Efforts to understand the generalization mystery in deep learning have led to
the belief that gradient-based optimization induces a form of implicit
regularization, a bias towards models of low "complexity." We study the
implicit regularization of gradient descent over deep linear neural networks
for matrix completion and sensing, a model referred to as deep matrix
factorization. Our first finding, supported by theory and experiments, is that
adding depth to a matrix factorization enhances an implicit tendency towards
low-rank solutions, oftentimes leading to more accurate recovery. Secondly, we
present theoretical and empirical arguments questioning a nascent view by which
implicit regularization in matrix factorization can be captured using simple
mathematical norms. Our results point to the possibility that the language of
standard regularizers may not be rich enough to fully encompass the implicit
regularization brought forth by gradient-based optimization.
Description
[1905.13655] Implicit Regularization in Deep Matrix Factorization
%0 Journal Article
%1 arora2019implicit
%A Arora, Sanjeev
%A Cohen, Nadav
%A Hu, Wei
%A Luo, Yuping
%D 2019
%K matrix-factorization optimization readings
%T Implicit Regularization in Deep Matrix Factorization
%U http://arxiv.org/abs/1905.13655
%X Efforts to understand the generalization mystery in deep learning have led to
the belief that gradient-based optimization induces a form of implicit
regularization, a bias towards models of low "complexity." We study the
implicit regularization of gradient descent over deep linear neural networks
for matrix completion and sensing, a model referred to as deep matrix
factorization. Our first finding, supported by theory and experiments, is that
adding depth to a matrix factorization enhances an implicit tendency towards
low-rank solutions, oftentimes leading to more accurate recovery. Secondly, we
present theoretical and empirical arguments questioning a nascent view by which
implicit regularization in matrix factorization can be captured using simple
mathematical norms. Our results point to the possibility that the language of
standard regularizers may not be rich enough to fully encompass the implicit
regularization brought forth by gradient-based optimization.
@article{arora2019implicit,
abstract = {Efforts to understand the generalization mystery in deep learning have led to
the belief that gradient-based optimization induces a form of implicit
regularization, a bias towards models of low "complexity." We study the
implicit regularization of gradient descent over deep linear neural networks
for matrix completion and sensing, a model referred to as deep matrix
factorization. Our first finding, supported by theory and experiments, is that
adding depth to a matrix factorization enhances an implicit tendency towards
low-rank solutions, oftentimes leading to more accurate recovery. Secondly, we
present theoretical and empirical arguments questioning a nascent view by which
implicit regularization in matrix factorization can be captured using simple
mathematical norms. Our results point to the possibility that the language of
standard regularizers may not be rich enough to fully encompass the implicit
regularization brought forth by gradient-based optimization.},
added-at = {2019-07-13T13:38:37.000+0200},
author = {Arora, Sanjeev and Cohen, Nadav and Hu, Wei and Luo, Yuping},
biburl = {https://www.bibsonomy.org/bibtex/200356b72a05d7c4fe325cbbf70a8415f/kirk86},
description = {[1905.13655] Implicit Regularization in Deep Matrix Factorization},
interhash = {1bb112131fca765bc145bd8d9a03a0fd},
intrahash = {00356b72a05d7c4fe325cbbf70a8415f},
keywords = {matrix-factorization optimization readings},
note = {cite arxiv:1905.13655},
timestamp = {2019-11-14T20:39:03.000+0100},
title = {Implicit Regularization in Deep Matrix Factorization},
url = {http://arxiv.org/abs/1905.13655},
year = 2019
}