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One of the main challenges of Topological Data Analysis (TDA) is to extractfeatures from persistent diagrams directly usable by machine learningalgorithms. Indeed, persistence diagrams are intrinsically (multi-)sets ofpoints in $\mathbb{R}^2$ and cannot be seen in a straightforward manner asvectors. In this article, we introduce $\texttt{Persformer}$, the firstTransformer neural network architecture that accepts persistence diagrams asinput. The $\texttt{Persformer}$ architecture significantly outperformsprevious topological neural network architectures on classical synthetic andgraph benchmark datasets. Moreover, it satisfies a universal approximationtheorem. This allows us to introduce the first interpretability method fortopological machine learning, which we explore in two examples.

Persformer: A Transformer Architecture for Topological Machine Learning