Research map / Architectures and efficiency / RNNs and normalization
Sharp Representation Theorems for ReLU Networks with Precise Dependence on Depth
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use D layers instead of D' < D layers | ReLU networks approximating functions in G_D · G_D | square-loss approximation rate: N^{-{D^{\prime}}/{D}} -> N^{-1} | Helped |
| Use frequency-multiplying triangle-wave compositions across layers | ReLU networks approximating high-frequency cosine components · cos(ωt) on [-1,1] | number of ReLU units required: Ω(ω) -> O(ω^{1/D}) | Helped |
| Increase depth from D to D+1 for the corresponding function class | ReLU networks with N_0 units · G_D | square loss: (D/N_0)^{D/D} -> ((D+1)/N_0)^{(D+1)/D} | Helped |
| Increase class index K, allowing less smooth functions | Function classes G_K · G_K | smoothness represented | Mixed |
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