Persformer: A Transformer Architecture for Topological Machine Learning
read the original 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.
This paper has not been read by Pith yet.
Forward citations
Cited by 3 Pith papers
-
A Closed-Form Persistence-Landmark Pipeline for Certified Point-Cloud and Graph Classification
PLACE delivers a closed-form certified classification method for point clouds and graphs based on persistent homology with explicit excess-risk bounds, selection rules, and training-time certificates.
-
nD-RoPE: A Generalized RoPE for n-Dimensional Position Embedding
nD-RoPE derives an isotropic n-dimensional RoPE from a translation-invariant Hilbert-space formulation and instantiates it via multi-scale regular-simplex wave vectors, reporting gains on multi-dimensional data.
-
A Closed-Form Persistence-Landmark Pipeline for Certified Point-Cloud and Graph Classification
PLACE delivers a closed-form persistent-homology classifier for point clouds and graphs with explicit margin bounds, descriptor selection, and training-time certificates derived solely from labels.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.