Relative gradient optimization of the Jacobian term in unsupervised deep learning - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Communication Dans Un Congrès Année : 2020

Relative gradient optimization of the Jacobian term in unsupervised deep learning

Résumé

Learning expressive probabilistic models correctly describing the data is a ubiquitous problem in machine learning. A popular approach for solving it is mapping the observations into a representation space with a simple joint distribution, which can typically be written as a product of its marginals-thus drawing a connection with the field of nonlinear independent component analysis. Deep density models have been widely used for this task, but their maximum likelihood based training requires estimating the log-determinant of the Jacobian and is computationally expensive, thus imposing a trade-off between computation and expressive power. In this work, we propose a new approach for exact training of such neural networks. Based on relative gradients, we exploit the matrix structure of neural network parameters to compute updates efficiently even in high-dimensional spaces; the computational cost of the training is quadratic in the input size, in contrast with the cubic scaling of naive approaches. This allows fast training with objective functions involving the log-determinant of the Jacobian, without imposing constraints on its structure, in stark contrast to autoregressive normalizing flows.
Fichier principal
Vignette du fichier
Log_det_jac_NeurIPS_2020.pdf (927.11 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02978662 , version 1 (26-10-2020)

Identifiants

  • HAL Id : hal-02978662 , version 1

Citer

Luigi Gresele, Giancarlo Fissore, Adrián Javaloy, Bernhard Schölkopf, Aapo Hyvärinen. Relative gradient optimization of the Jacobian term in unsupervised deep learning. NeurIPS 2020 - 34h Conference on Neural Information Processing Systems, Dec 2020, Vancouver / Virtuel, Canada. ⟨hal-02978662⟩
65 Consultations
393 Téléchargements

Partager

Gmail Facebook X LinkedIn More