Research map / Learning theory and algorithms / Kernels and regression theory
Exponential expressivity in deep neural networks through transient chaos
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a deep random network in the chaotic phase rather than the ordered phase | Random deep neural networks · Input manifolds propagated through the network | global curvature | Helped |
| Increase network depth in the chaotic regime | Random deep neural networks · Input manifolds propagated through the network | Euclidean length | Helped |
| Increase network depth in the chaotic regime | Random deep neural networks · Input manifolds propagated through the network | extrinsic curvature | Helped |
| Increase network depth in the chaotic regime | Random deep neural networks · Input manifolds propagated through the network | high-frequency function expressivity | Helped |
| Increase width of a one-hidden-layer network | Shallow neural network · Circle input; Fourier-basis function approximation | high-frequency prediction error | No clear effect |
| Use a shallow network instead of a deep network in the chaotic regime | Neural network representation · Circle input | Euclidean length | Hurt |
| Perturb weights in an earlier layer | Random deep neural network · Functions computed on a circle | function-space decorrelation | Helped |
| Backpropagate a linear decision boundary through increasing network depth | Random deep neural network · Input-space classification boundary | principal curvature | Helped |
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