Papers › SGD on Neural Networks Learns Functions of Increasing Complexity

SGD on Neural Networks Learns Functions of Increasing Complexity

28 May 2019NeurIPS 2019 12arXiv:1905.11604archive 2025-07-28

Preetum Nakkiran, Gal Kaplun, Dimitris Kalimeris, Tristan Yang, Benjamin L. Edelman, Fred Zhang, Boaz Barak

We perform an experimental study of the dynamics of Stochastic Gradient Descent (SGD) in learning deep neural networks for several real and synthetic classification tasks. We show that in the initial epochs, almost all of the performance improvement of the classifier obtained by SGD can be explained by a linear classifier. More generally, we give evidence for the hypothesis that, as iterations progress, SGD learns functions of increasing complexity. This hypothesis can be helpful in explaining why SGD-learned classifiers tend to generalize well even in the over-parameterized regime. We also show that the linear classifier learned in the initial stages is "retained" throughout the execution even if training is continued to the point of zero training error, and complement this with a theoretical result in a simplified model. Key to our work is a new measure of how well one classifier explains the performance of another, based on conditional mutual information.

PaperPDFConference PDFCode

In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.

Code

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

Not run by Syntology. Nothing on this page verifies that the listed code works.

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Methods

SGD

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections