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Gradient Descent Finds Global Minima of Deep Neural Networks
Simon Du · Jason Lee · Haochuan Li · Liwei Wang · Xiyu Zhai

Tue Jun 11 03:15 PM -- 03:20 PM (PDT) @ Grand Ballroom

Gradient descent finds a global minimum in training deep neural networks despite the objective function being non-convex. The current paper proves gradient descent achieves zero training loss in polynomial time for a deep over-parameterized neural network with residual connections (ResNet). Our analysis relies on the particular structure of the Gram matrix induced by the neural network architecture. This structure allows us to show the Gram matrix is stable throughout the training process and this stability implies the global optimality of the gradient descent algorithm. We further extend our analysis to deep residual convolutional neural networks and obtain a similar convergence result.

Author Information

Simon Du (Carnegie Mellon University)
Jason Lee (University of Southern California)
Haochuan Li (Peking University)
Liwei Wang (Peking University)
Xiyu Zhai (Massachusetts Institute of Technology)

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