Understanding user intent is essential for situational and context-aware decisionmaking.

Computer vision for animals holds great promise for wildlife research but often depends on large-scale data, while existing collection methods rely on controlled capture setups. Recent data-driven approaches show the potential of single-view, non-invasive analysis, yet current animal video datasets are limited--offering as few as 2.4K 15-frame clips and lacking key processing for animal-centric 3D/4D tasks. We introduce an automated pipeline that mines YouTube videos and processes them into object-centric clips, along with auxiliary annotations valuable for downstream tasks like pose estimation, tracking, and 3D/4D reconstruction. Using this pipeline, we amass 30K videos (2M frames)--an order of magnitude more than prior works. To demonstrate its utility, we focus on the 4D quadruped animal reconstruction task. To support this task, we present Animal-in-Motion (AiM), a benchmark of 230 manually filtered sequences with 11K frames showcasing clean, diverse animal motions. We evaluate state-of-the-art model-based and model-free methods on Animal-in-Motion, finding that 2D metrics favor the former despite unrealistic 3D shapes, while the latter yields more natural reconstructions but scores lower--revealing a gap in current evaluation. To address this, we enhance a recent model-free approach with sequence-level optimization, establishing the first 4D animal reconstruction baseline. Together, our pipeline, benchmark, and baseline aim to advance large-scale, markerless 4D animal reconstruction and related tasks from in-the-wild videos.

Estimating hidden states in dynamical systems, also known as optimal filtering, is a long-standing problem in various fields of science and engineering. In this paper, we introduce a general filtering framework, LLM-Filter1, which leverages large language models (LLMs) for state estimation by embedding noisy observations with text prototypes. In various experiments for classical dynamical systems, we find that first, state estimation can significantly benefit from the reasoning knowledge embedded in pre-trained LLMs. By achieving proper modality alignment with the frozen LLM, LLM-Filter outperforms the state-of-the-art learning-based approaches. Second, we carefully design the prompt structure, System-as-Prompt (SaP), incorporating task instructions that enable the LLM to understand the estimation tasks. Guided by these prompts, LLM-Filter exhibits exceptional generalization, capable of performing filtering tasks accurately in changed or even unseen environments. We further observe a scaling-law behavior in LLM-Filter, where accuracy improves with larger model sizes and longer training times. These findings make LLM-Filter a promising foundation model of filtering.

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.

We provide novel information-theoretic generalization bounds for stochastic gradient Langevin dynamics (SGLD) under the assumptions of smoothness and dissipativity, which are widely used in sampling and non-convex optimization studies. Our bounds are time-independent and decay to zero as the sample size increases, regardless of the number of iterations and whether the step size is fixed. Unlike previous studies, we derive the generalization error bounds by focusing on the time evolution of the Kullback-Leibler divergence, which is related to the stability of datasets and is the upper bound of the mutual information between output parameters and an input dataset. Additionally, we establish the first information-theoretic generalization bound when the training and test loss are the same by showing that a loss function of SGLD is sub-exponential. This bound is also time-independent and removes the problematic step size dependence in existing work, leading to an improved excess risk bound by combining our analysis with the existing non-convex optimization error bounds.

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.

Understanding the dynamics of optimization in deep learning is increasingly important as models scale. While stochastic gradient descent (SGD) and its variants reliably find solutions that generalize well, the mechanisms driving this generalization remain unclear. Notably, these algorithms often prefer flatter or simpler minima--particularly in overparameterized settings. Prior work has linked flatness to generalization, and methods like Sharpness-Aware Minimization (SAM) explicitly encourage flatness, but a unified theory connecting data structure, optimization dynamics, and the nature of learned solutions is still lacking. In this work, we develop a linear stability framework that analyzes the behavior of SGD, random perturbations, and SAM--particularly in two-layer ReLU networks. Central to our analysis is a coherence measure that quantifies how gradient curvature aligns across data points, revealing why certain minima are stable and favored during training.

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.

Large language models (LLMs) have achieved impressive success, but their high memory requirements present challenges for long-context token generation. In this paper we study the streaming complexity of attention approximation, a key computational primitive underlying token generation. Our main contribution is BalanceKV, a streaming algorithm for ϵ-approximating attention computations based on geometric process for selecting a balanced collection of Key and Value tokens as per Banaszczyk's vector balancing theory. We complement our algorithm with space lower bounds for streaming attention computation. Besides strong theoretical guarantees, BalanceKV exhibits empirically validated performance improvements over existing methods, both for attention approximation and end-to-end performance on various long context benchmarks.

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.