Reviews: Invariance and Stability of Deep Convolutional Representations

The primary focus of the paper is CKN (convolutional kernel network) [13, 14]. C 1 diffeomorphisms (such as translation), in the sense of Eq. (4)] of the representation formed by CKNs. They show that for norm-preserving and non-expansive kernels [(A1-A2) in line 193] stability holds for appropriately chosen patch sizes [(A3)]. Extension from (R d,) to locally compact groups is sketched in Section 4. The paper is nicely organized, clearly written, technically sound, combining ideas from two exciting areas (deep networks and kernels). The stability result can be of interest to the ML community.