Dynamical low-rank training of neural networks

Neural networks have achieved tremendous success in a large variety of applications. However, their space and time computational demand can limit their usage in resource limited devices. At the same time, overparametrization seems to be necessary in order to overcome the highly non-convex nature of the training optimization problem. An optimal trade-off is then to be found in order to reduce networks' dimension while mantaining high performance. Popular approaches in the current literature are based on pruning techniques that look for subnetworks able to mantain approximately the initial performance. Nevertheless, these techniques often are not able to reduce the memory footprint of the training phase. In this thesis we will present DLRT, a training algorithm that looks for "low-rank subnetworks" by using DLRA theory and techniques. These subnetworks and their ranks are determined and adapted already during the training phase, allowing the overall time and memory resources required by both training and evaluation phases to be reduced significantly.