Timezone: »

On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups
Risi Kondor · Shubhendu Trivedi

Fri Jul 13 09:15 AM -- 12:00 PM (PDT) @ Hall B #154

Convolutional neural networks have been extremely successful in the image recognition domain because they ensure equivariance with respect to translations. There have been many recent attempts to generalize this framework to other domains, including graphs and data lying on manifolds. In this paper we give a rigorous, theoretical treatment of convolution and equivariance in neural networks with respect to not just translations, but the action of any compact group. Our main result is to prove that (given some natural constraints) convolutional structure is not just a sufficient, but also a necessary condition for equivariance to the action of a compact group. Our exposition makes use of concepts from representation theory and noncommutative harmonic analysis and derives new generalized convolution formulae.

Author Information

Risi Kondor (The University of Chicago)
Shubhendu Trivedi (Toyota Technological Institute)

Related Events (a corresponding poster, oral, or spotlight)

More from the Same Authors