Title: SAIL: Leveraging LLMs to Generate Sound Abstract Interpreters

Abstract

The development of globally sound abstract interpreters capable of safely approximating program behavior continues to present a significant challenge in the field of abstract interpretation. This study demonstrates the efficacy of employing advanced Large Language Models (LLMs) to automate this labor-intensive task. Specifically targeting neural network verification, we utilize LLMs to synthesize complex, sound abstract transformers across a variety of abstract domains, exploring the solution space from the ground up. We frame this synthesis challenge as a constrained optimization problem, introducing a new, mathematically robust cost function designed to quantify the extent of unsoundness in each candidate transformer. Simultaneously, the system enforces strict syntactic and semantic validity constraints. Based on this framework, we present SAIL, an innovative unified approach that integrates model generation, rigorous validation, and cost-function-driven refinement to produce globally sound abstract transformers. Our evaluations indicate that SAIL achieves performance comparable to hand-crafted transformers. Furthermore, it successfully generates sound, high-precision transformers for complex non-linear operators that are absent from existing literature.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC