Towards Explaining Deep Neural Network Compression Through a Probabilistic Latent Space

Despite the impressive performance of deep neural networks (DNNs), their computational complexity and storage space consumption have led to the concept of network compression. While DNN compression techniques such as pruning and low-rank decomposition have been extensively studied, there has been insufficient attention paid to their theoretical explanation. In this paper, we propose a novel theoretical framework that leverages a probabilistic latent space of DNN weights and explains the optimal network sparsity by using the information-theoretic divergence measures. We introduce new analogous projected patterns (AP2) and analogous-in-probability projected patterns (AP3) notions for DNNs and prove that there exists a relationship between AP3/AP2 property of layers in the network and its performance. Further, we provide a theoretical analysis that explains the training process of the compressed network. The theoretical results are empirically validated through experiments conducted on standard pre-trained benchmarks, including AlexNet, ResNet50, and VGG16, using CIFAR10 and CIFAR100 datasets. Through our experiments, we highlight the relationship of AP3 and AP2 properties with fine-tuning pruned DNNs and sparsity levels.