# SPACE: Noise Contrastive Estimation Stabilizes Self-Play Fine-Tuning for Large Language Models

arXiv: https://arxiv.org/abs/2512.07175 · HTML: https://mlsanity.com/paper/2512.07175/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Self-rewarding alignment and self-training, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 68 of its 93 references that are in the map.
- First posted on arXiv 8 Dec 2025.

## Placed in

- Synthetic data and self-improvement for LLMs / [Self-rewarding alignment and self-training](https://mlsanity.com/synth/self-rewarding-alignment-and-self-training/)

## Builds on (most cited first, 30 of 68)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (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)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyond](https://mlsanity.com/paper/2308.12966/) (2023)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [Enhancing Chat Language Models by Scaling High-quality Instructional Conversations](https://mlsanity.com/paper/2305.14233/) (2023)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [DeepSeek-VL: Towards Real-World Vision-Language Understanding](https://mlsanity.com/paper/2403.05525/) (2024)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Data-Efficient Image Recognition with Contrastive Predictive Coding](https://mlsanity.com/paper/1905.09272/) (2019)
- [A Survey on Large Language Models for Code Generation](https://mlsanity.com/paper/2406.00515/) (2024)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [Zephyr: Direct Distillation of LM Alignment](https://mlsanity.com/paper/2310.16944/) (2023)

## Built on by (most cited first, 7 of 7)

- [Position: Agentic Evolution is the Path to Evolving LLMs](https://mlsanity.com/paper/2602.00359/) (2026)
- [Triplets Better Than Pairs: Towards Stable and Effective Self-Play Fine-Tuning for LLMs](https://mlsanity.com/paper/2601.08198/) (2026)
- [StoSignSGD: Unbiased Structural Stochasticity Fixes SignSGD for Training Large Language Models](https://mlsanity.com/paper/2604.15416/) (2026)
- [AERO: Autonomous Evolutionary Reasoning Optimization via Endogenous Dual-Loop Feedback](https://mlsanity.com/paper/2602.03084/) (2026)
- [Building Autonomous GUI Navigation via Agentic-Q Estimation and Step-Wise Policy Optimization](https://mlsanity.com/paper/2602.13653/) (2026)
- [IRIS: Interpolative R'enyi Iterative Self-play for Large Language Model Fine-Tuning](https://mlsanity.com/paper/2604.20933/) (2026)
- [SP-DocReader: Difference-Aware Self-Play for Precise Document OCR](https://mlsanity.com/paper/2610.11148/) (2026)

## Abstract (arXiv)

Self-play fine-tuning has demonstrated promising abilities in adapting large language models (LLMs) to downstream tasks with limited real-world data. The basic principle is to iteratively refine the model with real samples and synthetic ones generated from itself. However, the existing methods primarily focus on the relative gaps between the rewards for two types of data, neglecting their absolute values. Through theoretical analysis, we identify that the gap-based methods suffer from unstable evolution, due to the potentially degenerated objectives. To address this limitation, we introduce a novel self-play fine-tuning method, namely Self-PlAy via Noise Contrastive Estimation (SPACE), which leverages noise contrastive estimation to capture the real-world data distribution. Specifically, SPACE treats synthetic samples as auxiliary components, and discriminates them from the real ones in a binary classification manner. As a result, SPACE independently optimizes the absolute reward values for each type of data, ensuring a consistently meaningful objective and thereby avoiding the instability issue. Theoretically, we show that the optimal solution of the objective in SPACE aligns with the underlying distribution of real-world data, and SPACE guarantees a provably stable convergence to the optimal distribution. Empirically, we show that SPACE significantly improves the performance of LLMs over various tasks, and outperforms supervised fine-tuning that employs much more real-world samples. Compared to gap-based self-play fine-tuning methods, SPACE exhibits remarkable superiority and stable evolution.