One of the main challenges of Topological Data Analysis (TDA) is to extract meaningful features from persistent diagrams directly usable by machine learning algorithms. Indeed, persistence diagrams are intrinsically (multisets of points in $\mathbb R^2$ and cannot be seen straightforwardly as vectors).

This talk introduces Persformer, the first Transformer neural network architecture that accepts persistence diagrams as input. The Persformer architecture significantly outperforms previous topological neural network architectures on classical synthetic benchmark datasets and has competitive performance on graph datasets.

Furthermore, we introduce an interpretability method to topological machine learning to provide meaningful insights into the importance of the topological features in the persistence diagram of classical datasets. We show that having an expressive model like the Persformer allows us to find meaningful vector representations of persistence diagrams and analyze them using our interpretability method.

We expect our topological interpretability method to be helpful as an exploratory tool to understand use cases where the shape of a dataset is essential, such as biology or material science.