Multilevel Initialization for Layer-Parallel Deep Neural Network Training

TL;DR

This paper introduces a multilevel initialization approach for deep neural networks using layer-parallel multigrid methods, improving training efficiency and robustness by leveraging coarse-to-fine network refinements.

Contribution

It proposes a novel multilevel initialization strategy based on optimal control and multigrid concepts, enhancing deep network training scalability and stability.

Findings

Reduced training run time for equivalent accuracy

Improved initialization leading to better regularization effects

Decreased sensitivity to hyperparameters and initial conditions

Abstract

This paper investigates multilevel initialization strategies for training very deep neural networks with a layer-parallel multigrid solver. The scheme is based on the continuous interpretation of the training problem as a problem of optimal control, in which neural networks are represented as discretizations of time-dependent ordinary differential equations. A key goal is to develop a method able to intelligently initialize the network parameters for the very deep networks enabled by scalable layer-parallel training. To do this, we apply a refinement strategy across the time domain, that is equivalent to refining in the layer dimension. The resulting refinements create deep networks, with good initializations for the network parameters coming from the coarser trained networks. We investigate the effectiveness of such multilevel "nested iteration" strategies for network training, showing supporting numerical evidence of reduced run time for equivalent accuracy. In addition, we study whether the initialization strategies provide a regularizing effect on the overall training process and reduce sensitivity to hyperparameters and randomness in initial network parameters.