Accompanying code for the paper "Deep Learning Weight Pruning with RMT-SVD: Increasing Accuracy and Reducing Overfitting" Available at https://arxiv.org/abs/2303.08986
In this work, we present some applications of random matrix theory for the training of deep neural networks. Recently, random matrix theory (RMT) has been applied to the overfitting problem in deep learning. Specifically, it has been shown that the spectrum of the weight layers of a deep neural network (DNN) can be studied and understood using techniques from RMT. In this work, these RMT techniques will be used to determine which and how many singular values should be removed from the weight layers of a DNN during training, via singular value decomposition (SVD), so as to reduce overfitting and increase accuracy. We show the results on a simple DNN model trained on MNIST. In general, these techniques may be applied to any fully connected layer of a pretrained DNN to reduce the number of parameters in the layer while preserving and sometimes increasing the accuracy of the DNN.
It is a known technique to compute the SVD of fully connected layers and then prune some amount of the smallest values (giving a low rank approximation). This allows one to compress neural networks without changing the accuracy (by much), potentially lowering memory storage requirements and lowering the cost of running a network (one potential application being deploying the network on low power devices).
In existing literature, the number of singular values to prune is mostly decided in an ad-hoc manner (for instance, using energy methods or by iteratively checking the accuracy of the modified network). In this work, we propose a novel principled approach to deciding how many singular values to prune using random matrix theory(RMT) to decide which singular values can likely be pruned without modifying accuracy.
Specifically, we assume our weight matrix is of the form signal + noise, leading to a spiked eigenvalue model. Using the BEMA (Bulk Eigenvalue Matching Analysis) algorithm, we can classify each singular value in the spectrum of our weight matrix as noise or signal. With this we can then prune some of the noise singular values.
This theory can be used as either a modified training algorithm where one periodically prunes small singular values during training as a method of impeding overfitting, or it can be used on a pre-trained network for compression.
Authors contact info is yms5281@psu.edu, jtj5311@psu.edu, omk5165@psu.edu