  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}.
