ICLR 2026 论文列表

Persistence spheres are a new functional representation of persistence diagrams. In contrast to existing embeddings such as persistence images, landscapes, or kernel-based methods, persistence spheres define a bi-continuous mapping: they are Lipschitz continuous with respect to the 1-Wasserstein distance and admit a continuous inverse on their image. This provides, in a theoretically optimal sense, both stability and geometric fidelity, so that persistence spheres are the representation that most closely preserves the Wasserstein geometry of PDs in a linear space. We derive explicit formulas for persistence spheres, show that they can be computed efficiently, and note that they parallelize with minimal overhead. Empirically, we evaluate them on clustering, regression, and classification tasks involving functional data, time series, graphs, meshes, and point clouds. Across these benchmarks, persistence spheres consistently achieve state-of-the-art or competitive performance when compared with persistence images, persistence landscapes, persistence splines, and the sliced Wasserstein kernel. Additional simulations in the appendices further support the method and provide practical guidance for tuning its parameters.

Federated Learning (FL) enables a group of clients to collaboratively train a model without sharing individual data, but its performance drops when client data are heterogeneous. Clustered FL tackles this by grouping similar clients. However, existing clustered FL approaches rely solely on either data similarity or gradient similarity; however, this results in an incomplete assessment of client similarities. Prior clustered FL approaches also restrict knowledge and representation sharing to clients within the same cluster. This prevents cluster models from benefiting from the diverse client population across clusters. To address these limitations, FEDDAG introduces a clustered FL framework, FEDDAG, that employs a weighted, class-wise similarity metric that integrates both data and gradient information, providing a more holistic measure of similarity during clustering. In addition, FEDDAG adopts a dual-encoder architecture for cluster models, comprising a primary encoder trained on its own clients' data and a secondary encoder refined using gradients from complementary clusters. This enables cross-cluster feature transfer while preserving cluster-specific specialization. Experiments on diverse benchmarks and data heterogeneity settings show that FEDDAG consistently outperforms state-of-the-art clustered FL baselines in accuracy.

Mixed-curvature spaces have emerged as a powerful alternative to their Euclidean counterpart, enabling data representations better aligned with the intrinsic structure of complex datasets. However, comparing probability distributions in such spaces remains underdeveloped: existing measures such as KL divergence and Wasserstein either rely on strong assumptions on distributions or incur high computational costs. The Sliced-Wasserstein (SW) framework provides an alternative approach for constructing distributional distances; however, its reliance on one-dimensional projections limits its ability to capture the geometry of the ambient space. To address this limitation, the Tree-Sliced Wasserstein (TSW) framework employs tree structures as a richer projected space. Motivated by the intuition that such a space is particularly suitable for representing the geometric properties of mixed-curvature manifolds, we introduce the Mixed-Curvature Tree-Sliced Wasserstein (MC-TSW), a novel discrepancy measure that is computationally efficient while faithfully capturing both the topological and geometric structures of mixed-curvature spaces. Specifically, we introduce an adaptation of tree systems and Radon transform to mixed-curvature spaces, which yields a closed-form solution for the optimal transport problem on the tree system. We further provide theoretical analysis on the properties of the Radon transform and the MC-TSW distance. Experimental results demonstrate that MC-TSW improves distributional comparisons over product-space-based distance and line-based baselines, and that mixed-curvature representations consistently outperform constant-curvature alternatives, highlighting their importance for modeling complex datasets.

Pluralism, the capacity to engage with diverse perspectives without collapsing them into a single viewpoint, is critical for developing large language models that faithfully reflect human heterogeneity. Yet this characteristic has not been carefully examined within the LLM research community and remains absent from most alignment studies. Debate-oriented sources provide a natural entry point for pluralism research. Previous work builds on online debate sources but remains constrained by costly human validation. Other debate-rich platforms such as Reddit and Kialo also offer promising material: Reddit provides linguistic diversity and scale but lacks clear argumentative structure, while Kialo supplies explicit pro/con graphs but remains overly concise and detached from natural discourse. We introduce PERSPECTRA, a pluralist benchmark that integrates the structural clarity of Kialo debate graphs with the linguistic diversity of real Reddit discussions. Using a controlled retrieval-and-expansion pipeline, we construct 3,810 enriched arguments spanning 762 pro/con stances on 100 controversial topics. Each opinion is expanded into multiple naturalistic variants, enabling robust evaluation of pluralism. We initialise three tasks with PERSPECTRA: opinion counting (identifying distinct viewpoints), opinion matching (aligning supporting stances and discourse to source opinions), and polarity check (inferring aggregate stance in mixed discourse). Experiments with state-of-the-art open-source and proprietary LLMs, highlight systematic failures, such as overestimating the number of viewpoints and misclassifying concessive structures, underscoring the difficulty of pluralism-aware understanding and reasoning. By combining diversity with structure, PERSPECTRA establishes the first scalable, configurable benchmark for evaluating how well models represent, distinguish, and reason over multiple perspectives. We release PERSPECTRA as a resource with flexible configurations, enabling the creation of tasks beyond the demo tasks presented in this paper, and fostering progress toward pluralism-sensitive systems that more faithfully capture human heterogeneity.

