Persformer: A Transformer Architecture for Topological Machine Learning
This work addresses a key bottleneck in topological machine learning for researchers and practitioners by providing a novel neural network approach that outperforms prior methods.
The paper tackles the challenge of using persistence diagrams from Topological Data Analysis in machine learning by introducing Persformer, a Transformer architecture that directly processes these diagrams, achieving significant performance improvements on benchmark datasets and enabling interpretability methods.
One of the main challenges of Topological Data Analysis (TDA) is to extract features from persistent diagrams directly usable by machine learning algorithms. Indeed, persistence diagrams are intrinsically (multi-)sets of points in $\mathbb{R}^2$ and cannot be seen in a straightforward manner as vectors. In this article, we introduce $\texttt{Persformer}$, the first Transformer neural network architecture that accepts persistence diagrams as input. The $\texttt{Persformer}$ architecture significantly outperforms previous topological neural network architectures on classical synthetic and graph benchmark datasets. Moreover, it satisfies a universal approximation theorem. This allows us to introduce the first interpretability method for topological machine learning, which we explore in two examples.