ICLR 2026 论文列表

In this paper, we introduce SemHiTok, a unified image Tokenizer via Semantic-Guided Hierarchical codebook (SGHC) that provides consistent discrete representations for multimodal understanding and generation. Recently, unified image tokenizers have sparked exploration within the research community, which is designed to capture high-level semantic features for understanding and retaining low-level pixel features for generation. Previous works attempt to train a unified image tokenizer by combining loss for semantic distillation and pixel reconstruction. However, due to the differing levels of features prioritized by multimodal understanding and generation, joint training methods face significant challenges in achieving a good trade-off. SemHiTok addresses this challenge through a novel semantic-guided hierarchical codebook, which builds pixel sub-codebooks on a pretrained semantic codebook. This design decouples semantic and pixel in both terms of structure and training strategy, enabling the tokenizer to capture pixel features while retaining its ability to comprehend high-level semantic information. Our experiments demonstrate that SemHiTok achieves SOTA performance in image reconstruction and multimodal understanding under the LLaVA-v1.5 setting. Further, we develop a unified MLLM with SemHiTok, which exhibits superior performance across multimodal understanding and generation tasks. For understanding, SemHiTok achieves impressive performance on most benchmarks. For generation, our model achieves SOTA performance on MJHQ30K in unified MLLMs. Our code and models will be open source.

Adam [Kingma & Ba, 2015] is the de facto optimizer in deep learning, yet its theoretical understanding remains limited. Prior analyses show that Adam favors solutions aligned with $\ell_\infty$-geometry, but these results are restricted to the full-batch regime. In this work, we study the implicit bias of incremental Adam (using one sample per step) for logistic regression on linearly separable data, and show that its bias can deviate from the full-batch behavior. As an extreme example, we construct datasets on which incremental Adam provably converges to the $\ell_2$-max-margin classifier, in contrast to the $\ell_\infty$-max-margin bias of full-batch Adam. For general datasets, we characterize its bias using a proxy algorithm for the $\beta_2 \to 1$ limit. This proxy maximizes a data-adaptive Mahalanobis-norm margin, whose associated covariance matrix is determined by a data-dependent dual fixed-point formulation. We further present concrete datasets where this bias reduces to the standard $\ell_2$- and $\ell_\infty$-max-margin classifiers. As a counterpoint, we prove that Signum [Bernstein et al., 2018] converges to the $\ell_\infty$-max-margin classifier for any batch size. Overall, our results highlight that the implicit bias of Adam crucially depends on both the batching scheme and the dataset, while Signum remains invariant.

Code data has been shown to enhance the reasoning capabilities of large language models (LLMs), but it remains unclear which aspects of code are most responsible. We investigate this question with a systematic, data-centric framework. We construct parallel instruction datasets in ten programming languages and apply controlled perturbations that selectively disrupt structural or semantic properties of code. We then finetune LLMs from five model families and eight scales on each variant and evaluate their performance on natural language, math, and code tasks. Across 3,331 experiments, our results show that LLMs are more vulnerable to structural perturbations than semantic ones, particularly on math and code tasks. Appropriate abstractions like pseudocode and flowcharts can be as effective as code, while encoding the same information with fewer tokens without adhering to original syntax can often retain or even improve performance. Remarkably, even corrupted code with misleading signals remains competitive when surface-level regularities persist. Finally, syntactic styles also shape task-specific gains with Python favoring natural language reasoning and lower-level languages such as Java and Rust favoring math. Through our systematic framework, we aim to provide insight into how different properties of code influence reasoning and inform the design of training data for enhancing LLM reasoning capabilities.

We study the problem of graph and hypergraph sparsification in insertion-only data streams. The input is a hypergraph $H=(V, E, w)$ with $n$ nodes, $m$ hyperedges, and rank $r$, and the goal is to compute a hypergraph $\widehat{H}$ that preserves the energy of each vector $x \in \mathbb{R}^n$ in $H$, up to a small multiplicative error. In this paper, we give a streaming algorithm that achieves a $(1+\varepsilon)$-approximation, using $\mathcal{O}\left(\frac{rn}{\varepsilon^2} \log^2 n \log r\right) \cdot$ poly $(\log \log m)$ bits of space, matching the sample complexity of the best known offline algorithm up to poly $(\log \log m)$ factors. Our approach also provides a streaming algorithm for graph sparsification that achieves a $(1+\varepsilon)$-approximation, using $\mathcal{O}\left(\frac{n}{\varepsilon^2} \log n\right)\cdot\text{poly}(\log\log n)$ bits of space, improving the current bound by $\log n$ factors. Furthermore, we give a space-efficient streaming algorithm for min-cut approximation. Along the way, we present an online algorithm for $(1+\varepsilon)$-hypergraph sparsification, which is optimal up to poly-logarithmic factors. Hence, we achieve $(1+\varepsilon)$-hypergraph sparsification in the sliding window model, with space optimal up to poly-logarithmic factors. Lastly, we give an adversarially robust algorithm for hypergraph sparsification using $\frac{n}{\varepsilon^2} \cdot $ poly $(r, \log n, \log r, \log \log m)$ bits of space.

With the rapid growth of spatio-temporal data fueled by IoT deployments and urban infrastructure expansion, accurate and efficient continual forecasting has become a critical challenge. Most existing Spatio-Temporal Graph Neural Networks rely on static graph structures and offline training, rendering them inadequate for real-world streaming scenarios characterized by graph expansion and distribution shifts. Although Continual Spatio-Temporal Forecasting methods have been proposed to tackle these issues, they often adopt backbones with limited modeling capacity and lack effective mechanisms to balance stability and adaptability. To overcome these limitations, we propose STBP, a novel framework that integrates a general spatio-temporal backbone with a scalable contextual pattern bank. The backbone extracts stable representations in the frequency domain and captures dynamic spatial correlations through lightweight linear graph attention. To support continual adaptation and mitigate catastrophic forgetting, the contextual pattern bank is updated incrementally via parameter expansion, enabling the capture of evolving node-level heterogeneity and relevance. During incremental training, the backbone remains fixed to preserve general knowledge, while the pattern bank adapts to new scenarios and distributions. Extensive experiments demonstrate that STBP outperforms state-of-the-art baselines in both forecasting accuracy and scalability, validating its effectiveness for continual spatio-temporal forecasting. Code is available at https://github.com/Aoyu-Liu/STBP.

Membrane potential perturbation dynamic (MPPD) is an emerging approach to capture perturbation intensity and stabilize the performance of spiking neural networks (SNN). It discards the neuronal reset part to intuitively reduce fluctuations of dynamics, but this treatment may be insufficient in perturbation characterization. In this study, we prove that MPPD is total variation (TV), which is a widely-used methodology for robust signal reconstruction. Moreover, we propose a novel TV-$\ell_1$ framework for MPPD, which allows for a wider range of network functions and has better denoising advantage than the existing TV-$\ell_2$ framework, based on the coarea formula. Experiments show that MPPD-TV-$\ell_1$ achieves robust performance in both Gaussian noise training and adversarial training for image classification tasks. This finding may provide a new insight into the essence of perturbation characterization.

Large Language Model (LLM) agents excel at multi-step, tool-augmented tasks. However, smart homes introduce distinct challenges, requiring agents to handle latent user intents, temporal dependencies, device constraints, scheduling, and more. The main bottlenecks for developing smart home agents with such capabilities include the lack of a realistic simulation environment where agents can interact with devices and observe the results, as well as a challenging benchmark to evaluate them. To address this, we introduce $\textbf{SimuHome}$, a time-accelerated home environment that simulates smart devices, supports API calls, and reflects changes in environmental variables. By building the simulator on the Matter protocol, the global industry standard for smart home communication, SimuHome provides a high-fidelity environment, and agents validated in SimuHome can be deployed on real Matter-compliant devices with minimal adaptation. We provide a challenging benchmark of 600 episodes across twelve user query types that require the aforementioned capabilities. Our evaluation of 16 agents under a unified ReAct framework reveals distinct capabilities and limitations across models. Models under 7B parameters exhibited negligible performance across all query types. Even GPT-4.1, the best-performing standard model, struggled with implicit intent inference, state verification, and particularly temporal scheduling. While reasoning models such as GPT-5.1 consistently outperformed standard models on every query type, they required over three times the average inference time, which can be prohibitive for real-time smart home applications. This highlights a critical trade-off between task performance and real-world practicality. We will release our code and dataset upon publication of the paper.

