Research map / Learning theory and algorithms / Sample complexity
Besov Function Approximation and Binary Classification on Low-Dimensional Manifolds Using Convolutional Residual Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Design the ConvResNet to exploit the data’s intrinsic manifold dimension | ConvResNet approximation of Besov functions · Besov functions on a d-dimensional manifold | Network size scaling with approximation accuracy: M=O\left(\varepsilon^{-d/s}\right) | Helped |
| Use a properly chosen ConvResNet and empirical logistic risk minimization | Binary classification on a d-dimensional manifold · Binary classification on a d-dimensional manifold | Expected excess logistic risk: Cn^{-\frac{s}{2s+2(s\vee d)}}\log^4 n | Helped |
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