If this formalism works out then a few interesting directions spring to mind:<p>- we suddenly have a huge new toolbox from FP &#x2F; category theory that we can apply to understanding and extending DNNs. E.g. what happens if we apply differentiation in the manner of zippers to these structures? I have no idea but it might lead somewhere.<p>- The deep learning world gets a precise way to describe network architecture which makes communication much easier and research much more reproducible.<p>- With a formal model you can automate building and optimising implementations.