arXiv subjects

Chenying Lin

Publications and source records attributed to Chenying Lin.

3 recordsLinked to original sources

arXiv2026

CAX-Agent: A Lightweight Agent Harness for Reliable APDL Automation

Large language models deployed for MAPDL finite-element simulation face practical reliability challenges: without structured execution control, tool encapsulation, and fault recovery, outputs may be inconsistent and task failures are common. The Agent Harness paradigm addresses this by inserting domain-specific orchestration middleware that manages tool lifecycles, workflow state, and recovery escalation. This paper presents the architecture of CAX-Agent, a lightweight agent harness purpose-built for MAPDL automation, and empirically evaluates one of its core components -- the recovery policy.CAX-Agent organizes execution into three layers -- LLM service, agent harness, and solver backend -- with a recovery ladder that escalates from deterministic rule patching through model-driven regeneration to context enrichment and human intervention. We evaluate three recovery strategies (no_recovery, rule_only, and model_only) on 50 standard structural benchmarks with three repeated runs per strategy (450 case-runs total). Two independent human raters score task completion under blind conditions; inter-rater agreement is strong (quadratic weighted Cohen's kappa = 0.84, 96 percent of score pairs within one point). Model_only achieves the best completion rate (0.9267), task score (3.59/4), total score (9.16/10), and zero-intervention rate (0.84), outperforming rule_only (0.7733, 3.17/4, 7.03/10, 0.00) and no_recovery (0.6933, 2.74/4, 5.60/10, 0.00) with large effect sizes (Cliff's delta = 0.81-0.87). The benchmark uses deliberately simple geometries to isolate recovery-policy effects; we discuss the scope of these findings and directions for broader validation.

cs.AI↗

arXiv2025

Kneser's theorem for codes and $\ell$-divisible set families

A $k$-wise $\ell$-divisible set family is a collection $\mathcal{F}$ of subsets of ${ \{1,\ldots,n \} }$ such that any intersection of $k$ sets in $\mathcal{F}$ has cardinality divisible by $\ell$. If $k=\ell=2$, it is well-known that $|\mathcal{F}|\leq 2^{\lfloor n/2 \rfloor}$. We generalise this by proving that $|\mathcal{F}|\leq 2^{\lfloor n/p\rfloor}$ if $k=\ell=p$, for any prime number $p$. For arbitrary values of $\ell$, we prove that $4\ell^2$-wise $\ell$-divisible set families $\mathcal{F}$ satisfy $|\mathcal{F}|\leq 2^{\lfloor n/\ell\rfloor}$ and that the only families achieving the upper bound are atomic, meaning that they consist of all the unions of disjoint subsets of size $\ell$. This improves upon a recent result by Gishboliner, Sudakov and Timon, that arrived at the same conclusion for $k$-wise $\ell$-divisible families, with values of $k$ that behave exponentially in $\ell$. Our techniques rely heavily upon a coding-theory analogue of Kneser's Theorem from additive combinatorics.

math.CO↗

arXiv2024

Galois orbits of torsion points over polytopes near atoral sets

Given an essentially atoral Laurent polynomial $P$, we show an equidistribution theorem for the function $\operatorname{log}|P|$ on specific subsets of Galois orbits of torsion points of the $d$-dimensional algebraic torus $\mathbb{G}^d_m(\overline{\mathbb{Q}})$. The specific subsets under consideration are the preimages of $d$-dimensional polytopes within the hypercube $[0,1]^d$ under the cotropicalization map. This generalises an equidistribution theorem of V. Dimitrov and P. Habegger, who considered only all Galois orbits that correspond to the entire hypercube $[0,1]^d$. In addition, we provide an estimate for the convergence speed of this equidistribution, expressed as a negative power of the strictness degree. Our approach is to derive an alternative version of Koksma's inequality over polytopes. As an application, we provide the convergence speed of heights on a sequence of projective points for a specific two-dimensional example, answering a question posed by R. Gualdi and M. Sombra. In the appendix, we present an algorithm to compute the explicit value of the power of the strictness degree.

math.NT↗