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Equivariance Through Parameter-Sharing

2020-03-09 | |  85 |   35 |   0

Abstract

We propose to study equivariance in deep neural networks through parameter symmetries. In particular, given a group 图片.png that acts discretely on the input and output of a standard neural network layer 图片.png we show that 图片.png is equivariant with respect to 图片.png-action iff 图片.png explains the symmetries of the network parameters W. Inspired by this observation, we then propose two parameter-sharing schemes to induce the desirable symmetry on W. Our procedure for tying the parameters achieves 图片.png-equivariance and, under some conditions on the action of 图片.png, it guarantees sensitivity to all other permutation groups outside 图片.png.

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