Recent advances in large-scale 3D scene reconstruction using unmanned aerial vehicles (UAVs) have spurred increasing interest in neural rendering techniques. However, existing approaches with conventional cameras struggle to capture consistent multi-view images of scenes, particularly in extremely blurred and low-light environments, due to the inherent limitations in dynamic range caused by long exposure and motion blur resulting from camera motion. As a promising solution, bio-inspired event cameras exhibit robustness in extreme scenarios, thanks to their high dynamic range and microsecond-level temporal resolution. Nevertheless, dedicated event datasets specifically tailored for large-scale UAV 3D scene reconstruction remain limited. To bridge this gap, we introduce \textbf{SkyEvents}, a pioneering large-scale event-enhanced UAV dataset for 3D scene reconstruction, incorporating RGB, event, and LiDAR data. SkyEvents encompasses 22 sequences, spanning over 8 hours of video, captured across a diverse set of illumination conditions, scenarios, and flight altitudes. To facilitate the event-based 3D scene reconstruction with SkyEvents, we propose the Geometry-constrained Timestamp Alignment (\textbf{GTA}) module to align timestamps between the event and RGB cameras. Furthermore, we introduce Region-wise Event Rendering (\textbf{RER}) loss for supervising the rendering optimization. With SkyEvents, we aim to motivate and equip researchers to advance large-scale 3D scene reconstruction in challenging environments, harnessing the unique strengths of event cameras. Dataset and code will be available at \url{https://}.

Kolmogorov–Arnold Networks (KANs) are a recently introduced neural architecture that replace fixed nonlinearities with trainable activation functions, offering enhanced flexibility and interpretability. While KANs have been applied successfully across scientific and machine learning tasks, their initialization strategies remain largely unexplored. In this work, we study initialization schemes for spline-based KANs, proposing two theory-driven approaches inspired by LeCun and Glorot, as well as an empirical power-law family with tunable exponents. Our evaluation combines large-scale grid searches on function fitting and forward PDE benchmarks, an analysis of training dynamics through the lens of the Neural Tangent Kernel, and evaluations on a subset of the Feynman dataset. Our findings indicate that the Glorot-inspired initialization significantly outperforms the baseline in parameter-rich models, while power-law initialization achieves the strongest performance overall, both across tasks and for architectures of varying size. This work underscores initialization as a key factor in KAN performance and introduces practical strategies to improve it.

Recent progress in the reasoning capabilities of multimodal large language models (MLLMs) has empowered them to address more complex tasks such as scientific analysis and mathematical reasoning. Despite their promise, MLLMs’ reasoning abilities across different scenarios in real life remain largely unexplored and lack standardized benchmarks for evaluation. To address this gap, we introduce MMR-Life, a comprehensive benchmark designed to evaluate the diverse multimodal multi-image reasoning capabilities of MLLMs across real-life scenarios. MMR-Life consists of 2,676 multiple-choice questions based on 19,367 images primarily sourced from real-world contexts, comprehensively covering seven reasoning types: abductive, analogical, causal, deductive, inductive, spatial, and temporal. Unlike existing reasoning benchmarks, MMR-Life does not rely on domain-specific expertise but instead requires models to integrate information across multiple images and apply diverse reasoning abilities. The evaluation of 37 advanced models highlights the substantial challenge posed by MMR-Life. Even top models like GPT-5 achieve only 58% accuracy and display considerable variance in performance across reasoning types. Moreover, we analyze the reasoning paradigms of existing MLLMs, exploring how factors such as thinking length, reasoning method, and reasoning type affect their performance. In summary, MMR-Life establishes a comprehensive foundation for evaluating, analyzing, and improving the next generation of multimodal reasoning systems.

