Propose, Solve, Verify: Self-Play Through Formal Verification

arxiv:2512.18160

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Agents, open-endedness, AGI · 2025-12-20

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1. Part 1
2. Part 2
3. Part 3

Contents

• Propose, Solve, Verify: Self-Play Through Formal Verification
• Abstract
• Keywords:
• 1 Introduction
• 2 Related Work
• Verified code generation.
• Self-improving AI systems.
• Self-play reasoning systems
• 3 Propose, Solve, Verify ( PSV )
• Problem setting.
• 3.1 Propose, Solve, Verify ( PSV )
• Solving.
• Rejection-Finetuning.
• Proposing.
• 4 Experiments
• Datasets and evaluation.
• Settings.
• Baselines.
• Hyperparameters and design choices.
• 5 Results
• Transfer learning
• Test-time training
• 6 Analyses and Ablations
• 6.1 Scaling with Questions Per Iteration
• 6.2 Iterative Training
• 6.3 Ablations
• Verification
• Difficulty-awareness
• Diversity
• 7 Conclusion
• Acknowledgments
• Impact Statement
• Appendix A Full Proposer Prompt
• Appendix B Input & Target Proposal Settings
• Appendix C Transfer Learning Scaling Results
• Appendix D Spec Compilation
• Example: Finding the Maximum Element
• Appendix E Supervised Fine-Tuning (SFT) Training Details
• Reproducibility.
• Appendix F Verification Background
• Test-case verification is unsound.
• Formal verification is sound with respect to the specification.
• Appendix G Difficulty Unaware Ablation
• Instructions for reporting errors