No Fine-Tuning, No Cry: Robust SVD for Compressing Deep Networks

A common technique for compressing a neural network is to compute the k-rank [Formula: see text] approximation [Formula: see text] of the matrix [Formula: see text] via SVD that corresponds to a fully connected layer (or embedding layer). Here, d is the number of input neurons in the layer, n is the number in the next one, and [Formula: see text] is stored in [Formula: see text] memory instead of [Formula: see text]. Then, a fine-tuning step is used to improve this initial compression. However, end users may not have the required computation resources, time, or budget to run this fine-tuning stage. Furthermore, the original training set may not be available. In this paper, we provide an algorithm for compressing neural networks using a similar initial compression time (to common techniques) but without the fine-tuning step. The main idea is replacing the k-rank [Formula: see text] approximation with [Formula: see text] , for [Formula: see text] , which is known to be less sensitive to outliers but much harder to compute. Our main technical result is a practical and provable approximation algorithm to compute it for any [Formula: see text] , based on modern techniques in computational geometry. Extensive experimental results on the GLUE benchmark for compressing the networks BERT, DistilBERT, XLNet, and RoBERTa confirm this theoretical advantage.