Mathematical foundations of deep learning models and algorithms / Konstantinos Spiliopoulos, Richard Sowers, Justin Sirignano.

Author/creator Spiliopoulos, Konstantinos, 1980- author.
Other author Sowers, R. B. (Richard Bucher), 1965- author.
Other author Sirignano, Justin (Justin Anthony), 1988- author.
Format Book
PublicationProvidence, Rhode Island : American Mathematical Society, [2025]
Descriptionpages cm.
Subjects
Deep learning (Machine learning)--Mathematical models.
Neural networks (Computer science)--Mathematical models.
Regression analysis.
Convergence.
Kernel functions.
Apprentissage profond--Modèles mathématiques.
Réseaux neuronaux (Informatique)--Modèles mathématiques.
Analyse de régression.
Convergence (Mathématiques)
Noyaux (Mathématiques)

SeriesGraduate studies in mathematics, 1065-7339 ; volume 252
Graduate studies in mathematics ; volume 252. ^A347883
Contents Linear regression -- Logistic regression -- From perceptron to kernels to neural networks -- Feed forward neural networks -- Backpropagation -- Basics on stochastic gradient descent -- Stochastic gradient descent for multi-layer networks -- Regularization and dropout -- Batch normalization -- Training, validation, and testing -- Feature importance -- Recurrent neural networks and sequential data -- Convolution neural networks -- Variational inference and generative models -- Universal approximation theorems -- Convergence analysis of gradient descent -- Convergence analysis of stochastic gradient descent -- The neural tangent kernel regime -- Optimization in feature learning regime : mean field scaling -- Reinforcement learning -- Neural differential equations -- Distributed training -- Automatic differentiation.
Bibliography noteIncludes bibliographical references and index.
LCCN 2025030859
ISBN9781470481087 hardcover
ISBN1470481081
ISBN9781470483999 paperback
ISBN1470483998
ISBNebook