Attending to Topological Spaces: The Cellular Transformer
This work addresses the need for more effective topological deep learning methods, offering a novel approach for researchers in machine learning and data science, though it is incremental as it builds on existing transformer architectures.
The paper tackles the problem of enhancing neural network performance by leveraging topological structures in data, introducing the Cellular Transformer (CT) that generalizes graph-based transformers to cell complexes and achieves state-of-the-art performance on transformed graph datasets.
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.