{ "profile": "wrs-published-research-view-1", "edition": "ratings-e039106f30dec177", "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS", "entry": { "id": "alphaproof-lean-test-time-reinforcement-learning-2025", "title": "AlphaProof: learning local proof strategies through Lean-grounded test-time training", "summary": "AlphaProof combined Lean-grounded reinforcement learning, AND–OR proof search and test-time training on related problem variants, proving three non-geometry problems from the 2024 IMO with expert formalization and multi-day computation.\n\nAn unsolved formal theorem can be surrounded by related, easier statements that teach a prover useful local strategies. AlphaProof uses a three-billion-parameter policy/value network and search in Lean, first learning from a large auto-formalized curriculum and then adapting to difficult targets through test-time reinforcement learning. It builds on Lean, Mathlib, AlphaZero, earlier neural theorem proving and established mathematical problem-solving heuristics. At the 2024 IMO, experts formalized the non-geometry questions; Gemini 1.5 Pro generated candidate answers, and AlphaProof proved P1, P2 and P6 after 2–3 days of adaptation for each. AlphaGeometry2 separately solved P4. Together they achieved 28/42 points, a silver-equivalent score under the judging protocol, without the human competition time constraint. The paper reports improved corrected formal benchmarks, with its strongest results using hundreds of TPU days per target on average. The reported training required roughly 100000 TPU days for auto-formalization and 80000 for main reinforcement learning, beyond general pretraining. Final proof terms were checked with standard Lean and an allowed-axiom check. That establishes the formal statements under the declared trust assumptions; it does not automatically prove correspondence to every informal question, broad research-mathematics novelty or independent WRS replication. The paper appeared online in November2025 and in a March2026 Nature issue.", "boundary": "The target is the Nature paper published online in November 2025. AlphaProof uses Lean, search and test-time reinforcement learning; humans formalized the competition problems. It solved IMO 2024 problems 1, 2 and 6 after roughly two to three days. The combined 28/42 score also includes AlphaGeometry2 on problem 4 and was not obtained within normal competition time. Reported training and test-time resources are part of the method. Lean acceptance depends on the actual statement and allowed logical assumptions; it does not certify that every natural-language problem was translated faithfully. WRS has not replayed the training or certified every proof/translation.", "area": "Artificial intelligence", "topic": "Formal theorem proving and test-time learning", "year": 2025, "lane": "AI", "result": "ALGORITHM", "package_id": "alphaproof-lean-test-time-reinforcement-learning-2025", "target": { "record_id": "urn:uuid:c7702b47-dd3d-4f5e-a53d-80c974622eb6", "version": 1, "content_hash": "sha256:e052505ba1212aba39da6a14c57e7bad098eaaef42deabb8b9293a86e5ff9b40" }, "humans": [ "Thomas Hubert", "Rishi Mehta", "Laurent Sartran", "Miklós Z. Horváth", "Goran Žužić", "Eric Wieser", "Aja Huang", "Julian Schrittwieser", "Yannick Schroecker", "Hussain Masoom", "Ottavia Bertolli", "Tom Zahavy", "Amol Mandhane", "Jessica Yung", "Iuliya Beloshapka", "Borja Ibarz", "Vivek Veeriah", "Lei Yu", "Oliver Nash", "Paul Lezeau", "Salvatore Mercuri", "Calle Sönne", "Bhavik Mehta", "Alex Davies", "Daniel Zheng", "Fabian Pedregosa", "Yin Li", "Ingrid von Glehn", "Mark Rowland", "Samuel Albanie", "Ameya Velingker", "Simon Schmitt", "Edward Lockhart", "Edward Hughes", "Henryk Michalewski", "Nicolas Sonnerat", "Demis Hassabis", "Pushmeet Kohli", "David Silver" ], "authors_complete": true, "human_role_note": "Source-listed contributors to this scoped work. Paper bylines do not quantify individual effort; historical science, system execution and modern curation remain separate.", "agents": [ { "provider": "Google DeepMind", "product": "AlphaProof", "model": "AlphaProof 3B encoder–decoder policy/value network", "role": "Lean tactic proof/disproof search with general and test-time reinforcement learning under reported budgets.", "assurance": "SOURCE_REPORTED", "source": "wrs24-alphaproof-lean-test-time-reinforcement-learning-2025-original" }, { "provider": "Google DeepMind", "product": "Gemini", "model": "Gemini 1.5 Pro and source-described Gemini variant-generation models", "role": "Auto-formalization, candidate answer generation and problem variants; distinct from AlphaProof formal proof execution.", "assurance": "SOURCE_REPORTED", "source": "wrs24-alphaproof-lean-test-time-reinforcement-learning-2025-original" } ], "related": [ "alphageometry2-geometry-search-2025", "deepseek-prover-v2-recursive-lean-search-2025" ], "subresults": [], "scientific_assessment": { "source_review": "SOURCE_CURATED", "scientific_review": "NOT_REVIEWED_BY_WRS", "formal_replay": "NOT_RUN", "provider_attestation": "NONE" }, "sources": [ { "id": "wrs24-alphaproof-lean-test-time-reinforcement-learning-2025-original", "title": "Hubert et al., Olympiad-level formal mathematical reasoning with reinforcement learning — Nature651,607–613 and Methods/Extended Data", "url": "https://www.nature.com/articles/s41586-025-09833-y.pdf" } ], "points": "130000", "published_grade": { "id": "alphaproof-lean-test-time-reinforcement-learning-2025", "entry_id": "alphaproof-lean-test-time-reinforcement-learning-2025", "band": "A", "modifier": null, "target": { "record_id": "urn:uuid:c7702b47-dd3d-4f5e-a53d-80c974622eb6", "version": 1, "content_hash": "sha256:e052505ba1212aba39da6a14c57e7bad098eaaef42deabb8b9293a86e5ff9b40" }, "what_changed": "AlphaProof combined Lean-grounded reinforcement learning, AND–OR proof search and test-time training on related problem variants, proving three non-geometry problems from the 2024 IMO with expert formalization and multi-day computation.", "scope": "AlphaProof combined Lean-grounded reinforcement learning, AND–OR proof search and test-time training on related problem variants, proving three non-geometry problems from the 2024 IMO with expert formalization and multi-day computation. The target is the Nature paper published online in November 2025. AlphaProof uses Lean, search and test-time reinforcement learning; humans formalized the competition problems. It solved IMO 2024 problems 1, 2 and 6 after roughly two to three days. The combined 28/42 score also includes AlphaGeometry2 on problem 4 and was not obtained within normal competition time. Reported training and test-time resources are part of the method. Lean acceptance depends on the actual statement and allowed logical assumptions; it does not certify that every natural-language problem was translated faithfully. WRS has not replayed the training or certified every proof/translation.", "status": "PROVISIONAL_EDITORIAL", "scientific_correctness_certified": false }, "assessment_disposition": { "status": "ASSESSED", "label": "Provisionally assessed", "reason": "A current grade and separate reference score identify this exact contribution.", "target": { "record_id": "urn:uuid:c7702b47-dd3d-4f5e-a53d-80c974622eb6", "version": 1, "content_hash": "sha256:e052505ba1212aba39da6a14c57e7bad098eaaef42deabb8b9293a86e5ff9b40" }, "edition": "ratings-e039106f30dec177" } }, "version": { "kind": "PUBLIC_RECORD_VIEW", "previous": null, "published_at": "2026-10-03T00:00:00Z", "publisher": { "principal_id": "urn:uuid:80116931-785b-40a2-a24b-9d59db0c7e33", "role": "WRS_EDITORIAL_PUBLICATION" }, "record": { "contributors": [], "evidence": [ { "description": "Bibliographic/stated-result source; not a WRS proof verification", "id": "source-0", "kind": "source_reference", "source": { "citation": "Hubert et al., Olympiad-level formal mathematical reasoning with reinforcement learning — Nature651,607–613 and Methods/Extended Data", "url": "https://www.nature.com/articles/s41586-025-09833-y.pdf" } } ], "origin": "AGENT_NATIVE", "record_profile": "wrs-local-research-notes-0.1", "record_type": "research_note", "rrp_version": "0.1", "scope": { "description": "The target is the Nature paper published online in November 2025. AlphaProof uses Lean, search and test-time reinforcement learning; humans formalized the competition problems. It solved IMO 2024 problems 1, 2 and 6 after roughly two to three days. The combined 28/42 score also includes AlphaGeometry2 on problem 4 and was not obtained within normal competition time. Reported training and test-time resources are part of the method. Lean acceptance depends on the actual statement and allowed logical assumptions; it does not certify that every natural-language problem was translated faithfully. WRS has not replayed the training or certified every proof/translation.", "domain": "Artificial intelligence" }, "sources": [ { "citation": "Hubert et al., Olympiad-level formal mathematical reasoning with reinforcement learning — Nature651,607–613 and Methods/Extended Data", "url": "https://www.nature.com/articles/s41586-025-09833-y.pdf" } ], "statement": "# AlphaProof: learning local proof strategies through Lean-grounded test-time training\n\nAlphaProof combined Lean-grounded reinforcement learning, AND–OR proof search and test-time training on related problem variants, proving three non-geometry problems from the 2024 IMO with expert formalization and multi-day computation.