Richard B. Sowers – författare
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Deep learning uses multi-layer neural networks to model complex data patterns. Large models-with millions or even billions of parameters-are trained on massive datasets. This approach has produced revolutionary advances in image, text, and speech recognition and also has potential applications in a range of other fields such as engineering, finance, mathematics, and medicine. This book provides an introduction to the mathematical theory underpinning the recent advances in deep learning. Detailed derivations as well as mathematical proofs are presented for many of the models and optimization methods which are commonly used in machine learning and deep learning. Applications, code, and practical approaches to training models are also included. The book is designed for advanced undergraduates, graduate students, practitioners, and researchers. Divided into two parts, it begins with mathematical foundations before tackling advanced topics in approximation, optimization, and neural network training. Part 1 is written for a general audience, including students in mathematics, statistics, computer science, data science, or engineering, while select chapters in Part 2 present more advanced mathematical theory requiring familiarity with analysis, probability, and stochastic processes. Together, they form an ideal foundation for an introductory course on the mathematics of deep learning. Thoughtfully designed exercises and a companion website with code examples enhance both theoretical understanding and practical skills, preparing readers to engage more deeply with this fast-evolving field.
Del 176 - Lecture Notes in Control and Information Sciences
Stochastic Partial Differential Equations and Their Applications
Proceedings of IFIP WG 7/1 International Conference University of North Carolina at Charlotte, NC, June 6–8,1991
Häftad, Engelska, 1992
537 kr
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This volume consists of 24 papers submitted for publicationby the invited speakers of the IFIP International Conferenceon Stochastic Partial Differential Equations and their Ap-plications. Most of them are research papers, however, a fewsurveys written by world renowed experts are also included.The aim of the conference was to bring together mathematici-ans, physicists and engineers representing academic as wellas industrial fields, interested in the theory and applica-tions of SPDE's. The field of SPDE's is one of the most dy-namically developing areas at the cross roads of severalsciences. It is especially attractive for many because ofits interdisciplinary character and enormous richness ofal-ready existing as well as potential applications. There wereabout one hundred participants registered for the conferen-ce. With rare exceptions, all of the most active researchersin the field of SPDE's throughout the world were present atthe conference. The main topics for discussion at the confe-rence were: non-linear SPDE's and Markov property for randomfields, modern stochastic calculuses, numerical and asympto-tic methods for SPDE's, applications of SPDE's with emphasisonnon-linear filtering, stochastic control and statisticalfluid dynamics.