Scaling Self-Play with Self-Guidance (Apr 2026)

Title: Scaling Self-Play with Self-Guidance (Apr 2026)
Link: http://arxiv.org/abs/2604.20209v1
Date: April 2026

Summary:
This paper introduces Self-Guided Self-Play (SGS), an asymmetric self-play algorithm designed to overcome learning plateaus in LLM training. SGS utilizes a three-role system—Solver, Conjecturer, and Guide—where the Guide scores synthetic problems to prevent the Conjecturer from collapsing into generating irrelevant or overly complex 'hacked' problems. Applied to formal theorem proving in Lean4, the method demonstrates superior scaling properties, allowing a 7B parameter model to eventually outperform a 671B model's pass@4 performance.

Key Topics:
- Asymmetric Self-Play
- Large Language Models
- Reinforcement Learning
- Formal Theorem Proving (Lean4)
- Scaling Laws
- Synthetic Data Generation

Chapters:
00:00 - Introducing Self-Guided Self-Play
01:17 - Remarkable Efficiency Gains
02:40 - Explaining Reward Hacking
04:42 - Analyzing Logic Degradation
06:06 - Tri-Agent Architecture Overview
07:41 - Scoring Mathematical Elegance
08:58 - Unblocking Formatting Bottlenecks
10:21 - Preventing Entropy Collapse
11:53 - Binary Reward Landscapes
13:37 - Balancing Solver Difficulty
15:41 - Benchmarking Lean4 Performance
17:16 - Modeling Sigmoidal Scaling
19:34 - Evaluating Ablation Studies
21:01 - Broader Frontier Implications
22:28 - Future Comprehensibility Risks

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