In this work we introduce an algebraic formalism to describe and construct deep learning architectures as well as actions on them. We show how our algebraic formalism in conjunction with topological data analysis enables the construction of neural network architectures from a priori geometries, geometries obtained from data analysis, and purely data driven geometries. We also demonstrate how these techniques can improve the transparency and performance of deep neural networks.
CITATION STYLE
Carlsson, G., & Gabrielsson, R. B. (2020). Topological Approaches to Deep Learning. In Abel Symposia (Vol. 15, pp. 119–146). Springer. https://doi.org/10.1007/978-3-030-43408-3_5
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