Graph convolutional neural networks (GCNNs) have emerged as powerful tools for analyzing graph-structured data, achieving remarkable success across diverse applications. However, the theoretical understanding of the stability of these models, i.e., their sensitivity to small changes in the graph structure, remains in rather limited settings, hampering the development and deployment of robust and trustworthy models in practice. To fill this gap, we study how perturbations in the graph topology affect GCNN outputs and propose a novel formulation for analyzing model stability. Unlike prior studies that focus only on worst-case perturbations, our distribution-aware formulation characterizes output perturbations across a broad range of input data. This way, our framework enables, for the first time, a probabilistic perspective on the interplay between the statistical properties of the node data and perturbations in the graph topology. We conduct extensive experiments to validate our theoretical findings and demonstrate their benefits over existing baselines, in terms of both representation stability and adversarial attacks on downstream tasks. Our results demonstrate the practical significance of the proposed formulation and highlight the importance of incorporating data distribution into stability analysis.

With origins in game theory, probabilistic values like Shapley values, Banzhaf values, and semi-values have emerged as a central tool in explainable AI. They are used for feature attribution, data attribution, data valuation, and more. Since all of these values require exponential time to compute exactly, research has focused on efficient approximation methods using two techniques: Monte Carlo sampling and linear regression formulations. In this work, we present a new way of combining both of these techniques. Our approach is more flexible than prior algorithms, allowing for linear regression to be replaced with any function family whose probabilistic values can be computed efficiently. This allows us to harness the accuracy of tree-based models like XGBoost, while still producing unbiased estimates. From experiments across eight datasets, we find that our methods give state-of-the-art performance for estimating probabilistic values. For Shapley values, the error of our methods can be 6.5 lower than Permutation SHAP (the most popular Monte Carlo method), 3.8 lower than Kernel SHAP (the most popular linear regression method), and 2.6 lower than Leverage SHAP (the prior stateof-the-art Shapley value estimator). For more general probabilistic values, we can obtain error 215 lower than the best estimator from prior work.

This work introduces a hybrid non-Euclidean optimization method which generalizes gradient norm clipping by combining steepest descent and conditional gradient approaches. The method achieves the best of both worlds by establishing a descent property under a generalized notion of (L0,L1)-smoothness. Weight decay is incorporated in a principled manner by identifying a connection to the Frank-Wolfe short step. In the stochastic case, we show an order optimal O(n 1/4) convergence rate by leveraging a momentum based gradient estimator. We discuss how to instantiate the algorithms for deep learning, which we dub Clipped Scion, and demonstrate their properties on image classification and language modeling.

Specifically, through clustering, we first identify 1,291 user-focused topics from the million-scale real text-to-video prompt dataset, VidProM. Then, we use these topics to retrieve videos from YouTube, split the retrieved videos into clips, the clips and with generate specified both brief topics, and we detailed are left captions with about for each 1.09 clip. million After video verifying clips. Our experiments reveal that (1) current 16 text-to-video models do not achieve consistent performance across all user-focused topics; and (2) a simple model trained on VideoUFO outperforms others on worst-performing topics. The dataset and code are publicly available here and here under the CCBY 4.0 License.

We study the online multi-class selection problem with group fairness guarantees, where limited resources must be allocated to sequentially arriving agents.

Plus: Anthropic has shut down access to its top models after a US directive. That's good for our health, but bad for the planet: it already accounts for 7% of global electricity use and 3% of greenhouse-gas emissions. Feeling the heat, scientists and startups are hoping to amp up solid-state cooling. These systems move heat through conductive materials, which could cool spaces and surfaces with fewer messy side effects. The catch is whether it can match the efficiency of traditional AC. Find out how the unconventional coolers aim to dial down AC emissions .

