arXiv subjects

Hai Xia

Publications and source records attributed to Hai Xia.

4 recordsLinked to original sources

arXiv2026

Synthesizing Feature Extractors: An Agentic Approach for Algorithm Selection

Algorithm selection for constraint satisfaction problems requires extracting features that capture problem structure. Manually designing feature extractors demands deep domain expertise and quickly becomes a bottleneck when new problem classes appear. We present an automated approach that uses Large Language Models (LLMs) in an agentic check--fix--verify loop to synthesize executable Python scripts that act as interpretable, problem-specific feature extractors. Given a high-level MiniZinc model and an instance, the LLM agent generates code that constructs a typed graph representation and computes structural properties such as graph density, variable clustering, and constraint tightness. We evaluate our approach on three combinatorial problems (vehicle routing, car sequencing, fixed-length error-correcting codes) with a portfolio of five state-of-the-art solvers. The synthesized extractors yield algorithm selectors that consistently outperform both expert-curated mzn2feat features (up to $8.3$ percentage points (pp) test-set accuracy on FLECC) and the best transformer-based trans2feat variants. In the meanwhile, the synthesized feature extractors remain inspectable.

cs.AI↗

arXiv2026

LLM-Guided Graph Generation for Structure-Based Local Improvement Methods

Large neighborhood search normally selects a random subset of decision variables for iterative optimization. To efficiently solve various problems, researchers tend to design variable selection strategies that take into account structural features across different domains. In this paper, we build an automatic pipeline that is problem-agnostic to all problems in the MiniZinc format. By prompting an LLM with our semantic guidelines, we guide the LLM to produce a graph generator that maps any instance of a problem type to a uniform weighted graph, where nodes represent decision variables and edges represent constraint relationships. These problem-agnostic graphs guide our structure-based local improvement (SLIM) framework for variable selection. Meanwhile, the weighted graph enables all problem instances to share the same generic graph representation, from which the same graph features can be extracted and used for configuration selection. We evaluated our pipeline on instances across 20 MiniZinc competition problems, finding that algorithm selection achieves a 39.6% average problem-weighted win rate against a one-shot Gurobi baseline, more than doubling the best single configuration (19.3%). A post-hoc configuration and a feature ablation indicate a headroom of up to 44.0%, demonstrating that LLM-based semantic generation enables effective automated structure and feature extraction for constraint optimization.

cs.AI↗

arXiv2026

Agentic Neurosymbolic Collaboration for Mathematical Discovery: A Case Study in Combinatorial Design

We study mathematical discovery through the lens of neurosymbolic reasoning, where an AI agent powered by a large language model (LLM), coupled with symbolic computation tools, and human strategic direction, jointly produced a new result in combinatorial design theory. The main result of this human-AI collaboration is a tight lower bound on the imbalance of Latin squares for the notoriously difficult case $n \equiv 1 \pmod{3}$. We reconstruct the discovery process from detailed interaction logs spanning multiple sessions over several days and identify the distinct cognitive contributions of each component. The AI agent proved effective at uncovering hidden structure and generating hypotheses. The symbolic component consists of computer algebra, constraint solvers, and simulated annealing, which provides rigorous verification and exhaustive enumeration. Human steering supplied the critical research pivot that transformed a dead end into a productive inquiry. Our analysis reveals that multi-model deliberation among frontier LLMs proved reliable for criticism and error detection but unreliable for constructive claims. The resulting human-AI mathematical contribution, a tight lower bound of $4n(n{-}1)/9$, is achieved via a novel class of near-perfect permutations. The bound was formally verified in Lean 4. Our experiments show that neurosymbolic systems can indeed produce genuine discoveries in pure mathematics.

cs.AI↗

arXiv2025

Smart Cubing for Graph Search: A Comparative Study

Parallel solving via cube-and-conquer is a key method for scaling SAT solvers to hard instances. While cube-and-conquer has proven successful for pure SAT problems, notably the Pythagorean triples conjecture, its application to SAT solvers extended with propagators presents unique challenges, as these propagators learn constraints dynamically during the search. We study this problem using SAT Modulo Symmetries (SMS) as our primary test case, where a symmetry-breaking propagator reduces the search space by learning constraints that eliminate isomorphic graphs. Through extensive experimentation comprising over 10,000 CPU hours, we systematically evaluate different cube-and-conquer variants on three well-studied combinatorial problems. Our methodology combines prerun phases to collect learned constraints, various cubing strategies, and parameter tuning via algorithm configuration and LLM-generated design suggestions. The comprehensive empirical evaluation provides new insights into effective cubing strategies for propagator-based SAT solving, with our best method achieving speedups of 2-3x from improved cubing and parameter tuning, providing an additional 1.5-2x improvement on harder instances.

cs.AI↗