Liangju Li | Searcharxiv

arXiv2026

OpenHome: From Perception to Insight in Smart-Home Camera Videos

Vision language models (VLMs) have been increasingly adopted in consumer smart-home camera systems to interpret recorded videos and provide insights. However, video clips captured from smart-home cameras are different from curated web videos dominating existing VLM benchmarks. Smart-home video clips often do not contain subtitles or narration and are captured from different viewing angles, under various lighting conditions, and in diverse scenarios. However, the capabilities of the model in this domain, under sparse visual signals and limited context, are not fully assessed by existing VLM benchmarks. To close this gap, we introduce OpenHome, a visual-only, four-option multiple-choice benchmark for evaluating smart-home video understanding. It contains 2,254 questions on 1,118 real-world video clips and organizes 10 tasks into three capability levels. Perception evaluates visible content, Reasoning evaluates causal, spatial, and temporal relationships, and Insight evaluates subject intent, supporting evidence and appropriate homeowner responses. Based on the dataset, we describe the task design, data pipeline and evaluation protocol, and report results for 32 closed-source and open-weight VLMs. The best model, Gemini 4 Argon, reaches 81.2% overall accuracy. Frontier closed-source models outperform open-weight models on every level. The best closed-source model leads the best open-weight model by 16.3% on Perception, 22.4% on Reasoning and 37.4% on Insight.

cs.CV↗

arXiv2026

A Geometric Perspective on Polynomially Solvable Convex Maximization

Convex maximization encompasses a broad class of optimization problems and is generally NP-hard, even for low-rank objectives. This paper investigates structural conditions under which convex maximization becomes polynomially solvable. From a geometric perspective, we introduce comonotonicity, a structural property of the feasible region crucial for problem tractability, and establish mathematical characterizations of this property. Under comonotonicity and mild additional assumptions, we develop a unified enumerative framework showing that fixed-rank convex maximization is polynomially solvable. This viewpoint recovers several known tractability results that previously required separate analyses, such as fixed-rank convex matroid maximization and sparse principal component analysis (SPCA). Furthermore, for the more structured class of standard comonotone feasible regions, we refine the analysis via a lifting technique to achieve a square-root improvement in the complexity bound. Finally, applications to SPCA and its variants illustrate the broad applicability and effectiveness of the proposed framework.

math.OC↗