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

arXiv: https://arxiv.org/abs/2501.18580 · HTML: https://mlsanity.com/paper/2501.18580/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 11 references that are in the map.
- First posted on arXiv 30 Jan 2025.

## Builds on (most cited first, 2 of 2)

- [Solving the Rubik's Cube Without Human Knowledge](https://mlsanity.com/paper/1805.07470/) (2018)
- [Solving a Rubik's Cube Using its Local Graph Structure](https://mlsanity.com/paper/2408.07945/) (2024)

## Built on by (most cited first, 1 of 1)

- [Learning the Word Problem: Geodesic Lengths and Cryptographic Applications](https://mlsanity.com/paper/2607.26241/) (2026)

## Abstract (arXiv)

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.