enabling rigorous evaluation. As a byproduct of building this benchmark, we obtain two new SB algorithms, DLightSB and DLightSB-M, and additionally extend prior related work to construct the $\alpha$-CSBM algorithm. We demonstrate the utility of our benchmark by evaluating both existing and new solvers in high-dimensional discrete settings. This work provides the first step toward proper evaluation of SB methods on discrete spaces, paving the way for more reproducible future studies.

Deep Reinforcement Learning has achieved remarkable progress in solving NP-hard scheduling problems. However, existing methods primarily focus on optimizing average performance over training instances, overlooking the core objective of solving each individual instance with high quality. While several instance-wise adaptation mechanisms have been proposed, they are test-time approaches only and cannot share knowledge across different adaptation tasks. Moreover, they largely rely on gradient-based optimization, which could be ineffective in dealing with combinatorial optimization problems. We address the above issues by proposing an instance-wise meta-learning framework. It trains a meta model to acquire a generalizable initialization that effectively guides per-instance adaptation during inference, and overcomes the limitations of gradient-based methods by leveraging a derivative-free optimization scheme that is fully GPU parallelizable. Experimental results on representative scheduling problems demonstrate that our method consistently outperforms existing learning-based scheduling methods and instance-wise adaptation mechanisms under various task sizes and distributions.

The autoregressive nature of large language models (LLMs) fundamentally limits inference speed, as each forward pass generates only a single token and is often bottlenecked by memory bandwidth. Speculative decoding has emerged as a promising solution, adopting a draft-then-verify strategy to accelerate token generation. While the EAGLE series achieves strong acceleration, its requirement of training a separate draft head for each target model introduces substantial adaptation costs. In this work, we propose \textbf{PARD (PARallel Draft)}, a novel speculative decoding method featuring \textit{target-independence} and \textit{parallel token prediction}. Specifically, PARD enables a single draft model to be applied across an entire family of target models without requiring separate training for each variant, thereby minimizing adaptation costs. Meanwhile, PARD substantially accelerates inference by predicting multiple future tokens within a single forward pass of the draft phase. To further reduce the training adaptation cost of PARD, we propose a COnditional Drop-token (COD) mechanism based on the integrity of prefix key-value states, enabling autoregressive draft models to be adapted into parallel draft models at low-cost. Our experiments show that the proposed COD method improves draft model training efficiency by \textbf{3$\times$} compared with traditional masked prediction training. On the \texttt{vLLM} inference framework, PARD achieves up to \textbf{3.67$\times$} speedup on LLaMA3.1-8B, reaching \textbf{264.88} tokens per second, which is \textbf{1.15$\times$} faster than EAGLE-3.

Despite the impressive progress on understanding and generating images shown by the recent unified architectures, the integration of 3D tasks remains challenging and largely unexplored. In this paper, we introduce UniUGG, the first unified understanding and generation framework for 3D modalities. Our unified framework employs an LLM to comprehend and decode sentences and 3D representations. At its core, we propose a spatial decoder leveraging a latent diffusion model to generate high-quality 3D representations. This allows for the generation and imagination of 3D scenes based on a reference image and an arbitrary view transformation, while remaining supports for spatial visual question answering (VQA) tasks. Additionally, we propose a geometric-semantic learning strategy to pretrain the vision encoder. This design jointly captures the input's semantic and geometric cues, enhancing both spatial understanding and generation. Extensive experimental results demonstrate the superiority of our method in visual representation, spatial understanding, and 3D generation.

LLM unlearning is a technique to remove the impacts of undesirable knowledge from the model without retraining from scratch, which is indispensable towards trustworthy AI. Existing unlearning methods face significant limitations: conventional tuning-based unlearning is computationally heavy and prone to catastrophic forgetting. In contrast, in-contextualized unlearning is lightweight for precise unlearning but vulnerable to prompt removal or reverse engineering attacks. In response, we propose Distilled Unlearning from an Efficient Teacher (DUET), a novel distillation-based unlearning method that combines the merits of these two lines of work. It learns a student model to imitate the behavior of a prompt-steered teacher that effectively refuses undesirable knowledge generation while preserving general domain knowledge. Extensive evaluations on existing benchmarks with our enriched evaluation protocols demonstrated that DUET achieves significantly higher performance in both forgetting and utility preservation, while being orders of magnitude more data-efficient than state-of-the-art unlearning methods.

In independent, identically distributed (i.i.d.) training regimes, activation functions have been benchmarked extensively, and their differences often shrink once model size and optimization are tuned. In continual learning, however, the picture is different: beyond catastrophic forgetting, models can progressively lose the ability to adapt—loss of plasticity—and the role of the non-linearity in this failure mode remains underexplored. We show that activation choice is a primary, architecture-agnostic lever for mitigating plasticity loss. Building on a property-level analysis of negative-branch shape and saturation behavior, we introduce two drop-in nonlinearities—Smooth-Leaky and Randomized Smooth-Leaky—and evaluate them in two complementary settings: (i) supervised class-incremental benchmarks and (ii) reinforcement learning with non-stationary MuJoCo environments designed to induce controlled distribution and dynamics shifts. We also provide a simple stress protocol and diagnostics that link the shape of the activation to the adaptation under change. The takeaway is straightforward: thoughtful activation design offers a lightweight, domain-general way to sustain plasticity in continual learning without extra capacity or task-specific tuning.

We introduce MRMR, the first expert-level multidisciplinary multimodal retrieval benchmark requiring intensive reasoning. MRMR contains 1,435 queries spanning 23 domains, with positive documents carefully verified by human experts. Compared to prior benchmarks, MRMR introduces three key advancements. First, it challenges retrieval systems across diverse areas of expertise, enabling fine-grained model comparison across domains. Second, queries are reasoning-intensive, with images requiring deeper interpretation such as diagnosing microscopic slides. We further introduce Contradiction Retrieval, a novel task requiring models to identify conflicting concepts. Finally, queries and documents are constructed as image–text interleaved sequences. Unlike earlier benchmarks restricted to single images or unimodal documents, MRMR offers a realistic setting with multi-image queries and mixed-modality corpus documents. We conduct an extensive evaluation of 4 categories of multimodal retrieval systems and 14 frontier models on MRMR. The text embedding model Qwen3-Embedding with LLM-generated image captions achieves the highest performance, highlighting substantial room for improving multimodal retrieval models. Although latest multimodal models such as Ops-MM-Embedding perform competitively on expert-domain queries, they fall short on reasoning-intensive tasks. We believe that MRMR paves the way for advancing multimodal retrieval in more realistic and challenging scenarios.