{"id":"arxiv:2512.18160","title":"Propose, Solve, Verify: Self-Play Through Formal Verification","date":"2025-12-20","section":"Agents, open-endedness, AGI","quality":0.112256,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/","source_url":"https://arxiv.org/abs/2512.18160","text_available":true,"authors":["Alex Wilf","Pranjal Aggarwal","Bryan Parno","Daniel Fried"],"outgoing":[{"source":"arxiv:2512.18160","target":"arxiv:2402.03300","evidence":"id","id":"arxiv:2402.03300","title":"DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/636fb871904bc06f742cfdea069796f9e9665f95bd58dc63260eaff5154ef985/"},{"source":"arxiv:2512.18160","target":"url:ai.meta.com/research/publications/code-llama-open-foundation-models-for-code","evidence":"id","id":"url:ai.meta.com/research/publications/code-llama-open-foundation-models-for-code","title":"Code Llama: Open Foundation Models for Code","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/0dc2d6030e514e45150f64f511c0f50fc010fdc1ddae0bdca7edcd189b084d41/"}],"incoming":[],"text_parts":[{"start":0,"end":15202,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-1.html"},{"start":15202,"end":31147,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-2.html"},{"start":31147,"end":40744,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-3.html"}],"contents":[{"title":"Propose, Solve, Verify: Self-Play Through Formal Verification","offset":0,"level":1,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-1.html#text"},{"title":"Abstract","offset":65,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-1.html#text"},{"title":"Keywords:","offset":1100,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-1.html#text"},{"title":"1 Introduction","offset":1118,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-1.html#text"},{"title":"2 Related Work","offset":5741,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-1.html#text"},{"title":"Verified code generation.","offset":5760,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-1.html#text"},{"title":"Self-improving AI systems.","offset":6947,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-1.html#text"},{"title":"Self-play reasoning systems","offset":7825,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-1.html#text"},{"title":"3 Propose, Solve, Verify ( PSV )","offset":9038,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-1.html#text"},{"title":"Problem setting.","offset":9556,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-1.html#text"},{"title":"3.1 Propose, Solve, Verify ( PSV )","offset":10924,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-1.html#text"},{"title":"Solving.","offset":12642,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-1.html#text"},{"title":"Rejection-Finetuning.","offset":13434,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-1.html#text"},{"title":"Proposing.","offset":15185,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-1.html#text"},{"title":"4 Experiments","offset":16921,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-2.html#text"},{"title":"Datasets and evaluation.","offset":17034,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-2.html#text"},{"title":"Settings.","offset":18450,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-2.html#text"},{"title":"Baselines.","offset":18941,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-2.html#text"},{"title":"Hyperparameters and design choices.","offset":19411,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-2.html#text"},{"title":"5 Results","offset":20750,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-2.html#text"},{"title":"Transfer learning","offset":21086,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-2.html#text"},{"title":"Test-time training","offset":21566,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-2.html#text"},{"title":"6 Analyses and Ablations","offset":22430,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-2.html#text"},{"title":"6.1 Scaling with Questions Per Iteration","offset":22990,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-2.html#text"},{"title":"6.2 Iterative Training","offset":24005,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-2.html#text"},{"title":"6.3 Ablations","offset":25250,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-2.html#text"},{"title":"Verification","offset":25912,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-2.html#text"},{"title":"Difficulty-awareness","offset":27231,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-2.html#text"},{"title":"Diversity","offset":28555,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-2.html#text"},{"title":"7 Conclusion","offset":29529,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-2.html#text"},{"title":"Acknowledgments","offset":30742,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-2.html#text"},{"title":"Impact Statement","offset":31126,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-2.html#text"},{"title":"Appendix A Full Proposer Prompt","offset":31596,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-3.html#text"},{"title":"Appendix B Input & Target Proposal Settings","offset":31632,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-3.html#text"},{"title":"Appendix C Transfer Learning Scaling Results","offset":32578,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-3.html#text"},{"title":"Appendix D Spec Compilation","offset":33295,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-3.html#text"},{"title":"Example: Finding the Maximum Element","offset":33706,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-3.html#text"},{"title":"Appendix E Supervised Fine-Tuning (SFT) Training Details","offset":34326,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-3.html#text"},{"title":"Reproducibility.","offset":35106,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-3.html#text"},{"title":"Appendix F Verification Background","offset":35350,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-3.html#text"},{"title":"Test-case verification is unsound.","offset":37148,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-3.html#text"},{"title":"Formal verification is sound with respect to the specification.","offset":38247,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-3.html#text"},{"title":"Appendix G Difficulty Unaware Ablation","offset":39737,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-3.html#text"},{"title":"Instructions for reporting errors","offset":39780,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/part-3.html#text"}],"text_code_points":40744,"source_markdown":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/6b68bf20c3b0180fbf31bfbfb5f4e5f7800fc134d2c393106efb3320b67a64cd/source.md"}