Geometric Deep Learning for the Rubik's Cube Group

The Rubik's cube, a widely recognized combinatorial puzzle with an astronomically vast state space, has been the subject of various research experiments with neural networks used as heuristic estimators to navigate the state-space exploration. However, prior efforts have overlooked the intriguing symmetries inherent to this domain. Drawing on geometric deep learning principles, this article introduces a novel neural architecture that explicitly leverages these symmetries, grounded in a rigorous group-theoretical analysis. The design of the proposed symmetry-invariant model is then validated empirically through an innovative universal procedure for detecting model symmetry invariance. Finally, experimental results demonstrate that the symmetry-aware neural architecture exhibits enhanced generalization and problem-solving efficacy compared with the state of the art.