Implicit Regularization in Deep Tensor Factorization - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2021

Implicit Regularization in Deep Tensor Factorization

Résumé

Attempts of studying implicit regularization associated to gradient descent (GD) have identified matrix completion as a suitable test-bed. Late findings suggest that this phenomenon cannot be phrased as a minimization-norm problem, implying that a paradigm shift is required and that dynamics has to be taken into account. In the present work we address the more general setup of tensor completion by leveraging two popularized tensor factorization, namely Tucker and TensorTrain (TT). We track relevant quantities such as tensor nuclear norm, effective rank, generalized singular values and we introduce deep Tucker and TT unconstrained factorization to deal with the completion task. Experiments on both synthetic and real data show that gradient descent promotes solution with low-rank, and validate the conjecture saying that the phenomenon has to be addressed from a dynamical perspective.
Fichier principal
Vignette du fichier
main.pdf (558.1 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03211964 , version 1 (01-05-2021)

Identifiants

Citer

Paolo Milanesi, Hachem Kadri, Stéphane Ayache, Thierry Artières. Implicit Regularization in Deep Tensor Factorization. International Joint Conference on Neural Networks (IJCNN), Jul 2021, Online, China. ⟨hal-03211964⟩
124 Consultations
146 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More