Navigating the Labyrinth: Evaluating and Enhancing LLMs’ Ability to Reason About Search Problems

Nasim Borazjanizadeh, Roei Herzig, Trevor Darrell, Rogerio Feris, Leonid Karlinsky

Keywords: Mathematical & reasoning benchmark, Search & Combinatorial problems, A* algorithm

TL;DR: We introduce a novel benchmark of unique combinatorial problems that advanced LLMs fail to solve, and present a prompting and inference method using A* algorithm that significantly improves LLMs' performance.

Abstract: Recently, Large Language Models (LLMs) attained impressive performance in math and reasoning benchmarks. However, they still often struggle with multi-step reasoning which is relatively easy for humans. To further investigate this, we introduce a new benchmark, SearchBench, containing 11 unique combinatorial problems that avoid training contamination (each equipped with automated pipelines to generate an arbitrary number of instances) and analyze the feasibility, correctness, and optimality of LLM-generated solutions. We show that even the most advanced LLMs fail to solve these problems end-to-end in text, e.g., GPT4 and o1-preview respectively solve only 1.4% and 18.6% correctly. SearchBench problems require considering multiple pathways to the solution and backtracking, posing a significant challenge to auto-regressive models. Instructing LLMs to generate code that solves the problem helps only slightly. We next introduce an in-context learning approach that prompts the model to implement A*, an informed search algorithm, to comprehensively traverse the problem state space, improving the performance of models. We further extend this approach and propose the Multi-Stage-Multi-Try inference method which breaks down the A* algorithm implementation into two stages and auto-verifies the first stage against unit tests, raising GPT-4's performance above 57%.

Primary Area: datasets and benchmarks

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Submission Number: 7467