# V-STaR: Training Verifiers for Self-Taught Reasoners

arXiv: https://arxiv.org/abs/2402.06457 · HTML: https://mlsanity.com/paper/2402.06457/

## Key facts

- Cited by 217 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 32 of its 39 references that are in the map.
- First posted on arXiv 9 Feb 2024.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 32)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (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)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [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)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [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)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [Pretraining Language Models with Human Preferences](https://mlsanity.com/paper/2302.08582/) (2023)
- [LEVER: Learning to Verify Language-to-Code Generation with Execution](https://mlsanity.com/paper/2302.08468/) (2023)
- [ReFT: Reasoning with Reinforced Fine-Tuning](https://mlsanity.com/paper/2401.08967/) (2024)
- [Making Large Language Models Better Reasoners with Step-Aware Verifier](https://mlsanity.com/paper/2206.02336/) (2022)
- [Let's reward step by step: Step-Level reward model as the Navigators for Reasoning](https://mlsanity.com/paper/2310.10080/) (2023)
- [Learning From Mistakes Makes LLM Better Reasoner](https://mlsanity.com/paper/2310.20689/) (2023)
- [Solving Math Word Problems via Cooperative Reasoning induced Language Models](https://mlsanity.com/paper/2210.16257/) (2022)
- [Making Large Language Models Better Reasoners with Alignment](https://mlsanity.com/paper/2309.02144/) (2023)
- [Improving Large Language Model Fine-tuning for Solving Math Problems](https://mlsanity.com/paper/2310.10047/) (2023)

## Built on by (most cited first, 30 of 217)

- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Search](https://mlsanity.com/paper/2406.03816/) (2024)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [A Survey on Knowledge Distillation of Large Language Models](https://mlsanity.com/paper/2402.13116/) (2024)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [Iterative Reasoning Preference Optimization](https://mlsanity.com/paper/2404.19733/) (2024)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [Many-Shot In-Context Learning](https://mlsanity.com/paper/2404.11018/) (2024)
- [Large Language Model Agent: A Survey on Methodology, Applications and Challenges](https://mlsanity.com/paper/2503.21460/) (2025)
- [ThinkPrune: Pruning Long Chain-of-Thought of LLMs via Reinforcement Learning](https://mlsanity.com/paper/2504.01296/) (2025)
- [A Survey of Self-Evolving Agents: What, When, How, and Where to Evolve on the Path to Artificial Super Intelligence](https://mlsanity.com/paper/2507.21046/) (2025)
- [Recursive Introspection: Teaching Language Model Agents How to Self-Improve](https://mlsanity.com/paper/2407.18219/) (2024)
- [Direct Preference Optimization of Video Large Multimodal Models from Language Model Reward](https://mlsanity.com/paper/2404.01258/) (2024)
- [Scaling Laws for Reward Model Overoptimization in Direct Alignment Algorithms](https://mlsanity.com/paper/2406.02900/) (2024)
- [Improve Vision Language Model Chain-of-thought Reasoning](https://mlsanity.com/paper/2410.16198/) (2024)
- [Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scaling](https://mlsanity.com/paper/2502.06703/) (2025)
- [Advances and Challenges in Foundation Agents: From Brain-Inspired Intelligence to Evolutionary, Collaborative, and Safe Systems](https://mlsanity.com/paper/2504.01990/) (2025)
- [OpenVLThinker: Complex Vision-Language Reasoning via Iterative SFT-RL Cycles](https://mlsanity.com/paper/2503.17352/) (2025)
- [AgentGym: Evolving Large Language Model-based Agents across Diverse Environments](https://mlsanity.com/paper/2406.04151/) (2024)
- [OpenCodeReasoning: Advancing Data Distillation for Competitive Coding](https://mlsanity.com/paper/2504.01943/) (2025)
- [Steering Your Generalists: Improving Robotic Foundation Models via Value Guidance](https://mlsanity.com/paper/2410.13816/) (2024)
- [STaR-GATE: Teaching Language Models to Ask Clarifying Questions](https://mlsanity.com/paper/2403.19154/) (2024)
- [RL on Incorrect Synthetic Data Scales the Efficiency of LLM Math Reasoning by Eight-Fold](https://mlsanity.com/paper/2406.14532/) (2024)
- [Towards Scientific Intelligence: A Survey of LLM-based Scientific Agents](https://mlsanity.com/paper/2503.24047/) (2025)
- [DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solving](https://mlsanity.com/paper/2407.13690/) (2024)
- [A Survey on Self-Evolution of Large Language Models](https://mlsanity.com/paper/2404.14387/) (2024)
- [Inference-Aware Fine-Tuning for Best-of-N Sampling in Large Language Models](https://mlsanity.com/paper/2412.15287/) (2024)
- [Pass@K Policy Optimization: Solving Harder Reinforcement Learning Problems](https://mlsanity.com/paper/2505.15201/) (2025)

## Abstract (arXiv)

Common self-improvement approaches for large language models (LLMs), such as STaR, iteratively fine-tune LLMs on self-generated solutions to improve their problem-solving ability. However, these approaches discard the large amounts of incorrect solutions generated during this process, potentially neglecting valuable information in such solutions. To address this shortcoming, we propose V-STaR that utilizes both the correct and incorrect solutions generated during the self-improvement process to train a verifier using DPO that judges correctness of model-generated solutions. This verifier is used at inference time to select one solution among many candidate solutions. Running V-STaR for multiple iterations results in progressively better reasoners and verifiers, delivering a 4% to 17% test accuracy improvement over existing self-improvement and verification approaches on common code generation and math reasoning benchmarks with LLaMA2 models.