## Diagram: Automated Theorem Proving System Architecture ### Overview The diagram illustrates a multi-stage automated theorem proving system with iterative learning and curriculum adaptation. It shows data flow from GitHub repositories through a LeanAgent, curriculum learning framework, progressive training mechanisms, and specialized handling of "SORRY Theorems" (theorems that initially fail to prove). ### Components/Axes **Key Components:** 1. **Input Layer** - GitHub Repositories (source of theorems/proofs) - Extract Data Per Repository → Premise Corpus + Theorems + Proofs 2. **Core Processing** - LeanAgent (theorem proving engine) - Curriculum Learning (complexity-based adaptation) - Progressive Training (retriever evolution) 3. **Output Layer** - Dynamic Database (knowledge repository) - SORRY Theorem Proving (specialized handling) **Visual Elements:** - Color-coded complexity levels (green=low, yellow=medium, red=high) - Feedback loops between components - Iterative refinement arrows ### Detailed Analysis **1. Data Ingestion Pipeline** - GitHub repositories → Extract Data Per Repository - Creates: Premise Corpus + Theorems + Proofs **2. Curriculum Learning System** - Complexity → Theorem Complexities (e.g., 2.7, 7.4) - Complexity graph shows: - # Proof Steps vs Complexity - Distribution: Easy (green) → Medium (yellow) → Hard (red) - Descending # Easy Theorems over time **3. Progressive Training Mechanism** - Latest Retriever → Limited Exposure (1 epoch) - Balanced Training (Stability vs Plasticity) - New Retriever generation **4. SORRY Theorem Proving** - Input: SORRY Theorems - Process: - Retrieved Premises (updated retriever) - Generated Tactics - Best-First Tree Search - Output: New Proofs ### Key Observations 1. **Iterative Learning**: Feedback loops between components suggest continuous improvement 2. **Complexity Adaptation**: Curriculum learning adjusts difficulty based on proof complexity metrics 3. **Retriever Evolution**: Progressive training creates increasingly sophisticated theorem retrieval systems 4. **Specialized Handling**: SORRY Theorems use distinct processing pipeline with retrieval-augmented generation ### Interpretation This architecture demonstrates a sophisticated approach to automated theorem proving that: 1. **Adapts Difficulty**: Uses complexity metrics to create personalized learning paths 2. **Balances Stability/Plasticity**: Progressive training maintains core knowledge while enabling adaptation 3. **Handles Edge Cases**: Specialized SORRY Theorem Proving addresses previously unsolved problems 4. **Leverages Community Knowledge**: GitHub repositories serve as initial knowledge base The system appears designed to create self-improving theorem provers that can handle increasingly complex mathematical problems through iterative learning and curriculum adaptation. The "SORRY Theorem" handling suggests a focus on solving previously intractable problems through advanced retrieval and search strategies.