Not All Votes Count! Programs as Verifiers Improve Self-Consistency of Language Models for Math Reasoning
- URL: http://arxiv.org/abs/2410.12608v2
- Date: Tue, 17 Dec 2024 06:55:00 GMT
- Title: Not All Votes Count! Programs as Verifiers Improve Self-Consistency of Language Models for Math Reasoning
- Authors: Vernon Y. H. Toh, Deepanway Ghosal, Soujanya Poria,
- Abstract summary: We introduce Prove, a framework that leverages translated programs derived from natural language solutions as a verification mechanism.
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.
Our results show that Prove consistently outperforms vanilla majority voting for solving mathematical reasoning tasks across all model sizes and datasets.
- Score: 24.386388107656334
- License:
- 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.
Related papers
- UGMathBench: A Diverse and Dynamic Benchmark for Undergraduate-Level Mathematical Reasoning with Large Language Models [11.964085209696051]
UGMathBench comprises 5,062 problems across 16 subjects and 111 topics, featuring 10 distinct answer types.
Each problem includes three randomized versions, with additional versions planned for release as leading open-source LLMs become saturated in UGMathBench.
Our evaluation of 23 leading LLMs reveals that the highest EAcc robustness achieved is 56.3% by OpenAI-o1-mini, with large $Delta$ values observed across different models.
arXiv Detail & Related papers (2025-01-23T15:46:43Z) - Don't Trust: Verify -- Grounding LLM Quantitative Reasoning with Autoformalization [45.439933713342256]
Large language models (LLM) are becoming increasingly capable of solving mathematical quantitative reasoning problems.
We leverage the fact that if the training corpus of LLMs contained sufficiently many examples of formal mathematics, they can be prompted to translate into formal Isabelle code.
This provides a mechanism to automatically reject solutions whose formalized versions are inconsistent within themselves or with the formalized problem statement.
arXiv Detail & Related papers (2024-03-26T22:01:13Z) - GSM-Plus: A Comprehensive Benchmark for Evaluating the Robustness of LLMs as Mathematical Problem Solvers [68.77382332826167]
Large language models (LLMs) have achieved impressive performance across various mathematical reasoning benchmarks.
One essential and frequently occurring evidence is that when the math questions are slightly changed, LLMs can behave incorrectly.
This motivates us to evaluate the robustness of LLMs' math reasoning capability by testing a wide range of question variations.
arXiv Detail & Related papers (2024-02-29T15:26:14Z) - MAF: Multi-Aspect Feedback for Improving Reasoning in Large Language
Models [64.70153487607172]
Language Models (LMs) have shown impressive performance in various natural language tasks.
When it comes to natural language reasoning, LMs still face challenges such as hallucination, generating incorrect intermediate reasoning steps, and making mathematical errors.
Recent research has focused on enhancing LMs through self-improvement using feedback.
In this work, we propose Multi-Aspect Feedback, an iterative refinement framework that integrates multiple feedback modules, including frozen LMs and external tools, each focusing on a specific error category.
arXiv Detail & Related papers (2023-10-19T02:32:39Z) - MathPrompter: Mathematical Reasoning using Large Language Models [7.953723258038284]
Large Language Models (LLMs) have limited performance when solving arithmetic reasoning tasks.
MathPrompter uses the Zero-shot chain-of-thought prompting technique to generate multiple Algebraic expressions or Python functions to solve the same math problem in different ways.
arXiv Detail & Related papers (2023-03-04T04:43:49Z) - Large Language Models are Better Reasoners with Self-Verification [48.534270563880845]
Large language models (LLMs) have shown strong reasoning ability in several natural language processing tasks.
LLMs with chain of thought (CoT) prompting require multi-step prompting and multi-token prediction, which is highly sensitive to individual mistakes.
We propose and prove that LLMs also have similar self-verification abilities.
arXiv Detail & Related papers (2022-12-19T15:51:52Z) - PAL: Program-aided Language Models [112.94785609781503]
We present Program-Aided Language models (PaL) to understand natural language problems.
PaL offloads the solution step to a programmatic runtime such as a Python interpreter.
We set new state-of-the-art results in all 12 benchmarks.
arXiv Detail & Related papers (2022-11-18T18:56:13Z) - Making Large Language Models Better Reasoners with Step-Aware Verifier [49.16750018427259]
DIVERSE (Diverse Verifier on Reasoning Step) is a novel approach that further enhances the reasoning capability of language models.
We evaluate DIVERSE on the latest language model code-davinci and show that it achieves new state-of-the-art results on six of eight reasoning benchmarks.
arXiv Detail & Related papers (2022-06-06T03:38:36Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.