Attending to Topological Spaces: The Cellular Transformer

TL;DR

The paper introduces the Cellular Transformer, a novel neural network architecture that leverages topological structures like cell complexes to improve predictive performance on graph datasets, achieving state-of-the-art results.

Contribution

It presents a new transformer architecture tailored for cell complexes, with specialized attention mechanisms and positional encodings, advancing topological deep learning methods.

Findings

Achieves state-of-the-art performance on graph datasets.

Operates effectively without complex enhancements.

Leverages topological structures for improved learning.

Abstract

Topological Deep Learning seeks to enhance the predictive performance of neural network models by harnessing topological structures in input data. Topological neural networks operate on spaces such as cell complexes and hypergraphs, that can be seen as generalizations of graphs. In this work, we introduce the Cellular Transformer (CT), a novel architecture that generalizes graph-based transformers to cell complexes. First, we propose a new formulation of the usual self- and cross-attention mechanisms, tailored to leverage incidence relations in cell complexes, e.g., edge-face and node-edge relations. Additionally, we propose a set of topological positional encodings specifically designed for cell complexes. By transforming three graph datasets into cell complex datasets, our experiments reveal that CT not only achieves state-of-the-art performance, but it does so without the need for more complex enhancements such as virtual nodes, in-domain structural encodings, or graph rewiring.