# A Neurosymbolic Approach to Loop Invariant Generation via Weakest Precondition Reasoning

arXiv: https://arxiv.org/abs/2512.15816 · HTML: https://mlsanity.com/paper/2512.15816/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 10 of its 29 references that are in the map.
- First posted on arXiv 17 Dec 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 10 of 10)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [The Prompt Report: A Systematic Survey of Prompt Engineering Techniques](https://mlsanity.com/paper/2406.06608/) (2024)
- [Enchanting Program Specification Synthesis by Large Language Models using Static Analysis and Program Verification](https://mlsanity.com/paper/2404.00762/) (2024)
- [Can Large Language Models Transform Natural Language Intent into Formal Method Postconditions?](https://mlsanity.com/paper/2310.01831/) (2023)
- [SpecGen: Automated Generation of Formal Program Specifications via Large Language Models](https://mlsanity.com/paper/2401.08807/) (2024)
- [Lemur: Integrating Large Language Models in Automated Program Verification](https://mlsanity.com/paper/2310.04870/) (2023)
- [Finding Inductive Loop Invariants using Large Language Models](https://mlsanity.com/paper/2311.07948/) (2023)
- [Can ChatGPT support software verification?](https://mlsanity.com/paper/2311.02433/) (2023)
- [Invariant Generation for Multi-Path Loops with Polynomial Assignments](https://mlsanity.com/paper/1801.03967/) (2018)
- [SymInfer: Inferring Program Invariants using Symbolic States](https://mlsanity.com/paper/1903.11768/) (2019)

## Abstract (arXiv)

Loop invariant generation remains a critical bottleneck in automated program verification. Recent work has begun to explore the use of Large Language Models (LLMs) in this area, yet these approaches tend to lack a reliable and structured methodology, with little reference to existing program verification theory. This paper presents NeuroInv, a neurosymbolic approach to loop invariant generation. NeuroInv comprises two key modules: (1) a neural reasoning module that leverages LLMs and Hoare logic to derive and refine candidate invariants via backward-chaining weakest precondition reasoning, and (2) a verification-guided symbolic module that iteratively repairs invariants using counterexamples from OpenJML. We evaluate NeuroInv on a comprehensive benchmark of 150 Java programs, encompassing single and multiple (sequential) loops, multiple arrays, random branching, and noisy code segments. NeuroInv achieves a 99.5% success rate, substantially outperforming the other evaluated approaches. Additionally, we introduce a hard benchmark of 10 larger multi-loop programs (with an average of 7 loops each); NeuroInv's performance in this setting demonstrates that it can scale to more complex verification scenarios.