# Multi-step Problem Solving Through a Verifier: An Empirical Analysis on Model-induced Process Supervision

arXiv: https://arxiv.org/abs/2402.02658 · HTML: https://mlsanity.com/paper/2402.02658/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 30 of its 38 references that are in the map.
- First posted on arXiv 5 Feb 2024.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 30)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [DSPy: Compiling Declarative Language Model Calls into Self-Improving Pipelines](https://mlsanity.com/paper/2310.03714/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [Language Models can Solve Computer Tasks](https://mlsanity.com/paper/2303.17491/) (2023)
- [Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training](https://mlsanity.com/paper/2309.17179/) (2023)
- [Automatically Correcting Large Language Models: Surveying the landscape of diverse self-correction strategies](https://mlsanity.com/paper/2308.03188/) (2023)
- [REFINER: Reasoning Feedback on Intermediate Representations](https://mlsanity.com/paper/2304.01904/) (2023)
- [TinyGSM: achieving >80% on GSM8k with small language models](https://mlsanity.com/paper/2312.09241/) (2023)
- [Learning Math Reasoning from Self-Sampled Correct and Partially-Correct Solutions](https://mlsanity.com/paper/2205.14318/) (2022)
- [Critique Ability of Large Language Models](https://mlsanity.com/paper/2310.04815/) (2023)

## Built on by (most cited first, 30 of 52)

- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Models](https://mlsanity.com/paper/2501.09686/) (2025)
- [A Survey of Frontiers in LLM Reasoning: Inference Scaling, Learning to Reason, and Agentic Systems](https://mlsanity.com/paper/2504.09037/) (2025)
- [Does Math Reasoning Improve General LLM Capabilities? Understanding Transferability of LLM Reasoning](https://mlsanity.com/paper/2507.00432/) (2025)
- [Easy-to-Hard Generalization: Scalable Alignment Beyond Human Supervision](https://mlsanity.com/paper/2403.09472/) (2024)
- [OpenR: An Open Source Framework for Advanced Reasoning with Large Language Models](https://mlsanity.com/paper/2410.09671/) (2024)
- [Evolving Deeper LLM Thinking](https://mlsanity.com/paper/2501.09891/) (2025)
- [Offline Reinforcement Learning for LLM Multi-Step Reasoning](https://mlsanity.com/paper/2412.16145/) (2024)
- [A Comprehensive Survey of Reward Models: Taxonomy, Applications, Challenges, and Future](https://mlsanity.com/paper/2504.12328/) (2025)
- [Process-Driven Autoformalization in Lean 4](https://mlsanity.com/paper/2406.01940/) (2024)
- [Improving LLM Reasoning through Scaling Inference Computation with Collaborative Verification](https://mlsanity.com/paper/2410.05318/) (2024)
- [VersaPRM: Multi-Domain Process Reward Model via Synthetic Reasoning Data](https://mlsanity.com/paper/2502.06737/) (2025)
- [Understanding Chain-of-Thought in LLMs through Information Theory](https://mlsanity.com/paper/2411.11984/) (2024)
- [ReARTeR: Retrieval-Augmented Reasoning with Trustworthy Process Rewarding](https://mlsanity.com/paper/2501.07861/) (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)
- [AutoPSV: Automated Process-Supervised Verifier](https://mlsanity.com/paper/2405.16802/) (2024)
- [Process Supervision-Guided Policy Optimization for Code Generation](https://mlsanity.com/paper/2410.17621/) (2024)
- [A Tutorial on LLM Reasoning: Relevant Methods behind ChatGPT o1](https://mlsanity.com/paper/2502.10867/) (2025)
- [Step-by-Step Reasoning for Math Problems via Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2410.01920/) (2024)
- [Reasoning Through Execution: Unifying Process and Outcome Rewards for Code Generation](https://mlsanity.com/paper/2412.15118/) (2024)
- [Generative AI Act II: Test Time Scaling Drives Cognition Engineering](https://mlsanity.com/paper/2504.13828/) (2025)
- [FG-PRM: Fine-grained Hallucination Detection and Mitigation in Language Model Mathematical Reasoning](https://mlsanity.com/paper/2410.06304/) (2024)
- [Flow-DPO: Improving LLM Mathematical Reasoning through Online Multi-Agent Learning](https://mlsanity.com/paper/2410.22304/) (2024)
- [A Survey on Feedback-based Multi-step Reasoning for Large Language Models on Mathematics](https://mlsanity.com/paper/2502.14333/) (2025)
- [FreePRM: Training Process Reward Models Without Ground Truth Process Labels](https://mlsanity.com/paper/2506.03570/) (2025)
- [Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner](https://mlsanity.com/paper/2507.23317/) (2025)
- [Guided Search Strategies in Non-Serializable Environments with Applications to Software Engineering Agents](https://mlsanity.com/paper/2505.13652/) (2025)
- [Boosting Virtual Agent Learning and Reasoning: A Step-Wise, Multi-Dimensional, and Generalist Reward Model with Benchmark](https://mlsanity.com/paper/2503.18665/) (2025)

## Abstract (arXiv)

Process supervision, using a trained verifier to evaluate the intermediate steps generated by a reasoner, has demonstrated significant improvements in multi-step problem solving. In this paper, to avoid the expensive effort of human annotation on the verifier training data, we introduce Model-induced Process Supervision (MiPS), a novel method for automating data curation. MiPS annotates an intermediate step by sampling completions of this solution through the reasoning model, and obtaining an accuracy defined as the proportion of correct completions. Inaccuracies of the reasoner would cause MiPS underestimating the accuracy of intermediate steps, therefore, we suggest and empirically show that verification focusing on high predicted scores of the verifier shall be preferred over that of low predicted scores, contrary to prior observations on human curated data. Our approach significantly improves the performance of PaLM 2 on math and coding tasks (accuracy +0.67% on GSM8K, +4.16% on MATH, +0.92% on MBPP compared with an output supervision trained verifier). Additionally, our study demonstrates that the verifier exhibits strong generalization ability across different reasoning models.