Persistence-based operators in machine learning
This work addresses the problem of incorporating domain-specific constraints and symmetries into neural networks for researchers and practitioners in machine learning, representing an incremental advancement by combining existing methods.
The authors tackled the challenge of integrating mathematically grounded topological data analysis with neural networks by introducing persistence-based neural network layers, which allow injection of knowledge about data symmetries and can be composed with state-of-the-art architectures.
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.