Ranking LLM-Generated Loop Invariants for Program Verification

TL;DR

This paper introduces a re-ranking method for Large Language Model-generated loop invariants that improves the selection of correct invariants, reducing verifier calls and enhancing program verification efficiency.

Contribution

We propose a contrastive re-ranking approach that effectively distinguishes correct invariants from incorrect ones generated by LLMs, improving verification performance.

Findings

Re-ranking significantly increases correct invariant selection

Reduces number of verifier calls needed

Enhances automation in program verification

Abstract

Synthesizing inductive loop invariants is fundamental to automating program verification. In this work, we observe that Large Language Models (such as gpt-3.5 or gpt-4) are capable of synthesizing loop invariants for a class of programs in a 0-shot setting, yet require several samples to generate the correct invariants. This can lead to a large number of calls to a program verifier to establish an invariant. To address this issue, we propose a {\it re-ranking} approach for the generated results of LLMs. We have designed a ranker that can distinguish between correct inductive invariants and incorrect attempts based on the problem definition. The ranker is optimized as a contrastive ranker. Experimental results demonstrate that this re-ranking mechanism significantly improves the ranking of correct invariants among the generated candidates, leading to a notable reduction in the number of calls to a verifier. The source code and the experimental data for this paper are available in \url{https://github.com/microsoft/NeuralInvariantRanker}.