Assessing the privacy of large language models (LLMs) presents significant challenges. In particular, most existing methods for auditing *differential privacy* require the insertion of specially crafted canary data *during training*, making them impractical for auditing already-trained models without costly retraining. Additionally, *dataset inference*, which audits whether a suspect dataset was used to train a model, is *infeasible* without access to a private non-member held-out dataset. Yet, such held-out datasets are often unavailable or difficult to construct for real-world cases since they have to be from the same distribution (IID) as the suspect data. These limitations severely hinder the ability to conduct scalable, *post-hoc* audits. To enable such audits, this work introduces **natural identifiers (NIDs)** as a novel solution to the above-mentioned challenges. NIDs are structured random strings, such as cryptographic hashes and shortened URLs, naturally occurring in common LLM training datasets. Their format enables the generation of unlimited additional random strings from the same distribution, which can act as alternative canaries for audits and as same-distribution held-out data for dataset inference. Our evaluation highlights that indeed, using NIDs, we can facilitate post-hoc differential privacy auditing *without any retraining* and enable dataset inference for any suspect dataset containing NIDs without the need for a private non-member held-out dataset.

Large Language Models (LLMs) have demonstrated outstanding capabilities in various code-related tasks, including code completion, translation, or summarization. However, these pretrained models are static, posing a challenge to incorporate new knowledge into an LLM to correct erroneous behavior. Approaches such as retraining or fine-tuning demand extensive labeled datasets and might be computationally expensive, while prompt engineering fails to change models permanently. Knowledge Editing (KE) techniques offer a more efficient alternative, enabling model updates with minimal data, even just a single example. Nevertheless, existing KE methods often manipulate parameters within the Transformer's multi-layer perceptrons (MLPs), where neuronal polysemanticity hinders both the precision and interpretability of the edits. To address these limitations, we exploit TransCoder, an MLP-like model component with a wide and sparsely activated hidden feature vector. Specifically, we introduce **TransCoder-based Precise Editing** (**TCPE**), a novel method that leverages the sparsity and monosemanticity of the TransCoder’s neurons for highly localized knowledge editing. TCPE exhibits neuron-level mechanistic interpretability characteristics, revealing the correspondence between the edited neurons and the specific code-related knowledge. Furthermore, we present KECode, a new evaluation benchmark for code-to-code translation based on functional equivalence. Using KECode, we conduct a systematic evaluation of representative KE methods in the context of code-to-code translation. Our experimental results demonstrate that TCPE outperforms existing KE methods, achieving a substantial improvement of translation accuracy of CodeLlama-7b-Instruct from 57.5% to 64.0% in a low-resource scenario of Java-to-D translation.

Text-to-image (T2I) models have achieved remarkable success in generating high-fidelity images, but they often fail in handling complex spatial relationships, e.g., spatial perception, reasoning, or interaction. These critical aspects are largely overlooked by current benchmarks due to their short or information-sparse prompt design. In this paper, we introduce SpatialGenEval, a new benchmark designed to systematically evaluate the spatial intelligence of T2I models, covering two key aspects: (1) SpatialGenEval involves 1,230 long, information-dense prompts across 25 real-world scenes. Each prompt integrates 10 spatial sub-domains and corresponding 10 multi-choice question-answer pairs, ranging from object position and layout to occlusion and causality. Our extensive evaluation of 21 state-of-the-art models reveals that higher-order spatial reasoning remains a primary bottleneck. (2) To demonstrate that the utility of our information-dense design goes beyond simple evaluation, we also construct the SpatialT2I dataset. It contains 15,400 text-image pairs with rewritten prompts to ensure image consistency while preserving information density. Fine-tuned results on current foundation models (\ie, Stable Diffusion-XL, Uniworld-V1, OmniGen2) yield consistent performance gains (+4.2%, +5.7%, +4.4%) and more realistic effects in spatial relations, highlighting a data-centric paradigm to achieve spatial intelligence in T2I models.

This paper introduces GraphOmni, a comprehensive benchmark designed to evaluate the reasoning capabilities of LLMs on graph-theoretic tasks articulated in natural language. GraphOmni spans diverse graph types, serialization formats, and prompting schemes, substantially extending upon prior efforts in both scope and depth. Through systematic evaluation, we uncover critical interactions among these dimensions, revealing their decisive impact on model performance. Our experiments show that state-of-the-art closed-source models such as Claude-3.5 and o4-mini consistently lead overall, yet still leave considerable headroom, while open-source models display pronounced sensitivity to various design choices. Beyond the standard scope, larger graphs, real-world graphs, and additional NP-hard tasks are further discussed. We further analyze efficiency via output token usage, highlighting cost–accuracy trade-offs, and introduce a reinforcement learning-based optimizer that adaptively selects factor combinations, reducing evaluation cost by 75\% while retaining strong accuracy. This flexible and extensible benchmark not only deepens understanding of LLM performance on structured graph reasoning but also establishes a robust foundation for advancing model design and evaluation.

