  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.
