Generalization Error Bounds for Deep Neural Networks Trained by SGD

• URL: http://arxiv.org/abs/2206.03299v2
• Date: Mon, 29 May 2023 06:05:47 GMT
• Title: Generalization Error Bounds for Deep Neural Networks Trained by SGD
• Authors: Mingze Wang, Chao Ma
• Abstract summary: Generalization error bounds for deep trained by gradient descent (SGD) are derived. The bounds explicitly depend on the loss along the training trajectory. Results show that our bounds are non-vacuous and robust with the change of neural networks and network hypers.
• Score: 3.148524502470734
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Generalization error bounds for deep neural networks trained by stochastic gradient descent (SGD) are derived by combining a dynamical control of an appropriate parameter norm and the Rademacher complexity estimate based on parameter norms. The bounds explicitly depend on the loss along the training trajectory, and work for a wide range of network architectures including multilayer perceptron (MLP) and convolutional neural networks (CNN). Compared with other algorithm-depending generalization estimates such as uniform stability-based bounds, our bounds do not require $L$-smoothness of the nonconvex loss function, and apply directly to SGD instead of Stochastic Langevin gradient descent (SGLD). Numerical results show that our bounds are non-vacuous and robust with the change of optimizer and network hyperparameters.

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