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Persformer: A Transformer Architecture for Topological Machine Learning

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arxiv 2112.15210 v2 pith:PNLBNU6Z submitted 2021-12-30 cs.LG math.AT

Raphael Reinauer , Matteo Caorsi , Nicolas Berkouk This is my paper · ORCID
classification cs.LGmath.AT
keywords topologicalarchitecturediagramslearningmachinepersformerfirstintroduce
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. From Raw Data to Structural Semantics: Trade-offs among Distortion, Rate, and Inference Accuracy

    cs.IT 2024-12 reject novelty 6.0 of 10

    Using persistence diagrams as transmitted semantic summaries can drastically cut bit rate and improve error robustness for topology-based classification, but the reported rate advantage rests on a self-defined metric.

  2. SparseMeXT Unlocking the Potential of Sparse Representations for HD Map Construction

    cs.CV 2025-05 conditional novelty 5.0 of 10

    SparseMeXt, a sparse-query model for HD map construction, reaches 68.9% mAP on nuScenes at over 20 FPS, marginally outperforming the dense MapTRv2 baseline.

  3. Multiset Transformer: Advancing Representation Learning in Persistence Diagrams

    cs.LG 2024-11 conditional novelty 4.0 of 10

    A transformer with multiplicity-aware attention preserves permutation invariance, reduces complexity relative to Set Transformer, and improves persistence diagram classification over a PersLay baseline.

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