The Low-Rank Simplicity Bias in Deep Networks

Published: 21 Mar 2023, Last Modified: 21 Mar 2023Accepted by TMLREveryoneRevisionsBibTeX
Abstract: Modern deep neural networks are highly over-parameterized compared to the data on which they are trained, yet they often generalize remarkably well. A flurry of recent work has asked: why do deep networks not overfit to their training data? In this work, we make a series of empirical observations that investigate and extend the hypothesis that deeper networks are inductively biased to find solutions with lower effective rank embeddings. We conjecture that this bias exists because the volume of functions that maps to low effective rank embedding increases with depth. We show empirically that our claim holds true on finite width linear and non-linear models on practical learning paradigms and show that on natural data, these are often the solutions that generalize well. We then show that the simplicity bias exists at both initialization and after training and is resilient to hyper-parameters and learning methods. We further demonstrate how linear over-parameterization of deep non-linear models can be used to induce low-rank bias, improving generalization performance on CIFAR and ImageNet without changing the modeling capacity.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: Amended text suggested by the AC and the reviewers. Minor revision to the proof.
Assigned Action Editor: ~Stanislaw_Kamil_Jastrzebski1
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Number: 517