aiqbench analysis
SAIL demonstrates a viable approach to automating the synthesis of sound abstract transformers for neural network verification using LLMs, effectively addressing a longstanding bottleneck in program behavior approximation. By framing the task as a constrained optimization problem with mathematically grounded cost functions, the framework successfully generates high-precision transformers for complex non-linear operators that surpass existing literature. This work marks a significant step toward scalable, automated formal verification methods within programming languages and machine learning safety.
SAIL: Sound Abstract Interpreters with LLMs
arXiv:2511.13663v2 Announce Type: replace-cross Abstract: How to construct globally sound abstract interpreters to safely approximate program behaviors remains a bottleneck in abstract interpretation. In this paper, we show the potential of using state-of-the-art LLMs to automate this tedious process. Focusing on the neural network verification area, we synthesize non-trivial sound abstract transformers across diverse abstract domains using LLMs to search within infinite space from scratch. We formalize the synthesis task as a constrained optimization problem, for which we design a novel mathematically grounded cost function that measures the degree of unsoundness of each generated candidate transformer, while enforcing hard syntactic and semantic validity constraints. Building on this formulation, we introduce SAIL, a novel unified framework that combines model generation, syntactic and semantic validation, and cost-function-based refinement to synthesize globally sound abstract transformers. Evaluation results show that SAIL not only matches the performance of manually designed transformers, but also is able to synthesize sound and high-precision transformers that do not exist in the literature for complex non-linear operators.
Abstract:How to construct globally sound abstract interpreters to safely approximate program behaviors remains a bottleneck in abstract interpretation. In this paper, we show the potential of using state-of-the-art LLMs to automate this tedious process. Focusing on the neural network verification area, we synthesize non-trivial sound abstract transformers across diverse abstract domains using LLMs to search within infinite space from scratch. We formalize the synthesis task as a constrained optimization problem, for which we design a novel mathematically grounded cost function that measures the degree of unsoundness of each generated candidate transformer, while enforcing hard syntactic and semantic validity constraints. Building on this formulation, we introduce SAIL, a novel unified framework that combines model generation, syntactic and semantic validation, and cost-function-based refinement to synthesize globally sound abstract transformers. Evaluation results show that SAIL not only matches the performance of manually designed transformers, but also is able to synthesize sound and high-precision transformers that do not exist in the literature for complex non-linear operators.
Programming Languages (cs.PL); Machine Learning (cs.LG)
arXiv:2511.13663 [cs.PL]
(or arXiv:2511.13663v2 [cs.PL] for this version)
https://doi.org/10.48550/arXiv.2511.13663 Focus to learn more arXiv-issued DOI via DataCite
Proc. ACM Program. Lang. 10, PLDI, Article 230, 26 pages (2026)
https://doi.org/10.1145/3808308 Focus to learn more DOI(s) linking to related resources
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