Quality-Diversity (QD) algorithms constitute a branch of optimization that is concerned with discovering a diverse and high-quality set of solutions to an optimization problem. Current QD methods commonly maintain diversity by dividing the behavior space into discrete regions, ensuring that solutions are distributed across different parts of the space. The QD problem is then solved by searching for the best solution in each region. This approach to QD optimization poses challenges in large solution spaces, where storing many solutions is impractical, and in high-dimensional behavior spaces, where discretization becomes ineffective due to the curse of dimensionality. We present an alternative framing of the QD problem, called \emph{Soft QD}, that sidesteps the need for discretizations. We validate this formulation by demonstrating its desirable properties, such as monotonicity, and by relating its limiting behavior to the widely used QD Score metric. Furthermore, we leverage it to derive a novel differentiable QD algorithm, \emph{Soft QD Using Approximated Diversity (SQUAD)}, and demonstrate empirically that it is competitive with current state of the art methods on standard benchmarks while offering better scalability to higher dimensional problems.

Autoregressive models (ARMs) are hindered by slow sequential inference. While masked diffusion models (MDMs) offer a parallel alternative, they suffer from critical drawbacks: high computational overhead from precluding Key-Value (KV) caching, and incoherent generation arising from learning dependencies over an intractable space of token combinations. To address these limitations, we introduce ReFusion, a novel masked diffusion model that achieves superior performance and efficiency by elevating parallel decoding from the token level to a higher slot level, where each slot is a fixed-length, contiguous sub-sequence. This is achieved through an iterative ``plan-and-infill'' decoding process: a diffusion-based planning step first identifies a set of weakly dependent slots, and an autoregressive infilling step then decodes these selected slots in parallel. The slot-based design simultaneously unlocks full KV cache reuse with a unified causal framework and reduces the learning complexity from the token combination space to a manageable slot-level permutation space. Extensive experiments on seven diverse benchmarks show that ReFusion not only overwhelmingly surpasses prior MDMs with 32\% performance gains and an over 10$\times$ speedup on average, but also bridges the performance gap to strong ARMs while maintaining a 1.4$\times$ average speedup.

Although multi-view multi-label learning has been extensively studied, research on the dual-missing scenario, where both views and labels are incomplete, remains largely unexplored. Existing methods mainly rely on contrastive learning or information bottleneck theory to learn consistent representations under missing-view conditions, but relying solely on loss-based constraints limits the ability to capture stable and discriminative shared semantics. To address this issue, we introduce a more structured mechanism for consistent representation learning: we learn discrete consistent representations through a multi-view shared codebook and cross-view reconstruction, which naturally align different views within the limited shared codebook embeddings and reduce redundant features. At the decision level, we design a weight estimation method that evaluates the ability of each view to preserve label correlation structures, assigning weights accordingly to enhance the quality of the fused prediction. In addition, we introduce a fused-teacher self-distillation framework, where the fused prediction guides the training of view-specific classifiers and feeds the global knowledge back into the single-view branches, thereby enhancing the generalization ability of the model under missing-label conditions. The effectiveness of our proposed method is thoroughly demonstrated through extensive comparative experiments with advanced methods on five benchmark datasets.

Imputing missing node features in graphs is challenging, particularly under high missing rates. Existing methods based on latent representations or global diffusion often fail to produce reliable estimates, and may propagate errors across the graph. We propose FSD-CAP, a two-stage framework designed to improve imputation quality under extreme sparsity. In the first stage, a graph-distance-guided subgraph expansion localizes the diffusion process. A fractional diffusion operator adjusts propagation sharpness based on local structure. In the second stage, imputed features are refined using class-aware propagation, which incorporates pseudo-labels and neighborhood entropy to promote consistency. We evaluated FSD-CAP on multiple datasets. With 99.5% of features missing across five benchmark datasets, FSD-CAP achieves average accuracies of 80.06% (structural) and 81.01% (uniform) in node classification, close to the 81.31% achieved by a standard GCN with full features. For link prediction under the same setting, it reaches AUC scores of 91.65% (structural) and 92.41% (uniform), compared to 95.06% for the fully observed case. Furthermore, FSD-CAP demonstrates superior performance on both large-scale and heterophily datasets when compared to other models. Code conducting all experiments can be found at https://anonymous.4open.science/r/FSD-CAP-50E8.

