Neuro-Symbolic Sudoku Solver

TL;DR

This paper demonstrates that Neural Logic Machines can effectively solve Sudoku puzzles with high accuracy, showcasing their potential for complex problem-solving tasks where traditional neural networks struggle.

Contribution

The study extends NLMs to solve Sudoku, achieving 100% accuracy, and compares their convergence with backtracking algorithms, highlighting the importance of symbolic learning.

Findings

NLMs achieve 100% accuracy on Sudoku puzzles with 3-10 empty cells.

NLMs outperform traditional neural networks in solving complex combinatorial problems.

Comparison shows NLMs have competitive convergence times with backtracking algorithms.

Abstract

Deep Neural Networks have achieved great success in some of the complex tasks that humans can do with ease. These include image recognition/classification, natural language processing, game playing etc. However, modern Neural Networks fail or perform poorly when trained on tasks that can be solved easily using backtracking and traditional algorithms. Therefore, we use the architecture of the Neuro Logic Machine (NLM) and extend its functionality to solve a 9X9 game of Sudoku. To expand the application of NLMs, we generate a random grid of cells from a dataset of solved games and assign up to 10 new empty cells. The goal of the game is then to find a target value ranging from 1 to 9 and fill in the remaining empty cells while maintaining a valid configuration. In our study, we showcase an NLM which is capable of obtaining 100% accuracy for solving a Sudoku with empty cells ranging from 3 to 10. The purpose of this study is to demonstrate that NLMs can also be used for solving complex problems and games like Sudoku. We also analyze the behaviour of NLMs with a backtracking algorithm by comparing the convergence time using a graph plot on the same problem. With this study we show that Neural Logic Machines can be trained on the tasks that traditional Deep Learning architectures fail using Reinforcement Learning. We also aim to propose the importance of symbolic learning in explaining the systematicity in the hybrid model of NLMs.