arXiv subjects

Zihao Dai

Publications and source records attributed to Zihao Dai.

4 recordsLinked to original sources

arXiv2026

ResearchEnvBench: Benchmarking Agents on Environment Synthesis for Research Code Execution

Autonomous agents are increasingly expected to support scientific research, and recent benchmarks report progress in code repair and autonomous experimentation. However, these evaluations typically assume a pre-configured execution environment, which requires resolving complex software dependencies, aligning hardware and framework versions, and configuring distributed execution, yet this capability remains largely unbenchmarked. We introduce ResearchEnvBench, a benchmark for environment synthesis in research code execution. Given a research repository, documentation, and a target execution setting, agents must construct an environment that successfully executes at runtime. Evaluations on diverse research repositories reveal a substantial gap in current SOTA agents, with failures dominated by incomplete dependency resolution and brittle version coupling. ResearchEnvBench provides a realistic testbed for advancing autonomous agents toward reproducible scientific research.

cs.SE↗

arXiv2026

An Algorithm for Diagonalizing Matrices of Formal Power Series

This paper studies the unitary diagonalization of matrices over formal power series rings. Our main result shows that a normal matrix is unitarily diagonalizable if and only if its minimal polynomial completely splits over the ring and the associated spectral projections have entries in the ring. Building on this characterization, we develop an algorithm for deciding the unitary diagonalizability of matrices over regular local rings of algebraic varieties. A central ingredient of the algorithm is a decision procedure for determining whether a polynomial splits over a formal power series ring; we establish this using techniques from prime decomposition and the relative smoothness of integral closures in ramification theory.

math.AC↗

arXiv2025

LIBERO-Plus: In-depth Robustness Analysis of Vision-Language-Action Models

Visual-Language-Action (VLA) models report impressive success rates on robotic manipulation benchmarks, yet these results may mask fundamental weaknesses in robustness. We perform a systematic vulnerability analysis by introducing controlled perturbations across seven dimensions: objects layout, camera viewpoints, robot initial states, language instructions, light conditions, background textures and sensor noise. We comprehensively analyzed multiple state-of-the-art models and revealed consistent brittleness beneath apparent competence. Our analysis exposes critical weaknesses: models exhibit extreme sensitivity to perturbation factors, including camera viewpoints and robot initial states, with performance dropping from 95% to below 30% under modest perturbations. Surprisingly, models are largely insensitive to language variations, with further experiments revealing that models tend to ignore language instructions completely. Our findings challenge the assumption that high benchmark scores equate to true competency and highlight the need for evaluation practices that assess reliability under realistic variation.

cs.RO↗

arXiv2024

Whitney Stratification of Algebraic Boundaries of Convex Semi-algebraic Sets

Algebraic boundaries of convex semi-algebraic sets are closely related to polynomial optimization problems. Building upon Rainer Sinn's work, we refine the stratification of iterated singular loci to a Whitney (a) stratification, which gives a list of candidates of varieties whose dual is an irreducible component of the algebraic boundary of the dual convex body. We also present an algorithm based on Teissier's criterion to compute Whitney (a) stratifications, which employs conormal spaces and prime decomposition.

math.OC↗