Node Classification and Search on the Rubik's Cube Graph with GNNs

TL;DR

This paper explores using Graph Neural Networks to classify nodes in the Rubik's Cube graph, enabling heuristic search for solving the cube efficiently and comparing favorably to existing methods.

Contribution

It introduces a novel approach of reformulating cube solving as a node classification problem with GNNs and integrating it into heuristic search.

Findings

GNN-based heuristics outperform baseline methods

Effective node classification for cube states

Improved search efficiency in cube solving

Abstract

This study focuses on the application of deep geometric models to solve the 3x3x3 Rubik's Cube. We begin by discussing the cube's graph representation and defining distance as the model's optimization objective. The distance approximation task is reformulated as a node classification problem, effectively addressed using Graph Neural Networks (GNNs). After training the model on a random subgraph, the predicted classes are used to construct a heuristic for $A^*$ search. We conclude with experiments comparing our heuristic to that of the DeepCubeA model.