For actual neurobiology, try this:

• Kathryn Hess, Towards a categorical approach to neuroscience, ACT2018 talk.

I believe that Google’s Tensorflow is connected to monoidal categories:

• John Baez, Programming with data flow graphs, 5 June 2016.

but I haven’t had time to sort this out in my mind. (This is completely separate from whether there’s a graphical interface to Tensorflow; apparently there was not when I posted that article.)

Another thing worth looking at is this:

• Brendan Fong, David I. Spivak and Rémy Tuyéras, Backprop as functor: a compositional perspective on supervised learning.

There should be a *lot* more to say about applications of category theory to both neurobiology and artificial neural networks, but I haven’t seen enough work on this.

Being no expert, I don’t have a solid understanding of the Category theory. But I’ve been having the impression that the Category theory as I understand it is about a mathematical formulation or framework of the networks and can in principle be applied to anything involving a network.

My interested subject of research and study has lately been related to (Biological or Artificial) Neural Network, or distributed learning in the view of Connectionism (I’d say).

My question is, are you familiar with any research regarding Neural Networks where the idea or methods of Category Theory are used?

A paper I have found relevant in this line of research is:

The Representation Theory of Neural Networks

(https://arxiv.org/abs/2007.12213)

Marco Antonio Armenta, Pierre-Marc Jodoin

which used Quiver to formulate the network.

Anyhow, I admire your works and find them inspiring, although I have to learn more to fully appreciate them. Thank you for your contributions to community.

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