I tend to think of it in terms of topology — since that’s my background. The semantics of a system is mapping the topology of the input space to output space.

I tend to think of it in terms of topology — since that’s my background. The semantics of a system is mapping the topology of the input space to output space. DL expresses that relationship geometrically; symbolic reasoning expresses that relationship algebraically. For every geometric expression of semantics, there is some corresponding algebraic one — which we can view as the “internal language” of the DNN.