# Self-Consistency Preference Optimization

arXiv: https://arxiv.org/abs/2411.04109 · HTML: https://mlsanity.com/paper/2411.04109/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 40 of its 50 references that are in the map.
- First posted on arXiv 6 Nov 2024.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)
- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 30 of 40)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [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)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Ethical and social risks of harm from Language Models](https://mlsanity.com/paper/2112.04359/) (2021)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2307.15217/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [RewardBench: Evaluating Reward Models for Language Modeling](https://mlsanity.com/paper/2403.13787/) (2024)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Understanding the Effects of RLHF on LLM Generalisation and Diversity](https://mlsanity.com/paper/2310.06452/) (2023)
- [CodeT: Code Generation with Generated Tests](https://mlsanity.com/paper/2207.10397/) (2022)
- [Interpretable Preferences via Multi-Objective Reward Modeling and Mixture-of-Experts](https://mlsanity.com/paper/2406.12845/) (2024)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)

## Built on by (most cited first, 30 of 50)

- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [Skywork-Reward-V2: Scaling Preference Data Curation via Human-AI Synergy](https://mlsanity.com/paper/2507.01352/) (2025)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [NaturalReasoning: Reasoning in the Wild with 2.8M Challenging Questions](https://mlsanity.com/paper/2502.13124/) (2025)
- [Self-Generated Critiques Boost Reward Modeling for Language Models](https://mlsanity.com/paper/2411.16646/) (2024)
- [Self-rewarding correction for mathematical reasoning](https://mlsanity.com/paper/2502.19613/) (2025)
- [Can Large Reasoning Models Self-Train?](https://mlsanity.com/paper/2505.21444/) (2025)
- [Efficiently Scaling LLM Reasoning with Certaindex](https://mlsanity.com/paper/2412.20993/) (2024)
- [Seek in the Dark: Reasoning via Test-Time Instance-Level Policy Gradient in Latent Space](https://mlsanity.com/paper/2505.13308/) (2025)
- [CoT-Self-Instruct: Building high-quality synthetic prompts for reasoning and non-reasoning tasks](https://mlsanity.com/paper/2507.23751/) (2025)
- [Large Language Models Can Self-Improve in Long-context Reasoning](https://mlsanity.com/paper/2411.08147/) (2024)
- [Genius: A Generalizable and Purely Unsupervised Self-Training Framework For Advanced Reasoning](https://mlsanity.com/paper/2504.08672/) (2025)
- [Bootstrapping Language-Guided Navigation Learning with Self-Refining Data Flywheel](https://mlsanity.com/paper/2412.08467/) (2024)
- [Recursive Synthesis for Long-Horizon Terminal Tasks](https://mlsanity.com/paper/2608.05466/) (2026)
- [Learning to Generate Unit Tests for Automated Debugging](https://mlsanity.com/paper/2502.01619/) (2025)
- [On-Policy Self-Distillation without Any Supervision](https://mlsanity.com/paper/2608.06296/) (2026)
- [Superficial Self-Improved Reasoners Benefit from Model Merging](https://mlsanity.com/paper/2503.02103/) (2025)
- [Alignment and Safety in Large Language Models: Safety Mechanisms, Training Paradigms, and Emerging Challenges](https://mlsanity.com/paper/2507.19672/) (2025)
- [RESTRAIN: From Spurious Votes to Signals -- Self-Driven RL with Self-Penalization](https://mlsanity.com/paper/2510.02172/) (2025)
- [Sailing by the Stars: A Survey on Reward Models and Learning Strategies for Learning from Rewards](https://mlsanity.com/paper/2505.02686/) (2025)
- [Dual-IPO: Dual-Iterative Preference Optimization for Text-to-Video Generation](https://mlsanity.com/paper/2502.02088/) (2025)
- [HoneyBee: Data Recipes for Vision-Language Reasoners](https://mlsanity.com/paper/2510.12225/) (2025)
- [Certified Self-Consistency: Statistical Guarantees and Test-Time Training for Reliable Reasoning in LLMs](https://mlsanity.com/paper/2510.17472/) (2025)
- [CoVerRL: Breaking the Consensus Trap in Label-Free Reasoning via Generator-Verifier Co-Evolution](https://mlsanity.com/paper/2603.17775/) (2026)
- [Unsupervised Elicitation of Language Models](https://mlsanity.com/paper/2506.10139/) (2025)
- [Entropy-Preserving Reinforcement Learning](https://mlsanity.com/paper/2603.11682/) (2026)
- [Self-Harmony: Learning to Harmonize Self-Supervision and Self-Play in Test-Time Reinforcement Learning](https://mlsanity.com/paper/2511.01191/) (2025)
- [Optimal Self-Consistency for Efficient Reasoning with Large Language Models](https://mlsanity.com/paper/2511.12309/) (2025)

## Abstract (arXiv)

Self-alignment, whereby models learn to improve themselves without human annotation, is a rapidly growing research area. However, existing techniques often fail to improve complex reasoning tasks due to the difficulty of assigning correct rewards. An orthogonal approach that is known to improve correctness is self-consistency, a method applied at inference time based on multiple sampling in order to find the most consistent answer. In this work, we extend the self-consistency concept to help train models. We thus introduce self-consistency preference optimization (ScPO), which iteratively trains consistent answers to be preferred over inconsistent ones on unsupervised new problems. We show ScPO leads to large improvements over conventional reward model training on reasoning tasks such as GSM8K and MATH, closing the gap with supervised training with gold answers or preferences, and that combining ScPO with standard supervised learning improves results even further. On ZebraLogic, ScPO finetunes Llama-3 8B to be superior to Llama-3 70B, Gemma-2 27B, and Claude-3 Haiku.