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About contrastive unsupervised representation learning for classification and its convergence

Merad, Ibrahim; Yu, Yiyang; Bacry, Emmanuel; Gaïffas, Stéphane (2021), About contrastive unsupervised representation learning for classification and its convergence. https://basepub.dauphine.psl.eu/handle/123456789/22718

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Type
Document de travail / Working paper
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https://hal.archives-ouvertes.fr/hal-03438767
Date
2021
Titre de la collection
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Ville d’édition
Paris
Pages
17
Métadonnées
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Auteur(s)
Merad, Ibrahim
Yu, Yiyang
Bacry, Emmanuel cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Gaïffas, Stéphane
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Laboratoire de Probabilités, Statistique et Modélisation [LPSM (UMR_8001)]
Résumé (EN)
Contrastive representation learning has been recently proved to be very efficient for selfsupervised training. These methods have been successfully used to train encoders which perform comparably to supervised training on downstream classification tasks. A few works have started to build a theoretical framework around contrastive learning in which guarantees for its performance can be proven. We provide extensions of these results to training with multiple negative samples and for multiway classification. Furthermore, we provide convergence guarantees for the minimization of the contrastive training error with gradient descent of an overparametrized deep neural encoder, and provide some numerical experiments that complement our theoretical findings.
Mots-clés
unsupervised learning; constrative learning; deep neural networks; theoretical guarantees