Research map / Architectures and efficiency / RNNs and normalization
The Expressive Power of Neural Networks: A View from the Width
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Allow width n+4 rather than limiting width to n | Fully connected ReLU networks approximating Lebesgue-integrable functions · Lebesgue-integrable functions on ℝ^n | L1 approximation error: width d_m ≤ n+4: < ε; width d_m ≤ n: +∞ or ∫ |f(x)| dx | Helped |
| Increase width from at most n-1 to n+4 | Fully connected ReLU networks · Nonconstant-direction continuous functions on [-1,1]^n | L1 approximation error: width d_m ≤ n-1: ≥ ε*; width d_m ≤ n+4: < ε | Helped |
| Approximate width-2k², depth-3 targets using width-3k^(3/2), depth-k+2 networks | ReLU networks approximating randomly sampled target functions · n=1 and n=2, k=3,4,5 | Mean square error: Worst-case errors: 0.002248, 0.003263, 0.005643, 0.008729, 0.018852, 0.030114; average-case errors: 0.000345, 0.000892, | Helped |
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