# Not All Votes Count! Programs as Verifiers Improve Self-Consistency of Language Models for Math Reasoning

arXiv: https://arxiv.org/abs/2410.12608 · HTML: https://mlsanity.com/paper/2410.12608/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 10 of its 35 references that are in the map.
- First posted on arXiv 16 Oct 2024.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

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

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [LLMs Will Always Hallucinate, and We Need to Live With This](https://mlsanity.com/paper/2409.05746/) (2024)
- [Improving LLM Reasoning through Scaling Inference Computation with Collaborative Verification](https://mlsanity.com/paper/2410.05318/) (2024)

## Built on by (most cited first, 9 of 9)

- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [A Survey of Test-Time Compute: From Intuitive Inference to Deliberate Reasoning](https://mlsanity.com/paper/2501.02497/) (2025)
- [Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving](https://mlsanity.com/paper/2505.20869/) (2025)
- [Integrating Expert Knowledge into Logical Programs via LLMs](https://mlsanity.com/paper/2502.12275/) (2025)
- [Guided by the Plan: Enhancing Faithful Autoregressive Text-to-Audio Generation with Guided Decoding](https://mlsanity.com/paper/2601.14304/) (2026)
- [RETuning: Upgrading Inference-Time Scaling for Stock Movement Prediction with Large Language Models](https://mlsanity.com/paper/2510.21604/) (2025)
- [KACE: Knowledge-Adaptive Context Engineering for Mathematical Reasoning](https://mlsanity.com/paper/2606.00532/) (2026)
- [Routing Without Training: Controllable-Ratio LLM Offloading via Reliability Gating](https://mlsanity.com/paper/2607.20481/) (2026)
- [ACED: Reference-Anchored Aggregation of Natural-Language and Executable Evidence for Mathematical Reasoning](https://mlsanity.com/paper/2610.16635/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have shown increasing competence in solving mathematical reasoning problems. However, many open-source LLMs still struggle with errors in calculation and semantic understanding during intermediate reasoning steps. In this work, we introduce Prove, a simple yet effective framework that leverages translated programs derived from natural language solutions as a verification mechanism to filter out potentially incorrect reasoning paths before aggregating final answers. Unlike vanilla majority voting, our approach filters out solutions whose corresponding program output is inconsistent with the generated solution, aggregating only those that pass verification. We conducted extensive experiments using 13 open-source LLMs from various model families and sizes, ranging from 0.5B to 13B parameters, across eight mathematical benchmarks. Our results show that Prove consistently outperforms vanilla majority voting as a heuristic for solving mathematical reasoning tasks across all model sizes and datasets, achieving improvements of up to 18% on GSM8K and 8% on MATH-500. Our codes are available at https://github.com/declare-lab/prove.