Research map / Architectures and efficiency / RNNs and normalization
Neural Networks with Small Weights and Depth-Separation Barriers
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace arbitrary weights with polynomially bounded weights, allowing depth to increase to 3k+3 | Polynomial-width ReLU networks approximating approximately polynomially bounded functions · Continuous input distributions with almost-bounded support and conditional density | approximation capability at bounded depth | Helped |
| Replace arbitrary weights with polynomially bounded weights, allowing depth to increase to 3k+3 | Polynomial-width ReLU networks approximating approximately polynomially bounded functions · Discrete grid input distributions | approximation capability at bounded depth | Helped |
| Translate a neural-network depth separation into a threshold-circuit depth separation | ReLU networks of depths k and k', for k' > k >= 4 · Continuous input distributions with almost-bounded support and conditional density | threshold-circuit depth separation | Mixed |
| Translate a neural-network depth separation into a threshold-circuit depth separation | ReLU networks of depths k and k', for k' > k >= 4 · Discrete grid input distributions | threshold-circuit depth separation | Mixed |
| Use a depth-3 network instead of a general constant-depth network | Radial functions under radial input distributions · Radial functions | depth | Helped |
| Use a depth-2 network instead of a general constant-depth network | Additive functions on independent input components · Functions of the form sum_i f_i(x_i) | depth | Helped |
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