Text-guided image editing has been allowing users to transform and synthesize images through natural language instructions, offering considerable flexibility. However, most existing image editing models naively attempt to follow all user instructions, even if those instructions are inherently infeasible or contradictory, often resulting in nonsensical output. To address these challenges, we propose a contextaware method for image editing named as CAMILA (Context-Aware Masking for Image Editing with Language Alignment). CAMILA is designed to validate the contextual coherence between instructions and the image, ensuring that only relevant edits are applied to the designated regions while ignoring non-executable instructions. For comprehensive evaluation of this new method, we constructed datasets for both single-and multi-instruction image editing, incorporating the presence of infeasible requests. Our method achieves better performance and higher semantic alignment than state-of-the-art models, demonstrating its effectiveness in handling complex instruction challenges while preserving image integrity.

Iterative imputation is a prevalent method for missing data imputation, where each feature is imputed iteratively by treating it as a target variable estimated from all other features. However, iterative imputation method suffers from two principal limitations: it imposes a single parametric model form to impute all features, neglecting the potential for optimal models to vary among features, which risks model misspecification; and it assumes every feature contains missing values, overlooking the potential presence of non-missing features, termed as oracle features, which are informative for imputation. To address these limitations, we propose kernel point imputation (KPI), a bi-level optimization framework for iterative missing data imputation. At the inner level, KPI adaptively learns the optimal model form for each feature within a reproducing kernel Hilbert space, addressing limitation . At the outer level, KPI utilizes oracle features as supervisory signals to iteratively refine the imputations, addressing limitation . Experiments demonstrate that KPI outperforms competitive imputation methods. Code is available at https://github.com/FMLYD/kpi.git.

Mathematical modeling is a cornerstone of scientific discovery and engineering practice, enabling the translation of real-world problems into formal systems across domains such as physics, biology, and economics. Unlike mathematical reasoning, which assumes a predefined formulation, modeling requires open-ended problem analysis, abstraction, and principled formalization. While Large Language Models (LLMs) have shown strong reasoning capabilities, they fall short in rigorous model construction, limiting their utility in real-world problem-solving. To this end, we formalize the task of LLM-powered real-world mathematical modeling, where agents must analyze problems, construct domain-appropriate formulations, and generate complete end-to-end solutions. We introduce MM-Bench, a curated benchmark of 111 problems from the Mathematical Contest in Modeling (MCM/ICM) 1, spanning the years 2000 to 2025 and across ten diverse domains such as physics, biology, and economics. To tackle this task, we propose MM-Agent, an expertinspired framework that decomposes mathematical modeling into four stages: openended problem analysis, structured model formulation, computational problem solving, and report generation. Experiments on MM-Bench show that MM-Agent significantly outperforms baseline agents, achieving an 11.88% improvement over human expert solutions while requiring only 15 minutes and $0.88 per task using GPT-4o. Furthermore, under official MCM/ICM protocols, MM-Agent assisted two undergraduate teams in winning the Finalist Award (top 2.0% among 27,456 teams) in MCM/ICM 2025, demonstrating its practical effectiveness as a modeling copilot.

Federated clustering (FC) aims to discover global cluster structures across decentralized clients without sharing raw data, making privacy preservation a fundamental requirement. There are two critical challenges: (1) privacy leakage during collaboration, and (2) robustness degradation due to aggregation of proxy information from non-independent and identically distributed (Non-IID) local data, leading to inaccurate or inconsistent global clustering. Existing solutions typically rely on model-specific local proxies, which are sensitive to data heterogeneity and inherit inductive biases from their centralized counterparts, thus limiting robustness and generality. We propose Omni Federated Clustering (OmniFC), a unified and modelagnostic framework. Leveraging Lagrange coded computing, our method enables clients to share only encoded data, allowing exact reconstruction of the global distance matrix--a fundamental representation of sample relationships--without leaking private information, even under client collusion. This construction is naturally resilient to Non-IID data distributions. This approach decouples FC from model-specific proxies, providing a unified extension mechanism applicable to diverse centralized clustering methods. Theoretical analysis confirms both reconstruction fidelity and privacy guarantees, while comprehensive experiments demonstrate OmniFC's superior robustness, effectiveness, and generality across various benchmarks compared to state-of-the-art methods.