Low-rank lottery tickets: finding efficient low-rank neural networks via matrix differential equations

Steffen Schotthöfer, Emanuele Zangrando, Jonas Kusch, Gianluca Ceruti, Francesco Tudisco

Keywords: Neural Network Compression, Low Rank Matrices, Dynamical Low Rank Approximation, Neural Network Training, Pruning

TL;DR: The paper presents a novel neural network training algorithm, that allows for efficient low rank network training and search of low rank subnetworks

Abstract:

Neural networks have achieved tremendous success in a large variety of applications. However, their memory footprint and computational demand can render them impractical in application settings with limited hardware or energy resources. In this work, we propose a novel algorithm to find efficient low-rank subnetworks. Remarkably, these subnetworks are determined and adapted already during the training phase and the overall time and memory resources required by both training and evaluating them is significantly reduced. The main idea is to restrict the weight matrices to a
low-rank manifold and to update the low-rank factors rather than the full matrix during training. To derive training updates that are restricted to the prescribed manifold, we employ techniques from dynamic model order reduction for matrix differential equations. Moreover, our method automatically and dynamically adapts the ranks during training to achieve a desired approximation accuracy.
The efficiency of the proposed method is demonstrated through a variety of numerical experiments on fully-connected and convolutional networks.