PEA: Enhancing LLM Performance on Computational-Reasoning Tasks

TL;DR

This paper introduces the PEA framework, a formal method to improve LLMs' reasoning capabilities on computational tasks by decomposing problems into predicate and enumeration components, leading to significant accuracy gains.

Contribution

The paper presents the PEA framework, a novel formal approach for reasoning tasks that enhances LLM performance through program synthesis and execution.

Findings

Average accuracy improved by approximately 50% on benchmark tasks.

Demonstrated effectiveness on Boolean satisfiability, game of 24, and planning problems.

Increased efficiency in solving computational reasoning problems.

Abstract

Large Language Models (LLMs) have exhibited remarkable capabilities across diverse domains, prompting investigations into their potential as generic reasoning engines. While recent studies have explored inference-time computation to enhance model performance on complex problems, current research lacks a formal framework to characterize the complexity of reasoning tasks. This study introduces the Predicate-Enumeration-Aggregation (PEA) framework, a formal approach to describe and solve a class of important reasoning tasks termed computational reasoning problems. The PEA framework decomposes these problems into predicate and enumeration components, using LLMs to synthesize programs based on specified predicates, enumeration, and aggregation rules. These synthesized programs are then executed to obtain solutions to the computational tasks. We demonstrate the framework's efficacy on benchmark tasks including Boolean satisfiability problems, game of $24$, and planning problems. Empirical evaluation reveals that PEA substantially enhances the performance of underlying models on benchmark computational problems, yielding an average accuracy improvement of approximately $50\%$, coupled with increased efficiency.