A General Theory of Equivariant CNNs on Homogeneous Spaces.¶
Cohen, T. S., Geiger, & Weiler, M. (2019). A General Theory of Equivariant CNNs on Homogeneous Spaces. Advances in Neural Information Processing Systems 32 (NeurIPS), 9145-9156.
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Primes¶
- Equivariance
- The vocabulary lets a designer state precisely whether a representation should discard a symmetry (an invariant classifier label) or carry it forward (an equivariant feature map that later layers can still exploit), a layering distinction Cohen and colleagues (2019) formalize through the general theory of equivariant maps on homogeneous spaces.
This sourceGeneral theory of equivariant maps between fields on homogeneous spaces; shows the most general equivariant linear map corresponds to a generalized convolution with an equivariant kernel.
- The vocabulary lets a designer state precisely whether a representation should discard a symmetry (an invariant classifier label) or carry it forward (an equivariant feature map that later layers can still exploit), a layering distinction Cohen and colleagues (2019) formalize through the general theory of equivariant maps on homogeneous spaces.
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