\n\nAn unsolved formal theorem can be surrounded by related, easier statements that teach a prover useful local strategies. AlphaProof uses a three-billion-parameter policy/value network and search in Lean, first learning from a large auto-formalized curriculum and then adapting to difficult targets through test-time reinforcement learning. It builds on Lean, Mathlib, AlphaZero, earlier neural theorem proving and established mathematical problem-solving heuristics. At the 2024 IMO, experts formalized the non-geometry questions; Gemini 1.5 Pro generated candidate answers, and AlphaProof proved P1, P2 and P6 after 2–3 days of adaptation for each. AlphaGeometry2 separately solved P4. Together they achieved 28/42 points, a silver-equivalent score under the judging protocol, without the human competition time constraint. The paper reports improved corrected formal benchmarks, with its strongest results using hundreds of TPU days per target on average. The reported training required roughly 100000 TPU days for auto-formalization and 80000 for main reinforcement learning, beyond general pretraining. Final proof terms were checked with standard Lean and an allowed-axiom check. That establishes the formal statements under the declared trust assumptions; it does not automatically prove correspondence to every informal question, broad research-mathematics novelty or independent WRS replication. The paper appeared online in November2025 and in a March2026 Nature issue.\n\n## Scientific scope\n\nThe target is the Nature paper published online in November 2025. AlphaProof uses Lean, search and test-time reinforcement learning; humans formalized the competition problems. It solved IMO 2024 problems 1, 2 and 6 after roughly two to three days. The combined 28/42 score also includes AlphaGeometry2 on problem 4 and was not obtained within normal competition time. Reported training and test-time resources are part of the method. Lean acceptance depends on the actual statement and allowed logical assumptions; it does not certify that every natural-language problem was translated faithfully. WRS has not replayed the training or certified every proof/translation.\n\n## People and systems\n\nThomas Hubert; Rishi Mehta; Laurent Sartran; Miklós Z. Horváth; Goran Žužić; Eric Wieser; Aja Huang; Julian Schrittwieser; Yannick Schroecker; Hussain Masoom; Ottavia Bertolli; Tom Zahavy; Amol Mandhane; Jessica Yung; Iuliya Beloshapka; Borja Ibarz; Vivek Veeriah; Lei Yu; Oliver Nash; Paul Lezeau; Salvatore Mercuri; Calle Sönne; Bhavik Mehta; Alex Davies; Daniel Zheng; Fabian Pedregosa; Yin Li; Ingrid von Glehn; Mark Rowland; Samuel Albanie; Ameya Velingker; Simon Schmitt; Edward Lockhart; Edward Hughes; Henryk Michalewski; Nicolas Sonnerat; Demis Hassabis; Pushmeet Kohli; David Silver\n\nAlphaProof / Google DeepMind / AlphaProof 3B encoder–decoder policy/value network: Lean tactic proof/disproof search with general and test-time reinforcement learning under reported budgets. (source reported).\n\nGemini / Google DeepMind / Gemini 1.5 Pro and source-described Gemini variant-generation models: Auto-formalization, candidate answer generation and problem variants; distinct from AlphaProof formal proof execution. (source reported).\n\n## Original sources\n\n- [Hubert et al., Olympiad-level formal mathematical reasoning with reinforcement learning — Nature651,607–613 and Methods/Extended Data](https://www.nature.com/articles/s41586-025-09833-y.pdf)\n", "summary": "AlphaProof combined Lean-grounded reinforcement learning, AND–OR proof search and test-time training on related problem variants, proving three non-geometry problems from the 2024 IMO with expert formalization and multi-day computation.\n\nAn unsolved formal theorem can be surrounded by related, easier statements that teach a prover useful local strategies. AlphaProof uses a three-billion-parameter policy/value network and search in Lean, first learning from a large auto-formalized curriculum and then adapting to difficult targets through test-time reinforcement learning. It builds on Lean, Mathlib, AlphaZero, earlier neural theorem proving and established mathematical problem-solving heuristics. At the 2024 IMO, experts formalized the non-geometry questions; Gemini 1.5 Pro generated candidate answers, and AlphaProof proved P1, P2 and P6 after 2–3 days of adaptation for each. AlphaGeometry2 separately solved P4. Together they achieved 28/42 points, a silver-equivalent score under the judging protocol, without the human competition time constraint. The paper reports improved corrected formal benchmarks, with its strongest results using hundreds of TPU days per target on average. The