Deep Autoencoders: From Understanding to Generalization Guarantees

Romain Cosentino, Randall Balestriero, Richard Baraniuk, Behnaam Aazhang

Research output: Contribution to journalConference articlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)197-222
Number of pages26
JournalProceedings of Machine Learning Research
StatePublished - 2021
Event2nd Mathematical and Scientific Machine Learning Conference, MSML 2021 - Virtual, Online
Duration: Aug 16 2021Aug 19 2021


  • Affine Spline Deep Network
  • Deep Autoencoders
  • Deep Network
  • Generalization
  • Group Equivariant Network
  • Higher-order Regularization
  • Interpolation
  • Interpretability
  • Lie Algebra
  • Lie Group
  • Orbit
  • Partitioning
  • Piecewise Affine Deep Network
  • Piecewise Linear Deep Network
  • Regression

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


Dive into the research topics of 'Deep Autoencoders: From Understanding to Generalization Guarantees'. Together they form a unique fingerprint.

Cite this