Yesterday, researchers from Carnegie Mellon University, University of Southern California, Peking University, and Massachusetts Institute of Technology published a paper on a big optimization problem in deep learning. This study proves that randomly initialized gradient descent can achieve zero training loss in polynomial time for a deep over-parameterized neural network with residual connections (ResNet).
The key idea is to show that the Gram matrix is increasingly stable under overparameterization, and so every step of gradient descent decreases the loss at a geometric rate.
This study builds on two ideas from previous works on gradient descent for two-layer neural networks:
This study focuses on the least squares loss and assumes the activation is Lipschitz and smooth. Consider that there are n data points and the neural network has H layers with width m.
The following are the aims this study tries to prove:
To learn more, you can, read the full paper: Gradient Descent Finds Global Minima of Deep Neural Networks.
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