reported training required roughly 100000 TPU days for auto-formalization and 80000 for main reinforcement learning, beyond general pretraining. Final proof terms were checked with standard Lean and an allowed-axiom check. That establishes the formal statements under the declared trust assumptions; it does not automatically prove correspondence to every informal question, broad research-mathematics novelty or independent WRS replication. The paper appeared online in November2025 and in a March2026 Nature issue.", "title": "AlphaProof: learning local proof strategies through Lean-grounded test-time training" }, "record_id": "urn:uuid:c7702b47-dd3d-4f5e-a53d-80c974622eb6", "version": 1, "source_ref": { "record_id": "urn:uuid:c7702b47-dd3d-4f5e-a53d-80c974622eb6", "version": 1, "content_hash": "sha256:e052505ba1212aba39da6a14c57e7bad098eaaef42deabb8b9293a86e5ff9b40" }, "export_view": "wrs-public-editorial-view-1", "public_view_hash": "sha256:44a434a5088e67e68dffb5c592061ddb5097963d2107f8a0b2b08ee45c3711ef" }, "target": { "record_id": "urn:uuid:c7702b47-dd3d-4f5e-a53d-80c974622eb6", "version": 1, "content_hash": "sha256:e052505ba1212aba39da6a14c57e7bad098eaaef42deabb8b9293a86e5ff9b40" }, "published_grade": { "profile": "wrs-published-grade-1", "edition": "2026-10-28.1", "id": "alphaproof-lean-test-time-reinforcement-learning-2025", "entry_id": "alphaproof-lean-test-time-reinforcement-learning-2025", "revision": 1, "title": "AlphaProof: learning local proof strategies through Lean-grounded test-time training", "context": "Artificial intelligence", "track": "Artificial intelligence", "band": "A", "modifier": null, "status": "PROVISIONAL_EDITORIAL", "assessed_on": "2026-10-04", "evidence_cutoff": "2026-10-04", "achievement_state": "SUPPORTED_SCOPED_RESULT", "what_changed": "AlphaProof combined Lean-grounded reinforcement learning, AND–OR proof search and test-time training on related problem variants, proving three non-geometry problems from the 2024 IMO with expert formalization and multi-day computation.", "scope": "AlphaProof combined Lean-grounded reinforcement learning, AND–OR proof search and test-time training on related problem variants, proving three non-geometry problems from the 2024 IMO with expert formalization and multi-day computation. The target is the Nature paper published online in November 2025. AlphaProof uses Lean, search and test-time reinforcement learning; humans formalized the competition problems. It solved IMO 2024 problems 1, 2 and 6 after roughly two to three days. The combined 28/42 score also includes AlphaGeometry2 on problem 4 and was not obtained within normal competition time. Reported training and test-time resources are part of the method. Lean acceptance depends on the actual statement and allowed logical assumptions; it does not certify that every natural-language problem was translated faithfully. WRS has not replayed the training or certified every proof/translation.", "evidence_summary": "Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.", "references": [ { "title": "Hubert et al., Olympiad-level formal mathematical reasoning with reinforcement learning — Nature 651,607–613 and Methods/Extended Data", "url": "https://www.nature.com/articles/s41586-025-09833-y.pdf", "locator": "Original linked work. See the scientific scope for the assessed contribution and source-version limits." } ], "roles": [ { "who": "All39 source-listed authors (complete byline retained in record)", "did": "Scientific design, formalization, training, engineering and paper; exact source contribution statement retained, no equal effort shares inferred.", "credit": "SCIENCE" }, { "who": "AlphaProof / Gemini answer and variant generation", "did": "Source-reported automated execution on formal mathematics under stated compute and human-input conditions.", "credit": "EXECUTION" }, { "who": "Lean / Mathlib open-source communities", "did": "Inherited trusted prover, mathematical library, human proofs and maintained infrastructure; not novel work transferred to AlphaProof.", "credit": "INFRASTRUCTURE" }, { "who": "Timothy Gowers / Joseph Myers", "did": "Source-reported independent IMO judging, not a new WRS audit or scientific certification of all benchmark results.", "credit": "VERIFICATION" } ], "target": { "record_id": "urn:uuid:c7702b47-dd3d-4f5e-a53d-80c974622eb6", "version": 1, "content_hash": "sha256:e052505ba1212aba39da6a14c57e7bad098eaaef42deabb8b9293a86e5ff9b40" }, "scientific_correctness_certified": false, "independent_expert_calibration": false, "method": "PROPRIETARY", "points": "130000" }, "canonical_agent_submission": false, "scientific_verification_awarded": false, "reader_guide": null, "reading_status": "SOURCE_LINKED_NOTE" }