Solving Sudoku Using Oscillatory Neural Networks

Abstract: This paper explores the application of Oscillatory Neural Networks (ONNs) to solving Sudoku puzzles, presenting a biologically inspired approach based on phase synchronization. Each cell is represented by an oscillator whose phase encodes a digit, and the synchronization is governed by the Kuramoto model. The system dynamically evolves towards a valid solution by having the puzzle constraints encoded into the weight matrix of the network, and through a proposed novel phase mapping of the Sudoku digits. Experimental results show that ONNs achieve high performance for puzzles with moderate difficulty and outperform Hopfield Neural Networks, particularly in cases with up to 20 initially unknown values. Although the performance decreases with increased ambiguity, ONNs still produce correct solutions in some of the iterations, cases in which the baseline Hopfield Neural Network algorithm fails. The findings support ONNs as a viable alternative for solving constraint optimization problems and reinforce their relevance within emerging non-von Neumann computing paradigms.