Yanasse: Finding New Proofs from Deep Vision's Analogies, Part 1
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910145738440704 |
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| author | Linhares, Alexandre |
| author_facet | Linhares, Alexandre |
| contents | Project Yanasse presents a method for discovering new proofs of theorems in one area of mathematics by transferring proof strategy patterns (e.g., Lean 4 tactic invocation patterns) from a structurally distant area. The system extracts tactic usage distributions across 27 top-level areas of Mathlib (217,133 proof states), computes z-scores to identify tactics that are heavily used in a source area but rare or absent in a target area, matches source and target proof states via GPU-accelerated NP-hard analogy (running on a MacBook Air via Apple's MPS backend), and then asks an AI reasoning agent to semantically adapt--not symbol-substitute--the source tactics invocation pattern to the target theorem. In this first part of the study, the method is applied to the pair Probability -> Representation Theory, producing 4 Lean-verified new proofs out of 10 attempts (40%). The proofs compile with zero sorry declarations. The key finding is that tactic schemas decompose into a head (domain-gated, rarely transfers) and a modifier (domain-general, often transfers): filter upwards's head fails in representation theory (no Filter structure), but its [LIST] with ω modifier transfers cleanly as ext1 + simp [LIST] + rfl. Crucially, the underlying matching engine--deep vision lib.py--is entirely domain independent: the same optimization code for an NP-hard matching that matches chess positions by analogy matches Lean proof states by analogy, without knowing which domain it is processing. Only a relation extractor is domain-specific. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_17229 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Yanasse: Finding New Proofs from Deep Vision's Analogies, Part 1 Linhares, Alexandre Artificial Intelligence 03B35, 68T15 I.2.3; I.2.6; F.4.1 Project Yanasse presents a method for discovering new proofs of theorems in one area of mathematics by transferring proof strategy patterns (e.g., Lean 4 tactic invocation patterns) from a structurally distant area. The system extracts tactic usage distributions across 27 top-level areas of Mathlib (217,133 proof states), computes z-scores to identify tactics that are heavily used in a source area but rare or absent in a target area, matches source and target proof states via GPU-accelerated NP-hard analogy (running on a MacBook Air via Apple's MPS backend), and then asks an AI reasoning agent to semantically adapt--not symbol-substitute--the source tactics invocation pattern to the target theorem. In this first part of the study, the method is applied to the pair Probability -> Representation Theory, producing 4 Lean-verified new proofs out of 10 attempts (40%). The proofs compile with zero sorry declarations. The key finding is that tactic schemas decompose into a head (domain-gated, rarely transfers) and a modifier (domain-general, often transfers): filter upwards's head fails in representation theory (no Filter structure), but its [LIST] with ω modifier transfers cleanly as ext1 + simp [LIST] + rfl. Crucially, the underlying matching engine--deep vision lib.py--is entirely domain independent: the same optimization code for an NP-hard matching that matches chess positions by analogy matches Lean proof states by analogy, without knowing which domain it is processing. Only a relation extractor is domain-specific. |
| title | Yanasse: Finding New Proofs from Deep Vision's Analogies, Part 1 |
| topic | Artificial Intelligence 03B35, 68T15 I.2.3; I.2.6; F.4.1 |
| url | https://arxiv.org/abs/2604.17229 |