Pruning untrained neural networks: Principles and Analysis

Overparameterized neural networks display state-of-the art performance. However, there is a growing need for smaller, energy-efficient, neural networks to be able to use machine learning applications on devices with limited computational resources. A popular approach consists of using pruning techniques. While these techniques have traditionally focused on pruning pre-trained neural networks (e.g. LeCun et al. (1990) and Hassabi et al. (1993)), recent work by Lee et al. (2018) showed promising results where pruning is performed at initialization. However, such procedures remain unsatisfactory as the resulting pruned networks can be difficult to train and, for instance, these procedures do not prevent one layer being fully pruned. In this paper we provide a comprehensive theoretical analysis of pruning at initialization and training sparse architectures. This analysis allows us to propose novel principled approaches which we validate experimentally on a variety of network architectures. We particularly show that we can prune up to 99.9% of the weights while keeping the model trainable.