Solving Sudoku using oscillatory neural networks

TL;DR

This paper demonstrates that oscillatory neural networks can be effectively used to solve Sudoku puzzles by encoding the problem into a graph structure and leveraging phase dynamics, outperforming traditional Hopfield networks.

Contribution

The paper introduces a novel ONN-based mapping strategy for Sudoku, utilizing graph embeddings and phase dynamics modeled by Kuramoto equations, showing improved performance over HNN.

Findings

ONN mapping outperforms HNN in solving Sudoku

Phase dynamics modeled by Kuramoto equations are effective

Graph embedding encodes Sudoku constraints efficiently

Abstract

We explore the capabilities of physical computing with Oscillatory Neural Networks (ONN) to solve combinatorial optimization problems. To solve Sudokus with ONNs, we define a novel mapping strategy that utilizes the unique characteristics of the computation paradigm. The problem is encoded through a puzzle specific graph-embedding, which implements the constraints through different subgraphs. These subgraphs are then combined into a single adjacency matrix, which allows the natural dynamics of the phases of coupled oscillators to find a solution to the puzzle. We model the phase dynamics of the ONN by means of the Kuramoto differential equation. This novel approach is then compared to the well-established iterative method to solve Sudoku already used in binary Hopfield networks (HNN). Solving optimization problems typically requires a large amount of energy to solve on conventional hardware. Therefore, we are motivated to explore the mapping of Sudoku from a theoretical point of view to establish the validity of this approach. The simulation results show that the novel ONN mapping outperforms the established HNN methodology.