# Token-Supervised Value Models for Enhancing Mathematical Problem-Solving Capabilities of Large Language Models

arXiv: https://arxiv.org/abs/2407.12863 · HTML: https://mlsanity.com/paper/2407.12863/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 10 of its 18 references that are in the map.
- First posted on arXiv 12 Jul 2024.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 10 of 10)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [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)
- [Multi-step Problem Solving Through a Verifier: An Empirical Analysis on Model-induced Process Supervision](https://mlsanity.com/paper/2402.02658/) (2024)

## Built on by (most cited first, 8 of 8)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [AdaptiveStep: Automatically Dividing Reasoning Step through Model Confidence](https://mlsanity.com/paper/2502.13943/) (2025)
- [Generative AI Act II: Test Time Scaling Drives Cognition Engineering](https://mlsanity.com/paper/2504.13828/) (2025)
- [A Survey on Feedback-based Multi-step Reasoning for Large Language Models on Mathematics](https://mlsanity.com/paper/2502.14333/) (2025)
- [RFEval: Benchmarking Reasoning Faithfulness under Counterfactual Reasoning Intervention in Large Reasoning Models](https://mlsanity.com/paper/2602.17053/) (2026)
- [Enhancing Large Language Model Reasoning with Reward Models: An Analytical Survey](https://mlsanity.com/paper/2510.01925/) (2025)
- [Reward Modeling for Reinforcement Learning-Based LLM Reasoning: Design, Challenges, and Evaluation](https://mlsanity.com/paper/2602.09305/) (2026)
- [Unlocking Token Rewards via Training-Free Reward Attribution](https://mlsanity.com/paper/2610.18704/) (2026)

## Abstract (arXiv)

With the rapid advancement of test-time compute search strategies to improve the mathematical problem-solving capabilities of large language models (LLMs), the need for building robust verifiers has become increasingly important. However, all these inference strategies rely on existing verifiers originally designed for Best-of-N search, which makes them sub-optimal for tree search techniques at test time. During tree search, existing verifiers can only offer indirect and implicit assessments of partial solutions or under-value prospective intermediate steps, thus resulting in the premature pruning of promising intermediate steps. To overcome these limitations, we propose token-supervised value models (TVMs) - a new class of verifiers that assign each token a probability that reflects the likelihood of reaching the correct final answer. This new token-level supervision enables TVMs to directly and explicitly evaluate partial solutions, effectively distinguishing between promising and incorrect intermediate steps during tree search at test time. Experimental results demonstrate that combining tree-search-based inference strategies with TVMs significantly improves the accuracy of LLMs in mathematical problem-solving tasks, surpassing the performance of existing verifiers.