Papers › Equivariance Through Parameter-Sharing
Equivariance Through Parameter-Sharing
Siamak Ravanbakhsh, Jeff Schneider, Barnabas Poczos
We propose to study equivariance in deep neural networks through parameter symmetries. In particular, given a group 𝒢 that acts discretely on the input and output of a standard neural network layer ϕ_W: ᴹ →ᴺ, we show that ϕ_W is equivariant with respect to 𝒢-action iff 𝒢 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 procedures for tying the parameters achieve 𝒢-equivariance and, under some conditions on the action of 𝒢, they guarantee sensitivity to all other permutation groups outside 𝒢.
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