Deep Autoencoders: From Understanding to Generalization Guarantees

Abstract

A big mystery in deep learning continues to be the ability of methods to generalize when the number of model parameters is larger than the number of training examples. In this work, we take a step towards a better understanding of the underlying phenomena of Deep Autoencoders (AEs), a mainstream deep learning solution for learning compressed, interpretable, and structured data representations. In particular, we interpret how AEs approximate the data manifold by exploiting their continuous piecewise affine structure. Our reformulation of AEs provides new insights into their mapping, reconstruction guarantees, as well as an interpretation of commonly used regularization techniques. We leverage these findings to derive two new regularizations that enable AEs to capture the inherent symmetry in the data. Our regularizations leverage recent advances in the group of transformation learning to enable AEs to better approximate the data manifold without explicitly defining the group underlying the manifold. Under the assumption that the symmetry of the data can be explained by a Lie group, we prove that the regularizations ensure the generalization of the corresponding AEs. A range of experimental evaluations demonstrate that our methods outperform other state-of-the-art regularization techniques.

References in corpus (15)

• On the Number of Linear Regions of Deep Neural Networks
• Understanding Deep Convolutional Networks
• Deep Scattering Spectrum
• Group Equivariant Convolutional Networks
• Estimating the intrinsic dimension of datasets by a minimal neighborhood information
• Dropout Training as Adaptive Regularization
• On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups
• On the Spectral Bias of Neural Networks
• Explorations in Homeomorphic Variational Auto-Encoding
• Joint Time-Frequency Scattering for Audio Classification
• Unsupervised Deep Haar Scattering on Graphs
• An Unsupervised Algorithm For Learning Lie Group Transformations
• Why does Deep Learning work? - A perspective from Group Theory
• Hyperplane Arrangements of Trained ConvNets Are Biased
• Learning a Lie Algebra from Unlabeled Data Pairs