Equivariant Representation Learning with Equivariant Convolutional Kernel Networks

Soutrik Roy Chowdhury, Johan Suykens

Keywords: Equivariant representations, Kernel methods, Robustness

TL;DR: Construction of equivariant representations with multilayered convolutional kernel networks.

Abstract:

Convolutional Kernel Networks (CKNs) were proposed as multilayered representation
learning models that are based on stacking multiple Reproducing Kernel Hilbert
Spaces (RKHSs) in a hierarchical manner. CKN has been studied to understand the (near) group invariance
and (geometric) deformation stability properties of deep convolutional representations by exploiting
the geometry of corresponding RKHSs. The objective of this paper is two-fold: (1) Analyzing the construction of
group equivariant Convolutional Kernel Networks (equiv-CKNs) that induce in the model symmetries like translation, rotation etc., (2) Understanding
the deformation stability of equiv-CKNs
that takes into account the geometry of inductive biases and that of RKHSs. Multiple kernel based construction of
equivariant representations might be helpful in understanding the geometric model complexity of equivariant CNNs as well as shed lights on the construction practicalities of robust equivariant networks.

Type Of Submission: Extended Abstract (4 pages, non-archival)

Submission Number: 78