arXiv subjects

Zheyuan Lai

Publications and source records attributed to Zheyuan Lai.

5 recordsLinked to original sources

arXiv2026

When Shared Rollouts Fail in Defensive Driving Evaluation: A NAVSIM Score Basis Audit

Defensive driving scores are useful only when they preserve distinctions between policies that observe surrounding actors and those that do not. Re-simulation benchmarks may use reference-conditioned forgiveness, under which an agent receives credit when the logged human reference fails a compliance channel. When agent and reference share an unstable rollout transformation, this rule can propagate shared reference failures into broad compliance credit. We audit this risk in NAVSIM v2.2 original scene single-stage scoring. Under the affected documented-stack condition on the audited numerical backend, the route-blind Ignore-All probe and a route-aware actor-blind probe outrank human replay and PDM-Closed over the complete 12,146-token navtest split. A fresh installation following the public specification reproduces rollout divergence on a fixed 32-token diagnostic set. A same-source dependency stack control and an exact-input diagnostic isolate dependency-sensitive numerical behavior in the shared velocity refit. On a 450-token control pool, replacing only the solver eliminates rollout divergence and restores blind-last ordering while keeping forgiveness enabled. Thus, the numerical instability is the direct trigger. Reference-conditioned forgiveness propagates the resulting shared reference failures into compliance credit. We contribute an audit protocol requiring score basis and stack disclosure, blind probes, overwrite reporting, and rollout stability tests before using such scores for defensive driving claims.

cs.AI↗

arXiv2026

Information-theoretic coordinate subset and partition selection of multivariate Markov chains via submodular optimization

We study the problem of optimally projecting the transition matrix of a finite ergodic multivariate Markov chain onto a lower-dimensional state space, as well as the problem of finding an optimal partition of coordinates such that the factorized Markov chain gives minimal information loss compared to the original multivariate chain. Specifically, we seek to construct a Markov chain that optimizes various information-theoretic criteria under cardinality constraints. These criteria include entropy rate, information-theoretic distance to factorizability, independence, and stationarity. We formulate these tasks as best subset or partition selection problems over multivariate Markov chains and leverage the (k-)submodular (or (k-)supermodular) structures of the objective functions to develop efficient greedy-based algorithms with theoretical guarantees. Along the way, we introduce a generalized version of the distorted greedy algorithm, which may be of independent interest. Finally, we illustrate the theory and algorithms through extensive numerical experiments with publicly available code on multivariate Markov chains associated with the Bernoulli--Laplace and Curie--Weiss models.

math.PR↗

arXiv2026

Information-theoretic minimax and submodular optimization algorithms for multivariate Markov chains

We study an information-theoretic minimax problem for finite multivariate Markov chains on $d$-dimensional product state spaces. Given a family $\mathcal B=\{P_1,\ldots,P_n\}$ of $π$-stationary transition matrices and a class $\mathcal F = \mathcal{F}(\mathbf{S})$ of factorizable models induced by a partition $\mathbf S$ of the coordinate set $[d]$, we seek to minimize the worst-case information loss by analyzing $$\min_{Q\in\mathcal F}\max_{P\in\mathcal B} D_{\mathrm{KL}}^π(P\|Q),$$ where $D_{\mathrm{KL}}^π(P\|Q)$ is the $π$-weighted KL divergence from $Q$ to $P$. We recast the above minimax problem into concave maximization over the $n$-probability-simplex via strong duality and Pythagorean identities that we derive. This leads us to formulate an information-theoretic game and show that a mixed strategy Nash equilibrium always exists; and propose a projected subgradient algorithm to approximately solve the minimax problem with provable guarantee. By transforming the minimax problem into an orthant submodular function in $\mathbf{S}$, this motivates us to consider a max-min-max submodular optimization problem and investigate a two-layer subgradient-greedy procedure to approximately solve this generalization. Numerical experiments for Markov chains on the Curie-Weiss and Bernoulli-Laplace models illustrate the practicality of these proposed algorithms and reveals sparse optimal structures in these examples.

math.PR↗

arXiv2025

PriM: Principle-Inspired Material Discovery through Multi-Agent Collaboration

Complex chemical space and limited knowledge scope with biases holds immense challenge for human scientists, yet in automated materials discovery. Existing intelligent methods relies more on numerical computation, leading to inefficient exploration and results with hard-interpretability. To bridge this gap, we introduce a principles-guided material discovery system powered by language inferential multi-agent system (MAS), namely PriM. Our framework integrates automated hypothesis generation with experimental validation in a roundtable system of MAS, enabling systematic exploration while maintaining scientific rigor. Based on our framework, the case study of nano helix demonstrates higher materials exploration rate and property value while providing transparent reasoning pathways. This approach develops an automated-and-transparent paradigm for material discovery, with broad implications for rational design of functional materials. Code is publicly available at our \href{https://github.com/amair-lab/PriM}{GitHub}.

cs.LG↗

arXiv2024

ESP: Extro-Spective Prediction for Long-term Behavior Reasoning in Emergency Scenarios

Emergent-scene safety is the key milestone for fully autonomous driving, and reliable on-time prediction is essential to maintain safety in emergency scenarios. However, these emergency scenarios are long-tailed and hard to collect, which restricts the system from getting reliable predictions. In this paper, we build a new dataset, which aims at the long-term prediction with the inconspicuous state variation in history for the emergency event, named the Extro-Spective Prediction (ESP) problem. Based on the proposed dataset, a flexible feature encoder for ESP is introduced to various prediction methods as a seamless plug-in, and its consistent performance improvement underscores its efficacy. Furthermore, a new metric named clamped temporal error (CTE) is proposed to give a more comprehensive evaluation of prediction performance, especially in time-sensitive emergency events of subseconds. Interestingly, as our ESP features can be described in human-readable language naturally, the application of integrating into ChatGPT also shows huge potential. The ESP-dataset and all benchmarks are released at https://dingrui-wang.github.io/ESP-Dataset/.

cs.CV↗