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

Vernon Y. H. Toh, Deepanway Ghosal, Soujanya Poria

TL;DR

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, is introduced.

Abstract

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.

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

TL;DR

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, is introduced.

Abstract

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.

Paper Structure

This paper contains 35 sections, 6 equations, 7 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Prove
  3. Overview.
  4. Generating plan and solution.
  5. Translating plan and solution to Python program.
  6. Verification and selection.
  7. Experiments
  8. Setup
  9. Models and datasets.
  10. Implementation details.
  11. Baselines.
  12. Main Results
  13. Prove improves over baselines consistently on all evaluated LLMs across eight datasets.
  14. Prove provides larger performance gains for smaller models.
  15. Newer models closing the gap with larger ones.
  16. ...and 20 more sections

Figures (7)

  • Figure 1: Comparison of self-consistency and Prove.
  • Figure 2: Performance improvement of Prove over baseline methods across 13 LLMs evaluated on eight mathematical reasoning benchmarks.
  • Figure 3: The Prove Framework.
  • Figure 4: An actual example of the prompts used in our framework, along with the outputs generated by Phi3-mini-4k-instruct, for the GSM8K task.
  • Figure 5: Performance comparison of Prove and baseline methods across various LLMs evaluated on GSM8K with different numbers of samples.
  • ...and 2 more figures