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Memorization and Optimization in Deep Neural Networks with Minimum Over-parameterization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use minimum over-parameterization, with n_{L-2}n_{L-1} parameters between the last two hidden layers | Deep networks satisfying the stated assumptions · Training data under stated distribution assumptions | smallest NTK eigenvalue: \Omega(n_{L-2} n_{L-1}) | Helped |
| Use the proposed network with minimum over-parameterization to fit arbitrary real-valued labels | Deep network · N training samples with arbitrary real-valued labels | label-fitting error: \norm{F_L(\theta) - Y}_2 \leq \varepsilon | Helped |
| Use paired duplicate neurons, opposite output weights, and boosted output-weight variance at initialization | Gradient descent on the proposed deep network · N training samples with labels satisfying \norm{Y}_2 = \Theta(\sqrt N) | least-squares loss: \mathcal L(\theta_t) \leq \left( 1 - c \eta \gamma n_{L-2} n_{L-1}\right)^t \mathcal L(\theta_0) | Helped |
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