# Scaling Self-Play with Self-Guidance

arXiv: https://arxiv.org/abs/2604.20209 · HTML: https://mlsanity.com/paper/2604.20209/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Self-play RL for reasoning, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 36 of its 48 references that are in the map.
- First posted on arXiv 22 Apr 2026.

## Placed in

- Synthetic data and self-improvement for LLMs / [Self-play RL for reasoning](https://mlsanity.com/synth/self-play-rl-for-reasoning/)

## Builds on (most cited first, 30 of 36)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Genie: Generative Interactive Environments](https://mlsanity.com/paper/2402.15391/) (2024)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [Automatic Goal Generation for Reinforcement Learning Agents](https://mlsanity.com/paper/1705.06366/) (2017)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.11354/) (2025)
- [Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correction](https://mlsanity.com/paper/2508.03613/) (2025)
- [Intrinsic Motivation and Automatic Curricula via Asymmetric Self-Play](https://mlsanity.com/paper/1703.05407/) (2017)
- [Goedel-Prover: A Frontier Model for Open-Source Automated Theorem Proving](https://mlsanity.com/paper/2502.07640/) (2025)
- [Observational Scaling Laws and the Predictability of Language Model Performance](https://mlsanity.com/paper/2405.10938/) (2024)
- [Seed-Prover: Deep and Broad Reasoning for Automated Theorem Proving](https://mlsanity.com/paper/2507.23726/) (2025)
- [The Art of Scaling Reinforcement Learning Compute for LLMs](https://mlsanity.com/paper/2510.13786/) (2025)
- [SPICE: Self-Play In Corpus Environments Improves Reasoning](https://mlsanity.com/paper/2510.24684/) (2025)
- [STP: Self-play LLM Theorem Provers with Iterative Conjecturing and Proving](https://mlsanity.com/paper/2502.00212/) (2025)
- [Agent0: Unleashing Self-Evolving Agents from Zero Data via Tool-Integrated Reasoning](https://mlsanity.com/paper/2511.16043/) (2025)
- [Towards Robust Mathematical Reasoning](https://mlsanity.com/paper/2511.01846/) (2025)
- [Hilbert: Recursively Building Formal Proofs with Informal Reasoning](https://mlsanity.com/paper/2509.22819/) (2025)
- [Self-Questioning Language Models](https://mlsanity.com/paper/2508.03682/) (2025)
- [Learning Formal Mathematics From Intrinsic Motivation](https://mlsanity.com/paper/2407.00695/) (2024)
- [Seed-Prover 1.5: Mastering Undergraduate-Level Theorem Proving via Learning from Experience](https://mlsanity.com/paper/2512.17260/) (2025)
- [Language Self-Play For Data-Free Training](https://mlsanity.com/paper/2509.07414/) (2025)
- [POPE: Learning to Reason on Hard Problems via Privileged On-Policy Exploration](https://mlsanity.com/paper/2601.18779/) (2026)
- [Guided Self-Evolving LLMs with Minimal Human Supervision](https://mlsanity.com/paper/2512.02472/) (2025)
- [(Mis)Fitting: A Survey of Scaling Laws](https://mlsanity.com/paper/2502.18969/) (2025)
- [TTCS: Test-Time Curriculum Synthesis for Self-Evolving](https://mlsanity.com/paper/2601.22628/) (2026)

## Built on by (most cited first, 10 of 10)

- [SPADE: Self-Play in Adaptive Synthetic Executable Environments](https://mlsanity.com/paper/2608.19197/) (2026)
- [Survive or Collapse: The Asymmetric Roles of Data Gating and Reward Grounding in Self-Play RL](https://mlsanity.com/paper/2605.22217/) (2026)
- [BenchEvolver: Frontier Task Synthesis via Solution-Centric Evolution](https://mlsanity.com/paper/2606.01286/) (2026)
- [FrontierSmith: Synthesizing Open-Ended Coding Problems at Scale](https://mlsanity.com/paper/2605.14445/) (2026)
- [Self-Play Pretraining with Zero Data](https://mlsanity.com/paper/2609.30063/) (2026)
- [INFUSER: Influence-Guided Self-Evolution Improves Reasoning](https://mlsanity.com/paper/2606.09052/) (2026)
- [CompassPlay: Rewarding the Proposer for Where It Moves the Solver](https://mlsanity.com/paper/2609.32228/) (2026)
- [When Does Structured Knowledge Help Neural Theorem Proving?](https://mlsanity.com/paper/2609.34460/) (2026)
- [When Updating Stops Being Learning: Rethinking LLM Self-Evolution via learnable information gain](https://mlsanity.com/paper/2609.36535/) (2026)
- [Mulligan: Performance-Guided Data Collection for Efficient On-Robot Learning](https://mlsanity.com/paper/2610.05882/) (2026)

## Abstract (arXiv)

LLM self-play algorithms are notable in that, in principle, nothing bounds their learning: a Conjecturer model creates problems for a Solver, and both improve together. However, in practice, existing LLM self-play methods do not scale well with large amounts of compute, instead hitting learning plateaus. We argue this is because over long training runs, the Conjecturer learns to hack its reward, collapsing to artificially complex problems that do not help the Solver improve. To overcome this, we introduce Self-Guided Self-Play (SGS), a self-play algorithm in which the language model itself guides the Conjecturer away from degeneracy. In SGS, the model takes on three roles: Solver, Conjecturer, and a Guide that scores synthetic problems by their relevance to unsolved target problems and how clean and natural they are, providing supervision against Conjecturer collapse. Our core hypothesis is that language models can assess whether a subproblem is useful for achieving a goal. We evaluate the scaling properties of SGS by running training for significantly longer than prior works and by fitting scaling laws to cumulative solve rate curves. Applying SGS to formal theorem proving in Lean4, we find that it surpasses the asymptotic solve rate of our strongest RL baseline in fewer than 80 rounds of self-play and enables a 7B parameter model, after 200 rounds of self-play, to solve more problems than a 671B parameter model pass@4.