Solving Sudoku using oscillatory neural networks

2025/08/04 by Bram F. Haverkort, Haverkort, Bram F., Federico Sbravati +5 · 3 voices · 1 citation
Computer Science · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #Emerging Technologies (cs.ET) #FOS: Computer and information sciences #FOS: Physical sciences #cond-mat.dis-nn #cs.ET

paper · pdf · doi:10.48550/arxiv.2508.02250

arxiv published 2025/08/04 · arxiv updated 2025/12/08

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.

Citations

• A Study Of Sudoku Solving Algorithms: Backtracking and Heuristic
• Scalable 28nm IC implementation of coupled oscillator network featuring tunable topology and complexity
• Overcoming Quadratic Hardware Scaling for a Fully Connected Digital Oscillatory Neural Network
• Artificial Kuramoto Oscillatory Neurons
• Neuromorphic Artificial Intelligence Systems
• Physics for Neuromorphic Computing
• Searching for memories, Sudoku, implicit check-bits, and the iterative use of not-always-correct rapid neural computation
• Onset of cooperative entrainment in limit-cycle oscillators with uniform all-to-all interactions: bifurcation of the order function
• Can programming be liberated from the von Neumann style?

Cited by

• G-RRM: Guiding Symbolic Solvers with Recurrent Reasoning Models

Discussions

• #arXiv Solving Sudoku Using Oscillatory Neural Networks arxiv.org/abs/2508.02250 “a biologically inspired approach based on phase synchronization. Although the performance decreases with increased amb [bsky, 2 points, 0 comments]
• #arXiv Solving Sudoku Using Oscillatory Neural Networks https://arxiv.org/abs/2508.02250 “a biologically inspired approach based on phase synchronization. Although the performance decreases with incre [bsky, 1 points, 0 comments]
• # arXiv Solving Sudoku Using Oscillatory Neural Networks https:// arxiv.org/abs/2508.02250 “a biologically inspired approach based on phase synchronization. Although the performance decreases with inc [mastodon, 0 points, 0 comments]

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