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Globally Optimal Gradient Descent for a ConvNet with Gaussian Inputs
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Assume standard independent Gaussian inputs instead of an unconstrained input distribution | Gradient descent for no-overlap ReLU ConvNets · No-overlap ConvNet population risk | computational tractability: NP-complete -> polynomial time | Helped |
| Allow overlap between convolutional filters | Gradient descent for ReLU ConvNets · Gaussian inputs, two-dimensional filter example | probability of getting stuck in a sub-optimal region: ≥ 1/4 | Hurt |
| Use multiple random initializations | Gradient descent for overlapping ConvNets · Gaussian inputs, empirical study | basin of attraction of the global optimum: at least 1/17 | Helped |
| Train on Gaussian rather than reduction-constructed non-Gaussian data | AdaGrad for no-overlap ConvNets · Empirical illustration, datasets of size 800 | training loss: 0.06 | Helped |
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