Stabilize deep ResNet with a sharp scaling factor τ

Huishuai Zhang

doi:10.1007/s10994-022-06192-x

Stabilize deep ResNet with a sharp scaling factor τ

2022-08-01

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DOI：10.1007/s10994-022-06192-x

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We study the stability and convergence of training deep ResNets with gradient descent. Specifically, we show that the parametric branch in the residual block should be scaled down by a factor tau=O(1/L) to guarantee stable forward/backward process, where L is the number of residual blocks. Moreover, we establish a converse result that the forward process is unbounded when tau > L-1/2+c for any positive constant c. The above two results together establish a sharp value of the scaling factor in determining the stability of deep ResNet. Based on the stability result, we further show that gradient descent finds the global minima if the ResNet is properly over-parameterized, which significantly improves over the previous work with a much larger range of tau that admits global convergence. Moreover, we show that the convergence rate is independent of the depth, theoretically justifying the advantage of ResNet over vanilla feedforward network. Empirically, with such a factor tau, one can train deep ResNet without normalization layer. Moreover for ResNets with normalization layer, adding such a factor tau also stabilizes the training and obtains significant performance gain for deep ResNet.

Stabilize deep ResNet with a sharp scaling factor τ

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