Artificial intelligence, especially deep learning & neural networks for image processing and classfication, are related to statistics and physics e.g. as decribed in below papers.

Statistics and AI

Simoncelli + Olshausen.Natural images statistics and neural representation

Field.What the statistics of natural images tell us about visual coding

Physics and AI

A relation of deep learning and physics (renormalization group) is elaborated in:

Mehta + Schwab.An exact mapping between the Variational Renormalization Group and Deep Learning

Also category theory is used to describe neural systems and single aspects like e.g. back propagation.

Category theory and AI

MSE - Category Theory & Artificial Intelligence (AI)

Question. Are there interesting formulations and generalizations of (convolutional) neural networks (CNNs) / deep learning (or to machine learning in general) concepts in an algebraic context?

For example I read something about Clifford Neural Networks based on Clifford Algebras

Hitzer et al.Applications of Clifford’s Geometric Algebra

mentioning Clifford algebra neural computing. However as far as I understand, this is more a generalization of neuron's in- and output values rather than an algebraic formulation of neural network related concepts?

In a similar direction(?) goes e.g.

Bronstein et al.Geometric deep learning: going beyond Euclidean data

Remark. I am aware that this question could also be posted at stack overflow or some other stack exchange site. However my idea is that it could be better to ask it on the mathematics site, since it might rather be mathematicians that have some knowledge about such connections than e.g. computer scientists themselves.


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