MinesweeperEBRM: A Minesweeper Solver Based on the Energy-Based Reasoning Model

MinesweeperEBRM is an open-source project using the Energy-Based Reasoning Model (EBRM) to solve the classic Minesweeper game. It achieves a 94% win rate at maximum thinking depth and is implemented via Jupyter Notebook. This project demonstrates the potential of energy models in logical reasoning tasks involving constraint satisfaction and probabilistic decision-making.

Large language models excel in many tasks but struggle with complex reasoning. Methods like Chain-of-Thought (CoT) and Inference-Time Computation enhance reasoning. Energy-Based Models (EBMs) evaluate state quality via energy functions and find optimal states through minimization, fitting multi-step reasoning scenarios requiring logical consistency checks.

Created by developer training4usaco, MinesweeperEBRM applies EBM to Minesweeper (a game relying on logical inference). Implemented in Jupyter Notebook, it reaches a 94% win rate on standard 9x9 boards (10 mines) at maximum thinking depth—strong for learning-based solvers.

EBRM's key steps:

1. State Representation: Encode board state (revealed cells, flags, unrevealed cell probabilities).
2. Energy Function: High energy for inconsistent states (e.g., conflicting flagged cells), low for consistent ones.
3. Inference-Time Optimization: Iteratively search for low-energy states (simulating deep thinking).
4. Decision Sampling: Choose best action from optimized energy distribution; higher depth means more iterations.

Minesweeper tests multi-layered reasoning:

• Deterministic: Definitive safe/mined cells.
• Probabilistic: Risk assessment for uncertain cases.
• Global Constraints: Interconnected rules form complex networks.
• Risk Tradeoff: Balance risk/reward in uncertain choices. It evaluates local/global reasoning abilities.

MinesweeperEBRM uses a 13KB Jupyter Notebook codebase. Its 94% win rate outperforms human experts (80-90%) and rule-based solvers (struggle with probabilistic reasoning). Adjustable thinking depth lets users trade computation time for accuracy, similar to LLM inference-time expansion.

EBRM applies to:

• Constraint Satisfaction: Sudoku, logic puzzles.
• Planning: Pathfinding, resource allocation.
• Decision Support: Uncertain environment choices.
• Verification: System property testing. It also serves as an inference-time computation case study for LLMs.

Limitations: Closed rule-bound game (hard to expand to open domains), high computation cost. Future steps:

• Integrate EBRM with neural networks for better energy functions.
• Develop efficient optimization algorithms.
• Extend to real-world tasks.
• Study reasoning depth-performance relationship.