Algorithmic Regularization in Learning Deep Homogeneous Models: Layers are Automatically Balanced
Year: 2018
Type: preprint
Abstract: We study the implicit regularization imposed by gradient descent for learning multi-layer homogeneous functions including feed-forward fully connected and convolutional deep neural networks with linear, ReLU or Leaky ReLU activation. We rigorously prove that gradient flow (i.e. gradient descent with infinitesimal step size) effectively enforces the differences between squared norms across different layers to remain invariant without any explicit regularization. This result implies that if the weights are initially small, gradient flow automatically balances the magnitudes of all layers. Using a discretization argument, we analyze gradient descent with positive step size for the non-convex low-rank asymmetric matrix factorization problem without any regularization. Inspired by our findings for gradient flow, we prove that gradient descent with step sizes $η_t = O\left(t^{-\left( \frac12+δ\right)} \right)$ ($0
Source: arXiv (Cornell University)
Authors: Du, Simon S., Hu, Wei, Lee, Jason D.
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Army Research Office
Awards: G7452299184, G862988727
OpenAlex ID: W2806265408