Research map / Architectures and efficiency / RNNs and normalization
Depth-Width Trade-offs for ReLU Networks via Sharkovsky's Theorem
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Compose a function with period m × p, where p is odd and greater than one | Continuous maps from [0,1] to [0,1] · Map compositions | crossings: at least ρ^t | Helped |
| Use a shallow ReLU network with u ≤ ρ^{k/l}/8 | The constructed alternating-points classification task · Constructed alternating points | classification error: ≥ 1/4 | Hurt |
| Increase network depth while fixing width at 6 neurons per layer | ReLU networks on the smoothed alternating point problem · Smoothed alternating point problem | accuracy: 99.04\% at 5 layers | Helped |
| Use a map whose prime period is a power of two | Map compositions · Period-2 and period-4 examples | crossings: one; t+3 | No clear effect |
| Reduce the generalized triangle-wave slope from φ to φ−ε | Triangle wave with a period-3 cycle · Map dynamics | period-3 cycle | Hurt |
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