Persformer: A Transformer Architecture for Topological Machine Learning

TL;DR

Persformer is a novel Transformer-based neural network architecture designed to directly process persistence diagrams in topological data analysis, achieving superior performance and interpretability on benchmark datasets.

Contribution

It introduces the first Transformer architecture for topological data analysis that accepts persistence diagrams as input, with proven universal approximation capabilities.

Findings

Outperforms previous topological neural networks on benchmark datasets

Satisfies a universal approximation theorem

Enables the first interpretability method for topological machine learning

Abstract

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.