For one-hidden-layer equivariant networks, generalization bounds depend only on filter norms and the sample size, while suitable weight sharing can match equivariance and locality adds an extra gain.
Symmetries and discriminability in feedforward network architectures
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On the Sample Complexity of One Hidden Layer Networks with Equivariance, Locality and Weight Sharing
For one-hidden-layer equivariant networks, generalization bounds depend only on filter norms and the sample size, while suitable weight sharing can match equivariance and locality adds an extra gain.