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    "summary": "HyperTree Proof Search explores all required branches of a candidate proof and couples transformer tactic generation with online policy/critic training; Evariste reports gains on Metamath and Lean under explicit adaptive and held-out protocols.\n\nA proof step may produce several obligations, and every obligation must be proved. HyperTree Proof Search selects a promising partial proof tree, expands its unresolved leaves and updates search estimates across the whole tree. A transformer proposes tactics, while a learned critic guides exploration. The Evariste system trains on feedback from ongoing searches, including newly found short proofs. The2022 paper studies Metamath, Lean and a simpler Equations environment. Its strongest headline Metamath result,82.6%, is the cumulative fraction solved on validation statements used during online training. This is useful adaptive search, but is different from an untouched-test result. Table3 separately reports72.4% pass@32 on Metamath test statements; Table2 reports41.0% pass@64 on miniF2F-test for a model trained with miniF2F-valid statements. Existing human statements, libraries and formal kernels remain essential. The paper also describes earlier numeric-checking vulnerabilities and a Lean proof of an incorrectly formalized exercise. These examples show why exact checking and faithful statement translation are separate obligations. The trained models and formal proof pipeline have not been independently replayed here.",
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        "description": "This contribution is the proof-search method in arXiv 2205.11491v1. Its 82.6% headline is cumulative validation performance with adaptive online training, not an untouched held-out test success rate. The paper reports a 72.4% test result at pass@32; another test discussion concerns pass@8. Those evaluation budgets and adaptation conditions must remain distinct. Existing formal libraries and translated theorem statements are inherited inputs. WRS has not independently rerun the training, search or benchmark.",
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      "statement": "# Evariste and HyperTree Proof Search: learning from all proof obligations\n\nHyperTree Proof Search explores all required branches of a candidate proof and couples transformer tactic generation with online policy/critic training; Evariste reports gains on Metamath and Lean under explicit adaptive and held-out protocols.\n\nA proof step may produce several obligations, and every obligation must be proved. HyperTree Proof Search selects a promising partial proof tree, expands its unresolved leaves and updates search estimates across the whole tree. A transformer proposes tactics, while a learned critic guides exploration. The Evariste system trains on feedback from ongoing searches, including newly found short proofs. The2022 paper studies Metamath, Lean and a simpler Equations environment. Its strongest headline Metamath result,82.6%, is the cumulative fraction solved on validation statements used during online training. This is useful adaptive search, but is different from an untouched-test result. Table3 separately reports72.4% pass@32 on Metamath test statements; Table2 reports41.0% pass@64 on miniF2F-test for a model trained with miniF2F-valid statements. Existing human statements, libraries and formal kernels remain essential. The paper also describes earlier numeric-checking vulnerabilities and a Lean proof of an incorrectly formalized exercise. These examples show why exact checking and faithful statement translation are separate obligations. The trained models and formal proof pipeline have not been independently replayed here.\n\n## Scientific scope\n\nThis contribution is the proof-search method in arXiv 2205.11491v1. Its 82.6% headline is cumulative validation performance with adaptive online training, not an untouched held-out test success rate. The paper reports a 72.4% test result at pass@32; another test discussion concerns pass@8. Those evaluation budgets and adaptation conditions must remain distinct. Existing formal libraries and translated theorem statements are inherited inputs. WRS has not independently rerun the training, search or benchmark.\n\n## People and systems\n\nGuillaume Lample; Marie-Anne Lachaux; Thibaut Lavril; Xavier Martinet; Amaury Hayat; Gabriel Ebner; Aurélien Rodriguez; Timothée Lacroix\n\nEvariste / Meta AI Research (source-marked research affiliation) / Evariste encoder-decoder transformer:600M Metamath/Lean and440M Equations: Source-reported tactic generation and critic-guided HyperTree Proof Search with online training. (source reported).\n\n## Original sources\n\n- [Lample et al.2022: HyperTree Proof Search for Neural Theorem Proving — arXiv2205.11491v1](https://arxiv.org/pdf/2205.11491v1)\n",
      "summary": "HyperTree Proof Search explores all required branches of a candidate proof and couples transformer tactic generation with online policy/critic training; Evariste reports gains on Metamath and Lean under explicit adaptive and held-out protocols.\n\nA proof step may produce several obligations, and every obligation must be proved. HyperTree Proof Search selects a promising partial proof tree, expands its unresolved leaves and updates search estimates across the whole tree. A transformer proposes tactics, while a learned critic guides exploration. The Evariste system trains on feedback from ongoing searches, including newly found short proofs. The2022 paper studies Metamath, Lean and a simpler Equations environment. Its strongest headline Metamath result,82.6%, is the cumulative fraction solved on validation statements used during online training. This is useful adaptive search, but is different from an untouched-test result. Table3 separately reports72.4% pass@32 on Metamath test statements; Table2 reports41.0% pass@64 on miniF2F-test for a model trained with miniF2F-valid statements. Existing human statements, libraries and formal kernels remain essential. The paper also describes earlier numeric-checking vulnerabilities and a Lean proof of an incorrectly formalized exercise. These examples show why exact checking and faithful statement translation are separate obligations. The trained models and formal proof pipeline have not been independently replayed here.",
      "title": "Evariste and HyperTree Proof Search: learning from all proof obligations"
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    "title": "Evariste and HyperTree Proof Search: learning from all proof obligations",
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