Oscillatory Neural Networks Solve Sudoku with High Accuracy

Researchers have explored the application of Oscillatory Neural Networks (ONNs) for solving constrained combinatorial optimization problems, specifically Sudoku puzzles. ONNs represent a physics-based computing paradigm where a network of coupled oscillators minimizes an underlying energy function. In this work, the Sudoku problem is ingeniously reformulated as a Graph Coloring problem, a common approach in computational optimization. The proposed ONN-based solver builds upon an existing Graph Coloring solver, introducing modifications to make it computationally more efficient and adding an explicit term to ensure all Sudoku constraints are met. Empirical evaluations demonstrate that this enhanced ONN solver significantly surpasses the accuracy of previous solvers based on both Hopfield Neural Networks (HNNs) and other ONN architectures. The system achieved nearly flawless accuracy on 4x4 Sudoku puzzles and notably high accuracy on 9x9 puzzles, even with varying numbers of unknown digits, showcasing the potential of ONNs for complex constraint satisfaction problems.