Enhancing Accuracy in Deep Learning Using Random Matrix Theory

In this study, we explore the applications of random matrix theory (RMT) in the training of deep neural networks (DNNs), focusing on layer pruning to simplify DNN architecture and loss landscape. RMT, recently used to address overfitting in deep learning, enables the examination of DNN's weight layer spectra. We use these techniques to optimally determine the number of singular values to be removed from the weight layers of a DNN during training via singular value decomposition (SVD). This process aids in DNN simplification and accuracy enhancement, as evidenced by training simple DNN models on the MNIST and Fashion MNIST datasets. Our method can be applied to any fully connected or convolutional layer of a pretrained DNN, decreasing the layer's parameters and simplifying the DNN architecture while preserving or even enhancing the model's accuracy. By discarding small singular values based on RMT criteria, the accuracy of the test set remains consistent, facilitating more efficient DNN training without compromising performance. We provide both theoretical and empirical evidence supporting our claim that the elimination of small singular values based on RMT does not negatively impact the DNN's accuracy. Our results offer valuable insights into the practical application of RMT for the creation of more efficient and accurate deep-learning models.