MC-NEST -- Enhancing Mathematical Reasoning in Large Language Models with a Monte Carlo Nash Equilibrium Self-Refine Tree
- URL: http://arxiv.org/abs/2411.15645v1
- Date: Sat, 23 Nov 2024 20:31:58 GMT
- Title: MC-NEST -- Enhancing Mathematical Reasoning in Large Language Models with a Monte Carlo Nash Equilibrium Self-Refine Tree
- Authors: Gollam Rabby, Farhana Keya, Parvez Zamil, Sören Auer,
- Abstract summary: We introduce the Monte Carlo Nash Equilibrium Self-Refine Tree (MC-NEST) algorithm, an enhancement of the Monte Carlo Tree Self-Refine (MCTSr) approach.
By integrating Nash Equilibrium strategies with LLM-based self-refinement and self-evaluation processes, MC-NEST aims to improve decision-making for complex mathematical reasoning tasks.
We evaluate the effectiveness of MC-NEST on challenging Olympiad-level benchmarks, demonstrating its potential to significantly boost complex mathematical reasoning performance in LLMs.
- Score: 0.14999444543328289
- License:
- Abstract: Mathematical reasoning has proven to be a critical yet challenging task for large language models (LLMs), as they often struggle with complex multi-step problems. To address these limitations, we introduce the Monte Carlo Nash Equilibrium Self-Refine Tree (MC-NEST) algorithm, an enhancement of the Monte Carlo Tree Self-Refine (MCTSr) approach. By integrating Nash Equilibrium strategies with LLM-based self-refinement and self-evaluation processes, MC-NEST aims to improve decision-making for complex mathematical reasoning tasks. This method ensures balanced exploration and exploitation of potential solutions, leveraging Upper Confidence Bound (UCT) scores and various selection policies. Through iterative critique and refinement, MC-NEST enhances the reasoning capabilities of LLMs, particularly for problems requiring strategic decision-making. Comparative analysis reveals that GPT-4o, equipped with MC-NEST using an Importance Sampling Policy, achieved superior accuracy in domains such as Number Theory and Geometry. These results suggest that both LLMs GPT-4o and Phi-3-mini can benefit from MC-NEST, with iterative self-refinement proving especially effective in expanding the reasoning capacity and problem-solving performance of LLMs. We evaluate the effectiveness of MC-NEST on challenging Olympiad-level benchmarks, demonstrating its potential to significantly boost complex mathematical reasoning performance in LLMs.
Related papers
- Teaching LLMs According to Their Aptitude: Adaptive Reasoning for Mathematical Problem Solving [55.895917967408586]
Existing approaches to mathematical reasoning with large language models rely on Chain-of-Thought (CoT) for generalizability or Tool-Integrated Reasoning (TIR) for precise computation.
We propose TATA (Teaching LLMs According to Their Aptitude), an adaptive framework that enables LLMs to personalize their reasoning strategy spontaneously.
arXiv Detail & Related papers (2025-02-17T16:56:23Z) - MME-CoT: Benchmarking Chain-of-Thought in Large Multimodal Models for Reasoning Quality, Robustness, and Efficiency [63.23935582919081]
Chain-of-Thought (CoT) has significantly enhanced the reasoning capabilities of Large Language Models (LLMs)
We introduce MME-CoT, a specialized benchmark evaluating the CoT reasoning performance of LMMs.
We conduct an in-depth analysis of state-of-the-art LMMs, uncovering several key insights.
arXiv Detail & Related papers (2025-02-13T18:59:46Z) - LLaMA-Berry: Pairwise Optimization for O1-like Olympiad-Level Mathematical Reasoning [56.273799410256075]
The framework combines Monte Carlo Tree Search (MCTS) with iterative Self-Refine to optimize the reasoning path.
The framework has been tested on general and advanced benchmarks, showing superior performance in terms of search efficiency and problem-solving capability.
arXiv Detail & Related papers (2024-10-03T18:12:29Z) - Accessing GPT-4 level Mathematical Olympiad Solutions via Monte Carlo Tree Self-refine with LLaMa-3 8B [48.45472563225202]
This paper introduces the MCT Self-Refine (MCTSr) algorithm, an innovative integration of Large Language Models (LLMs) with Monte Carlo Tree Search (MCTS)
The algorithm constructs a Monte Carlo search tree through iterative processes of Selection, self-refine, self-evaluation, and Backpropagation.
Extensive experiments demonstrate MCTSr's efficacy in solving Olympiad-level mathematical problems.
arXiv Detail & Related papers (2024-06-11T16:01:07Z) - AlphaMath Almost Zero: Process Supervision without Process [6.318873143509028]
We propose an innovative framework, AlphaMath, that bypasses the need for process annotations by leveraging Monte Carlo Tree Search (MCTS)
This framework focuses on unleashing the potential of a well-pretrained LLM to autonomously enhance its mathematical reasoning.
The experimental results on both in-domain and out-of-domain datasets demonstrate that even without GPT-4 or human-annotated process supervision, our AlphaMath framework achieves comparable or superior results to previous state-of-the-art methods.
arXiv Detail & Related papers (2024-05-06T15:20:30Z) - Toward Self-Improvement of LLMs via Imagination, Searching, and Criticizing [56.75702900542643]
We introduce AlphaLLM for the self-improvements of Large Language Models.
It integrates Monte Carlo Tree Search (MCTS) with LLMs to establish a self-improving loop.
Our experimental results show that AlphaLLM significantly enhances the performance of LLMs without additional annotations.
arXiv Detail & Related papers (2024-04-18T15:21:34Z) - NPHardEval: Dynamic Benchmark on Reasoning Ability of Large Language
Models via Complexity Classes [32.154637177467684]
NPHardEval is designed to evaluate the reasoning abilities of Large Language Models (LLMs) across a broad spectrum of 900 questions.
It is meticulously chosen to represent a wide range of complexity class below the NP-hard complexity class.
It is designed with a dynamic update mechanism, where the datapoints are refreshed on a monthly basis.
arXiv Detail & Related papers (2023-12-22T18:07:44Z) - SciBench: Evaluating College-Level Scientific Problem-Solving Abilities of Large Language Models [70.5763210869525]
We introduce an expansive benchmark suite SciBench for Large Language Model (LLM)
SciBench contains a dataset featuring a range of collegiate-level scientific problems from mathematics, chemistry, and physics domains.
The results reveal that the current LLMs fall short of delivering satisfactory performance, with the best overall score of merely 43.22%.
arXiv Detail & Related papers (2023-07-20T07:01:57Z)
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.