ICLR 2026 Papers

This paper investigates how multilayer perceptrons (MLPs) can be represented in non-Euclidean spaces, with emphasis on the Poincaré model of hyperbolic geometry. We aim to capture the geometric evolution of their weighted topology and self-organization over time. Instead of restricting analysis to single checkpoints, we construct temporal parameter-graphs across $T$ snapshots of the optimization process. This reflects the view that neural networks encode information not only in their weights but also in the trajectory traced during training. Drawing on the idea that many complex networks admit embeddings in hidden metric spaces where distances correspond to connection likelihood, we present a geometric and temporal graph-based meta learning framework for obtaining dynamic hyperbolic representations of the underlying neural parameter graphs. Our model embeds temporal parameter-graphs in the Poincaré ball and learns from them while maintaining equivariance to within-snapshot neuron permutations and invariance to permutations of past snapshots. In doing so, it preserves functional equivalence across time and recovers the network’s latent geometry. Experiments on regression and classification tasks with trained MLPs show that hyperbolic temporal representations expose how structure emerges during training, offering intrinsic explanations of self-organisation in a given model training environment.

Numerous applications of large language models (LLMs) rely on their ability to perform step-by-step reasoning. However, the reasoning behavior of LLMs remains poorly understood, posing challenges to research, development, and safety. To address this gap, we introduce landscape of thoughts (LoT), the first landscape visualization tool to inspect the reasoning trajectories with certain reasoning methods on any multi-choice dataset. We represent the textual states in a trajectory as numerical features that quantify the states' distances to the answer choices. These features are then visualized in two-dimensional plots using t-SNE. Qualitative and quantitative analysis with the landscape of thoughts effectively distinguishes between strong and weak models, correct and incorrect answers, as well as different reasoning tasks. It also uncovers undesirable reasoning patterns, such as low consistency and high uncertainty. Additionally, users can adapt LoT to a model that predicts the property they observe. We showcase this advantage by adapting LoT to a lightweight verifier that evaluates the correctness of trajectories. Empirically, this verifier boosts the reasoning accuracy and the test-time scaling effect.

Machine unlearning as an emerging research topic for data regulations, aims to adjust a trained model to approximate a retrained one that excludes a portion of training data. Previous studies showed that class-wise unlearning is effective in forgetting the knowledge of a training class, either through gradient ascent on the forgetting data or fine-tuning with the remaining data. However, while these methods are useful, they are insufficient as the class label and the target concept are often considered to coincide. In this work, we expand the scope by considering the label domain mismatch and investigate three problems beyond the conventional all matched forgetting, e.g., target mismatch, model mismatch, and data mismatch forgetting. We systematically analyze the new challenges in restrictively forgetting the target concept and also reveal crucial forgetting dynamics in the representation level to realize these tasks. Based on that, we propose a general framework, namely, TARget-aware Forgetting (TARF). It enables the additional tasks to actively forget the target concept while maintaining the rest part, by simultaneously conducting annealed gradient ascent on the forgetting data and selected gradient descent on the hard-to-affect remaining data. Various experiments under our new settings are conducted to demonstrate the effectiveness of our TARF.

We present UniTrack, a plug-and-play graph-theoretic loss function designed to significantly enhance multi-object tracking (MOT) performance by directly optimizing tracking-specific objectives through unified differentiable learning. Unlike prior graph-based MOT methods that redesign tracking architectures, UniTrack provides a universal training objective that integrates detection accuracy, identity preservation, and spatiotemporal consistency into a single end-to-end trainable loss function, enabling seamless integration with existing MOT systems without architectural modifications. Through differentiable graph representation learning, UniTrack enables networks to learn holistic representations of motion continuity and identity relationships across frames. We validate UniTrack across diverse tracking models and multiple challenging benchmarks, demonstrating consistent improvements across all tested architectures and datasets including Trackformer, MOTR, FairMOT, ByteTrack, GTR, and MOTE. Extensive evaluations show up to 53\% reduction in identity switches and 12\% IDF1 improvements across challenging benchmarks, with GTR achieving peak performance gains of 9.7\% MOTA on SportsMOT. Code and additional resources are available at https://github.com/ostadabbas/UniTrack and https://ostadabbas.github.io/unitrack.github.io/.

