Related papers: Persistence-based operators in machine learning

Persistence-based operators in machine learning

URL: http://arxiv.org/abs/2212.13985v1
Date: Wed, 28 Dec 2022 18:03:41 GMT
Title: Persistence-based operators in machine learning
Authors: Mattia G. Bergomi, Massimo Ferri, Alessandro Mella, Pietro Vertechi
Abstract summary: We introduce a class of persistence-based neural network layers. Persistence-based layers allow the users to easily inject knowledge about symmetries respected by the data, are equipped with learnable weights, and can be composed with state-of-the-art neural architectures.
Score: 62.997667081978825
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topological data analysis allow users to design analysis pipelines fully aware of data constraints and symmetries. We introduce a class of persistence-based neural network layers. Persistence-based layers allow the users to easily inject knowledge about symmetries (equivariance) respected by the data, are equipped with learnable weights, and can be composed with state-of-the-art neural architectures.

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