HONet: Data-Efficient Learning for Exact Cover Problems via Hypergraph Optimization

Deep learning approaches typically require prohibitive amounts of data to approximate strict Exact Cover Problems, while existing neuro-symbolic methods often face training infeasibility and scalability bottlenecks. To bridge this divide, we propose the Hypergraph Optimization Network (HONet), an end-to-end framework integrating a topologically complete Deep Residual Hypergraph Encoder with a differentiable Equality-Constrained Quadratic Programming layer. By adopting a "Fixed Polytope" paradigm guided by the Geometric Consistency Loss, HONet explicitly shapes the objective landscape, forcing the valid discrete solution to align with the unique global energy minimum. Empirical results show that HONet rapidly achieves 100\% accuracy on $9 \times 9$ Sudoku using limited samples, exhibiting superior data efficiency over baselines while maintaining exceptional robustness in highly sparse regimes and additional tasks.