Deep Learning Architectures - A Mathematical Approach

The book is structured into four main parts, from simple to complex topics. The first one is an accessible introduction to the theory of neural networks; the second part treats neural networks as universal approximators; the third regards neural nets as information processors. The last part deals with the theory behind several topics of interest such as pooling, convolution, CNNs, RNNs, GANs, Boltzmann machines, and classification. For the sake of completeness, the book contains an Appendix with topics collected from Measure Theory, Probability Theory, Linear Algebra, and Functional Analysis. Each chapter ends with a summary and a set of end-of-chapter exercises. Full solutions or just hints for the proposed exercises are provided at the end of the book; also a comprehensive index is included.