On the training dynamics of deep networks with $L_2$ regularization
This work addresses the problem of optimizing regularization in deep learning for practitioners, offering incremental improvements in training efficiency and performance prediction.
The paper tackles the role of L2 regularization in deep learning by uncovering empirical relations between performance, regularization coefficient, learning rate, and training steps in overparameterized networks, leading to a dynamical schedule that improves performance and speeds up training, with theoretical support from gradient flow dynamics in infinitely wide networks.
We study the role of $L_2$ regularization in deep learning, and uncover simple relations between the performance of the model, the $L_2$ coefficient, the learning rate, and the number of training steps. These empirical relations hold when the network is overparameterized. They can be used to predict the optimal regularization parameter of a given model. In addition, based on these observations we propose a dynamical schedule for the regularization parameter that improves performance and speeds up training. We test these proposals in modern image classification settings. Finally, we show that these empirical relations can be understood theoretically in the context of infinitely wide networks. We derive the gradient flow dynamics of such networks, and compare the role of $L_2$ regularization in this context with that of linear models.