Generalist multimodal large language models (MLLMs) have achieved impressive performance across a wide range of vision-language tasks. However, their performance on medical tasks—particularly in zero-shot settings where generalization is critical—remains suboptimal. A key research gap is the limited understanding of why medical MLLMs underperform in medical image interpretation. **In this work**, we present a pioneering systematic investigation into the visual grounding capabilities of state-of-the-art medical MLLMs. To disentangle *visual grounding* from *semantic grounding*, we design VGMED, a novel evaluation dataset developed with expert clinical guidance, explicitly assessing the visual grounding capability of medical MLLMs. We introduce new quantitative metrics and conduct detailed qualitative analyses. Our study across **eight** state-of-the-art (SOTA) medical MLLMs validates that they often fail to ground their predictions in clinically relevant image regions. We note that this finding is specific to medical image analysis; in contrast, prior work has shown that MLLMs are capable of grounding their predictions in the correct image regions when applied to natural scene images. Motivated by these findings, we propose VGRefine, a simple yet effective inference-time method that refines attention distribution to improve visual grounding in medical settings. Our approach achieves SOTA performance across 6 diverse Med-VQA benchmarks (over 110K VQA samples from 8 imaging modalities) without requiring additional training or external expert models. Overall, our work, for the first time, systematically validates inadequate visual grounding as one of the key contributing factors for medical MLLMs' under-performance. Code and additional experiments are included in the Supp.

Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields. Despite their remarkable capacity for representing geometric structures, ENNs suffer from degraded expressivity when processing symmetric inputs: the output representations are invariant to transformations that extend beyond the input's symmetries. The mathematical essence of this phenomenon is that a symmetric input, after being processed by an equivariant map, experiences an increase in symmetry. While prior research has documented symmetry increase in specific cases, a rigorous understanding of its underlying causes and general reduction strategies remains lacking. In this paper, we provide a detailed and in-depth characterization of symmetry increase together with a principled framework for its reduction: (i) For any given feature space and input symmetry group, we prove that the increased symmetry admits an infimum determined by the structure of the feature space; (ii) Building on this foundation, we develop a computable algorithm to derive this infimum, and propose practical guidelines for feature design to prevent harmful symmetry increases. (iii) Under standard regularity assumptions, we demonstrate that for most equivariant maps, our guidelines effectively reduce symmetry increase. To complement our theoretical findings, we provide visualizations and experiments on both synthetic datasets and the real-world QM9 dataset. The results validate our theoretical predictions.

Recently, Multimodal Large Language Models (MLLMs) have achieved exceptional performance across diverse tasks, continually surpassing previous expectations regarding their capabilities. Nevertheless, their proficiency in perceiving emotions from images remains debated, with studies yielding divergent results in zero-shot scenarios. We argue that this inconsistency stems partly from constraints in existing evaluation methods, including the oversight of plausible responses, limited emotional taxonomies, neglect of contextual factors, and labor-intensive annotations. To facilitate customized visual emotion evaluation for MLLMs, we propose an Emotion Statement Judgment task that overcomes these constraints. Complementing this task, we devise an automated pipeline that efficiently constructs emotion-centric statements with minimal human effort. Through systematically evaluating prevailing MLLMs, our study showcases their stronger performance in emotion interpretation and context-based emotion judgment, while revealing relative limitations in comprehending perception subjectivity. When compared to humans, even top-performing MLLMs like GPT4o demonstrate remarkable performance gaps, underscoring key areas for future improvement. By developing a fundamental evaluation framework and conducting a comprehensive MLLM assessment, we hope this work contributes to advancing emotional intelligence in MLLMs. Project page: https://github.com/wdqqdw/MVEI.

Body composition analysis through CT and MRI imaging provides critical insights for cardio-metabolic health assessment but remains limited by accessibility barriers including radiation exposure, high costs, and infrastructure requirements. We present AbdCTBench, a large-scale dataset containing 23,506 CT-derived abdominal surface meshes from 18,719 patients, paired with 87 comorbidity labels, 31 specific diagnosis codes, and 16 CT-derived biomarkers. Our key insight is that external surface geometry is predictive of internal tissue composition, enabling accessible health screening through consumer devices. We establish comprehensive benchmarks across seven computer vision architectures (ResNet-18/34/50, DenseNet-121, EfficientNet-B0, ViT-Small, Swin Transformer-Base), demonstrating that models can learn robust surface-to-biomarker representations directly from 2D mesh projections. Our best-performing models achieve clinically relevant accuracy: age prediction with MAE 6.22 years (R²=0.757), mortality prediction with AUROC 0.839, and diabetes (with chronic complications) detection with AUROC 0.801. Notably, smaller architectures consistently matched or surpassed larger models, while medical-domain pre-training (RadImageNet) and self-supervised pre-training (DINOv2) showed competitive but not superior performance. AbdCTBench represents the largest publicly available dataset bridging external body geometry with internal clinical measurements, enabling future research in accessible medical AI. We plan to release the dataset, evaluation protocols, and baseline models to accelerate research in representation learning for medical applications, immediately following the review period.

