Der-Chen Chang Bücher

This book describes how neural networks operate from the mathematical point of view. As a result, neural networks can be interpreted both as function universal approximators and information processors. The book bridges the gap between ideas and concepts of neural networks, which are used nowadays at an intuitive level, and the precise modern mathematical language, presenting the best practices of the former and enjoying the robustness and elegance of the latter. This book can be used in a graduate course in deep learning, with the first few parts being accessible to senior undergraduates. In addition, the book will be of wide interest to machine learning researchers who are interested in a theoretical understanding of the subject.

Focusing on sub-Riemannian and Heisenberg manifolds, this comprehensive text presents a novel variational approach that blends theory with practical applications. It serves as both a detailed reference and an educational resource, emphasizing key concepts and methodologies in the field. The book is designed for researchers and graduate students, providing valuable insights into advanced mathematical frameworks and their implications in geometry and analysis.

Focusing on various methodologies, this monograph provides an in-depth examination of theories for deriving explicit formulas for heat kernels associated with elliptic and sub-elliptic operators. Each chapter is dedicated to a different method, highlighting the diversity and richness of approaches available in this field of study.

This bestselling textbook for higher-level courses was extensively revised in 1990 to accommodate developments in model theoretic methods. Topics include models constructed from constants, ultraproducts, and saturated and special models. 1990 edition.