I’m not sure if this will be helpful or if you’ve already explored this connection, but the field of abstract interpretation tries to understand the semantics of a computer program without fully executing it. The theme of “trying to understand what a program will do by just examining its source code” is also present in program analysis. If we can understand neural networks as typed functional programs maybe there’s something worth thinking about here.
I’m not sure if this will be helpful or if you’ve already explored this connection, but the field of abstract interpretation tries to understand the semantics of a computer program without fully executing it. The theme of “trying to understand what a program will do by just examining its source code” is also present in program analysis. If we can understand neural networks as typed functional programs maybe there’s something worth thinking about here.