A Theoretical Analysis of Fine-tuning with Linear Teachers

Gal Shachaf, Alon Brutzkus, Amir Globerson

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Fine-tuning is a common practice in deep learning, achieving excellent generalization results on downstream tasks using relatively little training data. Although widely used in practice, it is lacking strong theoretical understanding. Here we analyze the sample complexity of this scheme for regression with linear teachers in several architectures. Intuitively, the success of fine-tuning depends on the similarity between the source tasks and the target task, however measuring this similarity is non trivial. We show that generalization is related to a measure that considers the relation between the source task, target task and covariance structure of the target data. In the setting of linear regression, we show that under realistic settings a substantial sample complexity reduction is plausible when the above measure is low. For deep linear regression, we present a novel result regarding the inductive bias of gradient-based training when the network is initialized with pretrained weights. Using this result we show that the similarity measure for this setting is also affected by the depth of the network. We further present results on shallow ReLU models, and analyze the dependence of sample complexity on source and target tasks in this setting.

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
EditorsMarc'Aurelio Ranzato, Alina Beygelzimer, Yann Dauphin, Percy S. Liang, Jenn Wortman Vaughan
PublisherNeural information processing systems foundation
Pages15382-15394
Number of pages13
ISBN (Electronic)9781713845393
StatePublished - 2021
Event35th Conference on Neural Information Processing Systems, NeurIPS 2021 - Virtual, Online
Duration: 6 Dec 202114 Dec 2021

Publication series

NameAdvances in Neural Information Processing Systems
Volume19
ISSN (Print)1049-5258

Conference

Conference35th Conference on Neural Information Processing Systems, NeurIPS 2021
CityVirtual, Online
Period6/12/2114/12/21

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