Persformer: A Transformer Architecture for Topological Machine Learning

2021/12/30 by Raphael Reinauer, Reinauer, Raphael, Matteo Caorsi +3 · 3 citations
Computer Science · #Algebraic Topology (math.AT) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2112.15210

openalex publication_date 2021/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ℝ² and cannot be seen in a straightforward manner as vectors. In this article, we introduce 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 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.

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Related

• xPerT: Extended Persistence Transformer
• Unreduced Persistence Diagrams for Topological Machine Learning
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• Persistence-based operators in machine learning