Check out this 156-page tome: https://arxiv.org/abs/2104.13478:
"Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges"
The intro says that it "...serves a dual purpose: on one hand, it provides a common mathematical framework to study the most successful neural network architectures, such as CNNs, RNNs, GNNs, and Transformers. On the other hand, it gives a constructive procedure to incorporate prior physical knowledge into neural architectures and provide principled way to build future architectures yet to be invented."
Working all the way through that, besides relearning a lot of my undergrad EE math (some time in the previous century), I learned a whole new bunch of differential geometry that will help next time I open a General Relativity book for fun.
The intro says that it "...serves a dual purpose: on one hand, it provides a common mathematical framework to study the most successful neural network architectures, such as CNNs, RNNs, GNNs, and Transformers. On the other hand, it gives a constructive procedure to incorporate prior physical knowledge into neural architectures and provide principled way to build future architectures yet to be invented."
Working all the way through that, besides relearning a lot of my undergrad EE math (some time in the previous century), I learned a whole new bunch of differential geometry that will help next time I open a General Relativity book for fun.