# Graph Coloring Approach to Solving Sudoku with Oscillatory Neural Networks

arXiv: https://arxiv.org/abs/2607.15814 · HTML: https://mlsanity.com/paper/2607.15814/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 43 references that are in the map.
- First posted on arXiv 17 Jul 2026.

## Builds on (most cited first, 7 of 7)

- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Artificial Kuramoto Oscillatory Neurons](https://mlsanity.com/paper/2410.13821/) (2024)
- [Deep Oscillatory Neural Network](https://mlsanity.com/paper/2405.03725/) (2024)
- [Learning at the Speed of Physics: Equilibrium Propagation on Oscillator Ising Machines](https://mlsanity.com/paper/2510.12934/) (2025)
- [Overcoming Quadratic Hardware Scaling for a Fully Connected Digital Oscillatory Neural Network](https://mlsanity.com/paper/2504.20680/) (2025)
- [GPU-Accelerated Simulated Oscillator Ising/Potts Machine Solving Combinatorial Optimization Problems](https://mlsanity.com/paper/2505.22631/) (2025)

## Abstract (arXiv)

Oscillatory Neural Networks (ONNs) present an attractive physics-based computing paradigm rooted in the dynamics of a network of typically fully coupled oscillators aiming to minimize an underlying energy function. In this paper, we propose an ONN-based solver for one well-known constrained combinatorial optimization problem, namely a Sudoku, by formulating the problem as a Graph Coloring problem. By modifying the already existing Graph Coloring solver to a computationally cheaper version and introducing an additional term ensuring the fulfillment of the Sudoku constraints, our solver is shown to significantly outperform the existing HNN- and ONN solvers in terms of accuracy. In particular, we are able to achieve nearly flawless accuracies on 4 × 4 as well as rather high accuracies on 9 × 9 Sudoku puzzles for different numbers of unknown digits.