Geometric bias in eigenspace perturbation under random heterogeneous noise

Spectral methods rely fundamentally on the stability of principal eigenspaces under random perturbations. Classically, this stability is quantified by the Davis-Kahan and Wedin theorems, which bound the eigenspace error using the operator norm of the noise and the relevant spectral gaps. While these worst-case bounds are sharp for arbitrary deterministic perturbations, they can be wasteful in the low-rank signal-plus-random-noise setting, as they fail to capture the fine-grained interaction between the signal geometry and the noise distribution. In this paper, we study the spectral perturbation of signal-plus-noise matrices corrupted by sparse, random noise with an arbitrary, inhomogeneous variance profile. We demonstrate that under heterogeneous noise variances, the empirical eigenvectors suffer a systematic, deterministic geometric bias that is entirely invisible to classical perturbation bounds. By leveraging the Quadratic Vector Equation (QVE) and establishing fine-grained isotropic local laws, we derive near-optimal, non-asymptotic perturbation bounds for the leading eigenspaces in the operator and $2\to\infty$ norms. The bounds separate the usual signal-to-noise contribution, stochastic fluctuations, and structured geometric bias terms determined by the alignment between the signal eigenspaces and the row-wise variance profile.

Event-Driven Proactive Assistive Manipulation with Grounded Vision-Language Planning

Assistance in collaborative manipulation is often initiated by user instructions, making high-level reasoning request-driven. In fluent human teamwork, however, partners often infer the next helpful step from the observed outcome of an action rather than waiting for instructions. Motivated by this, we introduce a shift from request-driven assistance to event-driven proactive assistance, where robot actions are initiated by workspace state transitions induced by human--object interactions rather than user-provided task instructions. To this end, we propose an event-driven framework that tracks interaction progress with an event monitor and, upon event completion, extracts stabilized pre/post snapshots that characterize the resulting state transition. Given the stabilized snapshots, the planner analyzes the implied state transition to infer a task-level goal and decide whether to intervene; if so, it generates a sequence of assistive actions. To make outputs executable and verifiable, we restrict actions to a set of action primitives and reference objects via integer IDs. We evaluate the framework on a real tabletop number-block collaboration task, demonstrating that explicit pre/post state-change evidence improves proactive completion on solvable scenes and appropriate waiting on unsolvable ones.

Dynamic-I2V: Exploring Image-to-Video Generaion Models via Multimodal LLM

Recent advancements in image-to-video (I2V) generation have shown promising performance in conventional scenarios. However, these methods still encounter significant challenges when dealing with complex scenes that require a deep understanding of nuanced motion and intricate object-action relationships. To address these challenges, we present Dynamic-I2V, an innovative framework that integrates Multimodal Large Language Models (MLLMs) to jointly encode visual and textual conditions for a diffusion transformer (DiT) architecture. By leveraging the advanced multimodal understanding capabilities of MLLMs, our model significantly improves motion controllability and temporal coherence in synthesized videos. The inherent multimodality of Dynamic-I2V further enables flexible support for diverse conditional inputs, extending its applicability to various downstream generation tasks. Through systematic analysis, we identify a critical limitation in current I2V benchmarks: a significant bias towards favoring low-dynamic videos, stemming from an inadequate balance between motion complexity and visual quality metrics. To resolve this evaluation gap, we propose DIVE - a novel assessment benchmark specifically designed for comprehensive dynamic quality measurement in I2V generation. In conclusion, extensive quantitative and qualitative experiments confirm that Dynamic-I2V attains state-of-the-art performance in image-to-video generation, particularly revealing significant improvements of 42.5%, 7.9%, and 11.8% in dynamic range, controllability, and quality, respectively, as assessed by the DIVE metric in comparison to existing methods.