Research map / Learning theory and algorithms / Sample complexity
Approximation and non-parametric estimation of ResNet-type convolutional neural networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Realize a block-sparse FNN with M blocks by a ResNet-type CNN with constant width/channels and O(M) additional parameters | ResNet-type CNN (general block-sparse FNN approximation) · general function classes realizable by block-sparse FNNs | approximation rate | No clear effect |
| Use dense, constant-width ResNet-type CNN (fixed channel size and filter size) trained by clipped ERM instead of sparse optimal networks | beta-Holder regression · beta-Holder class | estimation error rate | Helped |
| Introduce scaling of identity mappings via channel masks (masked CNN) so residual block depth is constant | beta-Holder ResNet-type CNN · beta-Holder class | approximation/estimation rate with constant block depth | No clear effect |
| Rescale block-sparse FNN parameters (exploiting ReLU homogeneity) so that log of Lipschitz constant is O(1) in M | Barron and beta-Holder CNN estimation · Barron (s=2) and beta-Holder classes | estimation error rate | Helped |
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