We present Aurelius, a new framework that enables relation aware text-to-audio (TTA) generation research at scale. Given the lack of essential audio event and relation corpora, \emph{Aurelius} contributes a large-scale audio event corpus \emph{AudioEventSet} and another large-scale relation corpus \emph{AudioRelSet}. Comprising 110 event categories, AudioEventSet maximally covers all commonly heard audio events and each event is unique, realistic and of high-quality. AudioRelSet consists of 100 relations, comprehensively covering the relations that present in the physical world or can be neatly described by text. As the two corpora provide audio event and relation independently, they can be combined to create massive <text,audio> pairs with our pair generation strategy to support relation aware TTA investigation at scale. We comprehensively benchmark all existing TTA models from both general and relation aware evaluation perspective. We further provide in-depth investigation on scaling up existing TTA models' relation aware generation by either training from scratch or leveraging cross-domain general TTA knowledge. The introduced corpora and the findings through investigation in this work potentially facilitate future research on relation aware TTA generation.

Fairness has become an arising concern in machine learning with its prevalence in decision-making processes, and the trade-offs between various fairness notions and between fairness and accuracy has been empirically observed. However, the inheritance of such trade-offs, as well as the quantification of the best achievable trade-offs, i.e., the Pareto optimal trade-offs, under varied constraints on fairness notions has been rarely and improperly discussed. Owing to the sub-optimality of fairness interventions, existing work fails to provide informative characterization regarding these trade-offs. In light of existing limitations, in this work, we propose a reformulation of the model-specific (MS) Pareto optimal trade-off, where we frame it as convex optimization problems involving fairness notions and accuracy w.r.t. the confusion vector. Our formulation provides an efficient approximation of the best achievable accuracy under dynamic fairness constraints, and yields systematical analysis regarding the fairness-accuracy trade-off. Going beyond the discussion on fairness-accuracy trade-offs, we extend the discussion to the trade-off between fairness notions, which characterizes the impact of accuracy on the compatibility between fairness notions. Inspired by our reformulation, we propose a last-layer retraining framework with group-dependent bias, and we prove theoretically the superiority of our method over existing baselines. Experimental results demonstrate the effectiveness of our method in achieving better fairness-accuracy trade-off, and that our MS Pareto frontiers sufficiently quantify the two trade-offs.

We study the learnability of languages in the *Next Symbol Prediction* (NSP) setting, where a learner receives only positive examples from a language together with, for every prefix, (i) whether the prefix itself is in the language and (ii) which next symbols can lead to an accepting string. This setting has been used in prior work to empirically analyze neural sequence models, and additionally, we observe that efficient algorithms for the NSP setting can be used to learn the (truncated) support of language models. We first show that the class of DFAs with at most $n$ states is identifiable from positive examples augmented with these NSP labels. Nevertheless, even with this richer supervision, we show that PAC-learning DFAs remains computationally hard, and exact identification using only membership queries cannot be achieved in polynomial time. We then present $\mathrm{L_{nsp}^{\star}}$, an extension of Angluin’s $\mathrm{L}^{\star}$ algorithm, and show that DFAs can be PAC-learned efficiently using a language-model–based teacher that answers membership queries and generates valid strings conditioned on prefix prompts. Finally, we conduct a comprehensive experimental evaluation on 11 regular languages of varying complexity. Using $\mathrm{L}^{\star}_{\text{nsp}}$, we extract DFAs from Transformer-based language models trained on regular languages to evaluate the algorithm’s effectiveness and identify erroneous examples.

Deployed time-series forecasters suffer performance degradation under non-stationarity and distribution shifts. Test-time adaptation (TTA) for time-series forecasting differs from vision TTA because ground truth becomes observable shortly after prediction. Existing time-series TTA methods typically employ dual input/output adapters that indirectly modify data distributions, making their effect on the frozen model difficult to analyze. We introduce the Context-aware Output-Space Adapter (COSA), a minimal, plug-and-play adapter that directly corrects predictions of a frozen base model. COSA performs residual correction modulated by gating, utilizing the original prediction and a lightweight context vector that summarizes statistics from recently observed ground truth. At test time, only the adapter parameters (linear layer and gating) are updated under a leakage-free protocol, using observed ground truth with an adaptive learning rate schedule for faster adaptation. Across diverse scenarios, COSA demonstrates substantial performance gains versus baselines without TTA (13.91$\sim$17.03\%) and SOTA TTA methods (10.48$\sim$13.05\%), with particularly large improvements at long horizons, while adding a reasonable level of parameters and negligible computational overhead. The simplicity of COSA makes it architecture-agnostic and deployment-friendly. Source code: https://anonymous.4open.science/r/linear-adapter-A720