With the increasing deployment of machine learning models trained on personal data, machine unlearning has become crucial for data owners to exercise their "right to be forgotten" and protect their privacy. While model owners can retrain the models without the erased data to achieve this goal, this process is often prohibitively expensive. Previous works have shown that Newton's method can be applied to linear models to unlearn multiple data points in batch (batch unlearning) with minimal iterations. However, adapting this method to non-linear models, such as neural networks, poses significant challenges due to the presence of degenerate Hessians. This problem becomes more pronounced when unlearning is performed sequentially (sequential unlearning). Existing techniques that tried to tackle this degeneracy often 1) incur unlearning updates with excessively large norm that yield unsatisfactory unlearning performance and 2) may require manual tuning of regularization hyperparameters. In this work, we propose new unlearning algorithms that leverage cubic regularization for Newton's method to address both challenges. We discuss the theoretical benefits of our method and empirically show that our algorithms can efficiently achieve competitive performance in both batch and sequential unlearning on real-world datasets.

Formulaic alpha factor mining (FAFM) is a central problem in quantitative investment, where interpretable formulas are designed to extract predictive signals from historical financial series. With the emergence of large language models (LLMs), recent studies have begun to explore their roles in FAFM, yet their capabilities across different tasks and configurations remain unclear. In this work, we introduce AlphaBench, the first systematic benchmark for evaluating LLMs in FAFM. AlphaBench covers three core tasks, including factor generation, factor evaluation, and factor searching, which are all popular tasks integrated in the workflow of quantitative researchers. Beyond task-level evaluation, we further analyze how different LLM settings, including model type, prompting paradigm, and reasoning strategy, influence performance. Our experiments on a range of open-source and closed-source models reveal that LLMs hold strong potential in automating factor mining, while also facing persistent challenges in robustness, search efficiency, and practical usability. The project is available at: https://alphabench.cc/

Monocular normal estimation aims to estimate normal map from a single RGB image of an object under arbitrary lighting. Existing methods rely on deep models to directly predict normal maps. However, they often suffer from 3D misalignment: while the estimated normal maps may appear to have an overall correct color distribution, the reconstructed surfaces frequently fail to align with the geometry details. We argue that this misalignment stems from the current paradigm: the model struggles to distinguish and reconstruct spatially-various geometric, as they are represented in normal maps only by relatively subtle color variations. To address this issue, we propose a new paradigm that reformulates normal estimation as shading sequence estimation, where shading sequences are more sensitive to various geometry information. Building on this paradigm, we present RoSE, a method that leverages image-to-video generative models to predict shading sequences. The predicted shading sequences are then converted into normal maps by solving a simple ordinary least-squares problem. To enhance robustness and better handle complex objects, RoSE is trained on a synthetic dataset, dataset, with diverse shapes, materials, and light conditions. Experiments demonstrate that RoSE achieves state-of-the-art performance on real-world benchmark datasets for object-based monocular normal estimation. Codes and dataset will be released to facilitate reproducible research.

Although generative models have made remarkable progress in recent years, their use in critical applications has been hindered by an inability to reliably evaluate the quality of their generated samples. Quality refers to at least two complementary concepts: fidelity and coverage. Current quality metrics often lack reliable, interpretable values due to an absence of calibration or insufficient robustness to outliers. To address these shortcomings, we introduce two novel metrics: $\textit{Clipped Density}$ and $\textit{Clipped Coverage}$. By clipping individual sample contributions, as well as the radii of nearest neighbor balls for fidelity, our metrics prevent out-of-distribution samples from biasing the aggregated values. Through analytical and empirical calibration, these metrics demonstrate linear score degradation as the proportion of bad samples increases. Thus, they can be straightforwardly interpreted as equivalent proportions of good samples. Extensive experiments on synthetic and real-world datasets demonstrate that $\textit{Clipped Density}$ and $\textit{Clipped Coverage}$ outperform existing methods in terms of robustness, sensitivity, and interpretability when evaluating generative models.