# MC-NEST: Enhancing Mathematical Reasoning in Large Language Models leveraging a Monte Carlo Self-Refine Tree arXiv: https://arxiv.org/abs/2411.15645 ยท HTML: https://mlsanity.com/paper/2411.15645/ ## Key facts - Cited by 7 papers in the map (data through 14 Oct 2026). - Placed in Mathematical reasoning, one of 17 directions in LLM reasoning. - Builds on 31 of its 42 references that are in the map. - First posted on arXiv 23 Nov 2024. ## Placed in - LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/) ## Builds on (most cited first, 30 of 31) - [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023) - [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022) - [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021) - [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020) - [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021) - [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022) - [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021) - [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023) - [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017) - [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023) - [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022) - [AlpacaFarm: A Simulation Framework for Methods that Learn from Human Feedback](https://mlsanity.com/paper/2305.14387/) (2023) - [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023) - [Complexity-Based Prompting for Multi-Step Reasoning](https://mlsanity.com/paper/2210.00720/) (2022) - [Self-critiquing models for assisting human evaluators](https://mlsanity.com/paper/2206.05802/) (2022) - [The Faiss library](https://mlsanity.com/paper/2401.08281/) (2024) - [Evaluating Large Language Models at Evaluating Instruction Following](https://mlsanity.com/paper/2310.07641/) (2023) - [Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training](https://mlsanity.com/paper/2309.17179/) (2023) - [AlphaMath Almost Zero: Process Supervision without Process](https://mlsanity.com/paper/2405.03553/) (2024) - [Monte Carlo Tree Search: A Review of Recent Modifications and Applications](https://mlsanity.com/paper/2103.04931/) (2021) - [Accessing GPT-4 level Mathematical Olympiad Solutions via Monte Carlo Tree Self-refine with LLaMa-3 8B](https://mlsanity.com/paper/2406.07394/) (2024) - [Comparing Humans, GPT-4, and GPT-4V On Abstraction and Reasoning Tasks](https://mlsanity.com/paper/2311.09247/) (2023) - [MathOdyssey: Benchmarking Mathematical Problem-Solving Skills in Large Language Models Using Odyssey Math Data](https://mlsanity.com/paper/2406.18321/) (2024) - [Bidirectional Language Models Are Also Few-shot Learners](https://mlsanity.com/paper/2209.14500/) (2022) - [No Train Still Gain. Unleash Mathematical Reasoning of Large Language Models with Monte Carlo Tree Search Guided by Energy Function](https://mlsanity.com/paper/2309.03224/) (2023) - [Critique Ability of Large Language Models](https://mlsanity.com/paper/2310.04815/) (2023) - [Monte-Carlo Tree Search for Multi-Agent Pathfinding: Preliminary Results](https://mlsanity.com/paper/2307.13453/) (2023) - [PhyPlan: Compositional and Adaptive Physical Task Reasoning with Physics-Informed Skill Networks for Robot Manipulators](https://mlsanity.com/paper/2402.15767/) (2024) - [An Integrated Framework Integrating Monte Carlo Tree Search and Supervised Learning for Train Timetabling Problem](https://mlsanity.com/paper/2311.00971/) (2023) - [General Method for Solving Four Types of SAT Problems](https://mlsanity.com/paper/2312.16423/) (2023) ## Built on by (most cited first, 7 of 7) - [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025) - [Generative AI Act II: Test Time Scaling Drives Cognition Engineering](https://mlsanity.com/paper/2504.13828/) (2025) - [ProRefine: Inference-Time Prompt Refinement with Textual Feedback](https://mlsanity.com/paper/2506.05305/) (2025) - [Iterative Hypothesis Generation for Scientific Discovery with Monte Carlo Nash Equilibrium Self-Refining Trees](https://mlsanity.com/paper/2503.19309/) (2025) - [AlphaApollo: A System for Deep Agentic Reasoning](https://mlsanity.com/paper/2510.06261/) (2025) - [Test-time Scaling of LLMs: A Survey from A Subproblem Structure Perspective](https://mlsanity.com/paper/2511.14772/) (2025) - [From Knowledge to Action: Outcomes of the 2025 Large Language Model (LLM) Hackathon for Applications in Materials Science and Chemistry](https://mlsanity.com/paper/2605.03205/) (2026) ## Abstract (arXiv) Mathematical reasoning presents significant challenges for large language models (LLMs). To enhance their capabilities, we propose Monte Carlo Self-Refine Tree (MC-NEST), an extension of Monte Carlo Tree Search that integrates LLM-based self-refinement and self-evaluation for improved decision-making in complex reasoning tasks. MC-NEST balances exploration and exploitation using Upper Confidence Bound (UCT) scores combined with diverse selection policies. Through iterative critique and refinement, LLMs learn to reason more strategically. Empirical results demonstrate that MC-NEST with an importance sampling policy substantially improves GPT-4o's performance, achieving state-of-the-art pass@1 scores on Olympiad-level benchmarks. Specifically, MC-NEST attains a pass@1 of 38.6 on AIME and 12.6 on MathOdyssey. The solution quality for MC-NEST using GPT-4o and Phi-3-mini reaches 84.0% and 82.08%, respectively, indicating robust consistency across different LLMs. MC-NEST performs strongly across Algebra, Geometry, and Number Theory, benefiting from its ability to handle abstraction, logical deduction, and multi-step reasoning -- core skills in mathematical problem solving.