Recent benchmarks and datasets have been proposed to improve spatial reasoning in vision-language models (VLMs), yet existing open resources remain limited in scale, visual diversity, and instruction expressiveness. In this work, we introduce InternSpatial, the largest open-source dataset for spatial reasoning in VLMs, along with InternSpatial-Bench, a corresponding evaluation benchmark designed to assess spatial understanding under diverse instruction formats. InternSpatial comprises 12 million QA pairs spanning both single-view and multi-view settings, drawn from diverse visual environments and supporting 19 instruction formats that reflect varied query styles. For evaluation, we propose InternSpatial-Bench for single-view tasks and expand multi-view reasoning by introducing a novel rotation angle prediction task that has not been explored in prior work. Experimental results show that models trained on InternSpatial achieve 12.1% improvement on InternSpatial-Bench and 10.7% on VSI-Bench, while maintaining strong performance on general-purpose benchmarks. We hope these resources will support the development of spatially capable VLMs in practical applications such as robotics and embodied AI.

Diffusion-based large language models (dLLMs) are trained to model extreme flexibility/dependence in the data-distribution; however, how to best utilize this at inference time remains an open problem. In this work, we uncover an interesting property of these models: dLLMs {trained on textual data} implicitly learn a mixture of semi-autoregressive experts, where different generation orders reveal different specialized behaviors. We show that committing to any single, fixed inference time schedule, a common practice, collapses performance by failing to leverage this latent ensemble. To address this, we introduce HEX (Hidden semi-autoregressive EXperts for test-time scaling), a training-free inference method that ensembles across heterogeneous block schedules. By doing a majority vote over diverse block-sized generation paths, HEX robustly avoids failure modes associated with any single fixed schedule. On reasoning benchmarks such as GSM8K, it boosts accuracy by up to 3.56× (from 24.72\% to 88.10\%), outperforming top-K margin inference and specialized fine-tuned methods like GRPO, without additional training. HEX even yields significant gains on MATH benchmark from 16.40\% to 40.00\%, scientific reasoning on ARC-C from 54.18\% to 87.80\%, and TruthfulQA from 28.36\% to 57.46\%. Our results establish test-time scaling as a powerful principle for dLLMs, showing that the sequence in which masking is done can play a significant role in test-time scaling/inferencing of dLLMs.

Spiking neural networks (SNNs) offer an energy-efficient alternative to traditional neural networks due to their event-driven computing paradigm. However, recent advancements in spiking transformers have focused on improving accuracy with large-scale architectures, which require significant computational resources and limit deployment on resource-constrained devices. In this paper, we propose a simple yet effective token pruning method for spiking transformers, termed TP-Spikformer, that reduces storage and computational overhead while maintaining competitive performance. Specifically, we first introduce a heuristic spatiotemporal information-retaining criterion that comprehensively evaluates tokens' importance, assigning higher scores to informative tokens for retention and lower scores to uninformative ones for pruning. Based on this criterion, we propose an information-retaining token pruning framework that employs a block-level early stopping strategy for uninformative tokens, instead of removing them outright. This also helps preserve more information during token pruning. We demonstrate the effectiveness, efficiency and scalability of TP-Spikformer through extensive experiments across diverse architectures, including Spikformer, QKFormer and Spike-driven Transformer V1 and V3, and a range of tasks such as image classification, object detection, semantic segmentation and event-based object tracking. Particularly, TP-Spikformer performs well in a training-free manner. These results reveal its potential as an efficient and practical solution for deploying SNNs in real-world applications with limited computational resources.

We study function spaces parametrized by neural networks, referred to as neuromanifolds. Specifically, we focus on deep Multi-Layer Perceptrons (MLPs) and Convolutional Neural Networks (CNNs) with an activation function that is a sufficiently generic polynomial. First, we address the identifiability problem, showing that, for almost all functions in the neuromanifold of an MLP, there exist only finitely many parameter choices yielding that function. For CNNs, the parametrization is generically one-to-one. As a consequence, we compute the dimension of the neuromanifold. Second, we describe singular points of neuromanifolds. We characterize singularities completely for CNNs, and partially for MLPs. In both cases, they arise from sparse subnetworks. For MLPs, we prove that these singularities often correspond to critical points of the mean-squared error loss, which does not hold for CNNs. This provides a geometric explanation of the sparsity bias of MLPs. All of our results leverage tools from algebraic geometry.