Reasoning has emerged as a pivotal capability in Large Language Models (LLMs). Through Reinforcement Learning (RL), typically Group Relative Policy Optimization (GRPO), these models are able to solve complex tasks such as mathematics and code generation. Building on these advances, recent research has sought to extend reasoning to Vision-Language Models (VLMs), yielding promising results across diverse visual tasks. Despite this progress, our study uncovers the dual nature of multimodal reasoning: while it substantially enhances logical inference and facilitates performance on challenging problems, longer reasoning length may gradually impair perceptual grounding, leading to recognition failures on otherwise basic visual questions. Through further analysis, we attribute this phenomenon to visual forgetting, wherein prolonged reasoning ength causes models to disregard visual input. To address this, we propose Vision-Anchored Policy Optimization (VAPO), a simple yet effective method that explicitly steers the reasoning process toward visually grounded trajectories. Our result model, VAPO-Thinker-7B, significantly strengthens the model's reliance on visual information and achieves new state-of-the-art results on various benchmarks.

Large language models (LLMs) sometimes memorize undesirable knowledge, which must be removed after deployment. Prior work on machine unlearning has focused largely on optimization methods that adjust parameters to enforce forgetting while preserving retention. However, these approaches assume that the forget and retain sets are readily available, which rarely holds in practice. Unlearning is typically triggered by an undesired generation at inference time, making the retrieval of relevant data the central challenge. We introduce the notion of \emph{data Pareto improvement} for LLM unlearning, which formalizes how retrieval can expand the achievable trade-off frontier between forgetting and retention. To realize this principle, we propose Randomized Antipodal Search on Linearized Influence Kernel (RASLIK), a retrieval algorithm that combines permutation–projection hashing with randomized antipodal search. RASLIK reduces selection variance, achieves sublinear complexity, and yields a double gain in both quality and efficiency. Across multiple models, datasets, and unlearning algorithms, RASLIK consistently outperforms deterministic baselines and even oracle sampling, establishing randomized search as a principled and scalable solution for data-centric unlearning.

Deep learning-based approaches, particularly graph neural networks (GNNs), have gained prominence in simulating flexible deformations and contacts of solids, due to their ability to handle unstructured physical fields and nonlinear regression on graph structures. However, existing GNNs commonly represent meshes with graphs built solely from vertices and edges. These approaches tend to overlook higher-dimensional spatial features, e.g. 2D facets and 3D cells, from the original geometry. As a result, it is challenging to accurately capture boundary representations and volumetric characteristics, though this information is critically important for modeling contact interactions and internal physical quantity propagation, particularly under sparse mesh discretization. In this paper, we introduce MAVEN, a mesh-aware volumetric encoding network for simulating 3D flexible deformation, which explicitly models geometric mesh elements of higher dimension to achieve a more accurate and natural physical simulation. MAVEN establishes learnable mappings among 3D cells, 2D facets, and vertices, enabling flexible mutual transformations. Explicit geometric features are incorporated into the model to alleviate the burden of implicitly learning geometric patterns. Experimental results show that MAVEN consistently achieves state-of-the-art performance across established datasets and a novel metal stretch-bending task featuring large deformations and prolonged contacts.

We introduce ODE-GS, a novel approach that integrates 3D Gaussian Splatting with latent neural ordinary differential equations (ODEs) to enable future extrapolation of dynamic 3D scenes. Unlike existing dynamic scene reconstruction methods, which rely on time-conditioned deformation networks and are limited to interpolation within a fixed time window, ODE-GS eliminates timestamp dependency by modeling Gaussian parameter trajectories as continuous-time latent dynamics. Our approach first learns an interpolation model to generate accurate Gaussian trajectories within the observed window, then trains a Transformer encoder to aggregate past trajectories into a latent state evolved via a neural ODE. Finally, numerical integration produces smooth, physically plausible future Gaussian trajectories, enabling rendering at arbitrary future timestamps. On the D-NeRF, NVFi, and HyperNeRF benchmarks, ODE-GS achieves state-of-the-art extrapolation performance, improving metrics by 19.8% compared to leading baselines, demonstrating its ability to accurately represent and predict 3D scene dynamics.

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.