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Fast Convergence of Natural Gradient Descent for Over-Parameterized Neural Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use exact natural gradient descent instead of gradient descent | Two-layer ReLU networks · Overparameterized networks, squared error | convergence rate: \mathcal{O}(\lambda_0 / n) improvement | Helped |
| Use exact natural gradient descent instead of gradient descent | Two-layer ReLU networks · Overparameterized networks | maximum allowable learning rate: \mathcal{O}(1/n) to \mathcal{O}(1) | Helped |
| Use K-FAC as an approximate natural-gradient optimizer | Two-layer ReLU networks · Overparameterized networks | convergence to a global minimum: linear rate | Helped |
| Apply a data transformation followed by normalization to make the input covariance condition number 1 | K-FAC · Two-layer ReLU networks | convergence bound: \kappa_{\mathbf{Z}^\top \mathbf{Z}} = 1 | Helped |
| Use natural gradient descent while training near initialization | Two-layer ReLU networks · Generalization | expected loss upper bound: matches the bound for gradient descent | No clear effect |
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