Research map / Learning theory and algorithms / Kernels and regression theory
Why Robust Generalization in Deep Learning is Difficult: Perspective of Expressive Power
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a ReLU network of size \mathcal{O}(Nd) to robustly fit finite separated training data | ReLU network · Separated finite training data | network size for zero robust training error: \mathcal{O}(Nd) | Helped |
| Require robust generalization rather than only fitting finite training data | ReLU network · Separated data in ambient dimension d | network size requirement: \mathcal{O}(Nd) -> \exp(\Omega(d)) | Hurt |
| Add linear-separability structure to the data while retaining robust generalization | ReLU network · Linear-separable data | network size lower bound for low robust generalization error: \exp(\Omega(d)) | No clear effect |
| Assume data lies on a k-dimensional manifold instead of relying on ambient dimension d | ReLU network · k-dimensional manifold data | network size sufficient for low robust generalization error: \exp(\mathcal{O}(d)) -> \exp(\mathcal{O}(k)) | Helped |
| Retain robust generalization on a k-dimensional manifold | ReLU network · k-dimensional manifold data | network size lower bound: \exp(\Omega(k)) | Hurt |
| Use a parameterized model whose VC dimension is polynomial in its number of parameters | Parameterized models · Linear-separable, well-separated data | network size needed to avoid constant robust test error: \exp(\Omega(d)) | Hurt |
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