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We do. If you’re interested in the architecture particulars (I.e. which layer types, layer shapes, layer parameters, activation functions, etc) you’ll commonly see these in deep learning papers as a directed acyclic graph with layers represented by a collection of vertices or rectangles. Other architecture specifics are sometimes noted with text alongside layers. We also have more general representations of deep models which look like, and sometimes are exactly, Probabilistic Graphical Models. PGMs have their own formal language which makes it quite easy to write complex models describing a joint distribution very simply.

However, this is different than interpreting how a deep model works. “Interpreting” is an overloaded and poorly-defined term of active research. The sense I get from my friends in the interpretability/explainability research world is that despite the buzz, there is no common definition that lends to a clear set of requirements for an acceptable interpretation of a neural network.