# OVM, Outcome-supervised Value Models for Planning in Mathematical Reasoning

arXiv: https://arxiv.org/abs/2311.09724 · HTML: https://mlsanity.com/paper/2311.09724/

## Key facts

- Cited by 85 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 18 of its 26 references that are in the map.
- First posted on arXiv 16 Nov 2023.

## Placed in

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

## Builds on (most cited first, 18 of 18)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Reasoning with Language Model is Planning with World Model](https://mlsanity.com/paper/2305.14992/) (2023)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Selection-Inference: Exploiting Large Language Models for Interpretable Logical Reasoning](https://mlsanity.com/paper/2205.09712/) (2022)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training](https://mlsanity.com/paper/2309.17179/) (2023)
- [Making Large Language Models Better Reasoners with Step-Aware Verifier](https://mlsanity.com/paper/2206.02336/) (2022)
- [Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verification](https://mlsanity.com/paper/2308.07921/) (2023)
- [Generate & Rank: A Multi-task Framework for Math Word Problems](https://mlsanity.com/paper/2109.03034/) (2021)
- [Solving Math Word Problems via Cooperative Reasoning induced Language Models](https://mlsanity.com/paper/2210.16257/) (2022)
- [MuggleMath: Assessing the Impact of Query and Response Augmentation on Math Reasoning](https://mlsanity.com/paper/2310.05506/) (2023)

## Built on by (most cited first, 30 of 85)

- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [JudgeBench: A Benchmark for Evaluating LLM-based Judges](https://mlsanity.com/paper/2410.12784/) (2024)
- [A Survey on Knowledge Distillation of Large Language Models](https://mlsanity.com/paper/2402.13116/) (2024)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [Orca-Math: Unlocking the potential of SLMs in Grade School Math](https://mlsanity.com/paper/2402.14830/) (2024)
- [A Comprehensive Survey of Scientific Large Language Models and Their Applications in Scientific Discovery](https://mlsanity.com/paper/2406.10833/) (2024)
- [OpenR: An Open Source Framework for Advanced Reasoning with Large Language Models](https://mlsanity.com/paper/2410.09671/) (2024)
- [On Designing Effective RL Reward at Training Time for LLM Reasoning](https://mlsanity.com/paper/2410.15115/) (2024)
- [MAPoRL: Multi-Agent Post-Co-Training for Collaborative Large Language Models with Reinforcement Learning](https://mlsanity.com/paper/2502.18439/) (2025)
- [TinyGSM: achieving >80% on GSM8k with small language models](https://mlsanity.com/paper/2312.09241/) (2023)
- [Revisiting the Test-Time Scaling of o1-like Models: Do they Truly Possess Test-Time Scaling Capabilities?](https://mlsanity.com/paper/2502.12215/) (2025)
- [Training Large Language Models for Reasoning through Reverse Curriculum Reinforcement Learning](https://mlsanity.com/paper/2402.05808/) (2024)
- [MindJourney: Test-Time Scaling with World Models for Spatial Reasoning](https://mlsanity.com/paper/2507.12508/) (2025)
- [CoD, Towards an Interpretable Medical Agent using Chain of Diagnosis](https://mlsanity.com/paper/2407.13301/) (2024)
- [LLM Critics Help Catch Bugs in Mathematics: Towards a Better Mathematical Verifier with Natural Language Feedback](https://mlsanity.com/paper/2406.14024/) (2024)
- [Ensembling Large Language Models with Process Reward-Guided Tree Search for Better Complex Reasoning](https://mlsanity.com/paper/2412.15797/) (2024)
- [UI-Genie: A Self-Improving Approach for Iteratively Boosting MLLM-based Mobile GUI Agents](https://mlsanity.com/paper/2505.21496/) (2025)
- [Self-Explore: Enhancing Mathematical Reasoning in Language Models with Fine-grained Rewards](https://mlsanity.com/paper/2404.10346/) (2024)
- [MM-PRM: Enhancing Multimodal Mathematical Reasoning with Scalable Step-Level Supervision](https://mlsanity.com/paper/2505.13427/) (2025)
- [Flow of Reasoning: Training LLMs for Divergent Reasoning with Minimal Examples](https://mlsanity.com/paper/2406.05673/) (2024)
- [Learning Long-Context Diffusion Policies via Past-Token Prediction](https://mlsanity.com/paper/2505.09561/) (2025)
- [Adversarial Reasoning at Jailbreaking Time](https://mlsanity.com/paper/2502.01633/) (2025)
- [video-SALMONN-o1: Reasoning-enhanced Audio-visual Large Language Model](https://mlsanity.com/paper/2502.11775/) (2025)
- [The Lighthouse of Language: Enhancing LLM Agents via Critique-Guided Improvement](https://mlsanity.com/paper/2503.16024/) (2025)
- [Stepwise Guided Policy Optimization: Coloring your Incorrect Reasoning in GRPO](https://mlsanity.com/paper/2505.11595/) (2025)
- [Large Language Models Struggle with Unreasonability in Math Problems](https://mlsanity.com/paper/2403.19346/) (2024)
- [Towards a Unified View of Preference Learning for Large Language Models: A Survey](https://mlsanity.com/paper/2409.02795/) (2024)
- [STaR-SQL: Self-Taught Reasoner for Text-to-SQL](https://mlsanity.com/paper/2502.13550/) (2025)

## Abstract (arXiv)

Large language models (LLMs) often struggle with maintaining accuracy throughout multiple multiple reasoning steps, especially in mathematical reasoning where an error in earlier steps can propagate to subsequent ones and it ultimately leading to an incorrect answer. To reduce error propagation, guided decoding is employed to direct the LM decoding on a step-by-step basis. We argue that in guided decoding, assessing the potential of an incomplete reasoning path can be more advantageous than simply ensuring per-step correctness, as the former approach leads towards a correct final answer. This transforms the task into a textitvalue estimation problem in planning. Inspired by the findings that textitoutcome supervision for guided decoding essentially acts as a value model, we propose Outcome-supervised Value Model (OVM) that employs outcome supervision for training a value model, which prioritizes steps that lead to accurate conclusions. Furthermore, the OVM eliminates the need for labor-intensive annotations of step-level correctness, thereby significantly enhancing its scalability. Our experiments on two multi-step mathematical reasoning datasets, GSM8K and Game of 24, demonstrate the superior performance of the OVM model. Notably, in GSM8K, our OVM-7B model achieves state-of-the-art results among LLMs up to 13B parameters; especially it does not utilize GPT-4 or code execution. These findings offer a novel perspective on the role of outcome supervision in training value models for multi-step reasoning tasks and provide theoretical justification for its advantage in value estimation for guided decoding.