Exploring the Common Principal Subspace of Deep Features in Neural Networks

• URL: http://arxiv.org/abs/2110.02863v1
• Date: Wed, 6 Oct 2021 15:48:32 GMT
• Title: Exploring the Common Principal Subspace of Deep Features in Neural Networks
• Authors: Haoran Liu, Haoyi Xiong, Yaqing Wang, Haozhe An, Dongrui Wu, and Dejing Dou
• Abstract summary: We find that different Deep Neural Networks (DNNs) trained with the same dataset share a common principal subspace in latent spaces. Specifically, we design a new metric $mathcalP$-vector to represent the principal subspace of deep features learned in a DNN. Small angles (with cosine close to $1.0$) have been found in the comparisons between any two DNNs trained with different algorithms/architectures.
• Score: 50.37178960258464
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We find that different Deep Neural Networks (DNNs) trained with the same dataset share a common principal subspace in latent spaces, no matter in which architectures (e.g., Convolutional Neural Networks (CNNs), Multi-Layer Preceptors (MLPs) and Autoencoders (AEs)) the DNNs were built or even whether labels have been used in training (e.g., supervised, unsupervised, and self-supervised learning). Specifically, we design a new metric $\mathcal{P}$-vector to represent the principal subspace of deep features learned in a DNN, and propose to measure angles between the principal subspaces using $\mathcal{P}$-vectors. Small angles (with cosine close to $1.0$) have been found in the comparisons between any two DNNs trained with different algorithms/architectures. Furthermore, during the training procedure from random scratch, the angle decrease from a larger one ($70^\circ-80^\circ$ usually) to the small one, which coincides the progress of feature space learning from scratch to convergence. Then, we carry out case studies to measure the angle between the $\mathcal{P}$-vector and the principal subspace of training dataset, and connect such angle with generalization performance. Extensive experiments with practically-used Multi-Layer Perceptron (MLPs), AEs and CNNs for classification, image reconstruction, and self-supervised learning tasks on MNIST, CIFAR-10 and CIFAR-100 datasets have been done to support our claims with solid evidences. Interpretability of Deep Learning, Feature Learning, and Subspaces of Deep Features

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