[XuMiao]

Algebra geometry view makes sense to me. Considering ML as a learning to approximate scheme algorithm. Tensor representation is similar to the SDP trick achieving the optimal max-sat approximation. The difference is that DL approximates from inside of the high dimensional space (concave) while SDP approximates from outside (convex). The later one turns into polynomial algorithm, but the former one remains NP-hard. The success of DL just proved that there is a long way to go for P equals NP. Whenever we figure that out, symbolic approach and Tensor approach will merge.

[zmgsabst]

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.