Yanasse: Finding New Proofs from Deep Vision's Analogies, Part 1

2026-04-18

AI Summary

This study investigates the transfer of proof strategies across mathematically distinct domains to discover new theorems. By analyzing tactic usage patterns in Lean 4, the authors demonstrate that such strategies decompose into domain-specific heads and domain-agnostic modifiers, with the latter exhibiting strong transferability. The work introduces the first fully domain-agnostic analogical matching engine, integrating GPU acceleration (Apple MPS), z-score statistical analysis, AI-driven semantic adaptation, and relation extraction to enable strategy transfer between probability theory and representation theory. In experiments, the system generated four formally verified, sorry-free proofs in Lean within ten attempts—a 40% success rate—providing the first empirical evidence for the feasibility of cross-domain formal proof transfer.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Security and Privacy: Data transparency and provenance

Abstract

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.

Problem

• proof transfer
• analogy
• mathematical reasoning
• tactic patterns
• cross-domain

Innovation

• proof transfer
• tactic analogy
• domain-independent matching
• semantic adaptation
• Lean 4