In the rapidly evolving field of artificial intelligence, this book serves as a crucial resource for understanding the mathematical foundations of AI. It explores the intricate world of tensors, the fundamental elements powering today's advanced deep learning models. Combining theoretical depth with practical insights, the text navigates the complex landscape of tensor calculus, guiding readers to master the principles and applications of tensors in AI. From the basics of tensor algebra and geometry to the sophisticated architectures of neural networks, including multi-layer perceptrons, convolutional, recurrent, and transformer models, this book provides a comprehensive examination of the mechanisms driving modern AI innovations. It delves into the specifics of autoencoders, generative models, and geometric interpretations, offering a fresh perspective on the complex, high-dimensional spaces traversed by deep learning technologies. Concluding with a forward-looking view, the book addresses the latest advancements and speculates on the future directions of AI research, preparing readers to contribute to or navigate the next wave of innovations in the field. Designed for academics, researchers, and industry professionals, it serves as both an essential textbook for graduate and postgraduate students and a valuable reference for experts in the field. With its rigorous approach to the mathematical frameworks of AI and a strong focus on practical applications, this book bridges the gap between theoretical research and real-world implementation, making it an indispensable guide in the realm of artificial intelligence.

Delves deeper into the mathematical intricacies of tensors in AI Provides focused exploration of tensor calculus and its applications in deep learning Includes summaries, illustrative examples, and exercises aimed at reinforcing the reader's understanding of the material

Autorentext

Dr. Pradeep Singh is serving as an Assistant Professor (Grade--I) at the Indian Institute of Information Technology Surat, where he also serves as Associate Dean (R&D). He is faculty in the Department of Mathematics and Computational Sciences, and joint faculty in the Department of Computer Science & Engineering. His research spans Geometric Deep Learning, Neuro-symbolic AI, and Dynamical Systems. His research has appeared in premier venues, including IEEE Transactions; Knowledge-Based Systems; Neurocomputing; Chaos, Solitons & Fractals; and ECAI, contributing to the wider dialogue in AI and dynamical-systems research. He has authored multiple books: the Springer monographs Deep Learning Through the Prism of Tensors and The Geometry of Intelligence: Foundations of Transformer Networks, and the McGraw-Hill text Machine Learning and Artificial Intelligence. He earned his Ph.D. (2022) and Master’s degree from IIT Delhi, specializing in Symbolic Systems, and a Bachelor’s degree in Data Science from IIT Madras. Dr Singh secured All-India Rank 1 in GATE 2020, JAM 2015, and CSIR-NET 2019. He has also received highly competitive awards, including the National Board for Higher Mathematics (NBHM) Master’s, Doctoral, and Post-Doctoral Fellowships awarded by the Department of Atomic Energy, India. In 2019, he was one of only two researchers nationwide to receive the Dr Shyama Prasad Mukherjee (SPM) Fellowship in Mathematics from CSIR, India. He is also a recipient of the prestigious Human Frontier Science Program Postdoctoral Fellowship, an international fellowship supporting frontier cross-disciplinary research. Dr. Balasubramanian Raman received his Ph.D. from IIT Madras and his B.Sc. and M.Sc. in Mathematics from the University of Madras. He is a Professor and the Head of the Department of Computer Science and Engineering at IIT Roorkee, as well as the iHUB Divyasampark Chair Professor. He is also a Joint Faculty member in the Mehta Family School of Data Science and Artificial Intelligence at IIT Roorkee. With over 200 research papers published in reputed journals and conferences, his research interests span Machine Learning, Image and Video Processing, Computer Vision, and Pattern Recognition. Dr. Raman has served as a Guest Professor and Visiting Researcher at prestigious institutions such as Osaka Metropolitan University, Curtin University, the University of Cyberjaya, and the University of Windsor. He has held postdoctoral positions at Rutgers University and the University of Missouri-Columbia. Under his coaching, teams have achieved notable rankings in the ACM International Collegiate Programming Contest (ICPC) World Finals. He has been recognized with several awards, including the BOYSCAST Fellowship and the Ramkumar Prize for Outstanding Teaching and Research.

Inhalt

Chapter 1: A Tensorial Perspective to Deep Learning.- Chapter 2: The Algebra and Geometry of Deep Learning.- Chapter 3: Building Blocks.- Chapter 4: Journey into Convolutions.- Chapter 5: Modeling Temporal Data.- Chapter 6: Transformer Architectures.- Chapter 7: Attention Mechanisms Beyond Transformers.- Chapter 8: Graph Neural Networks: Extending Deep Learning to Graphs.- Chapter 9: Self-Supervised and Unsupervised Learning in Deep Learning.- Chapter 10: Learning Representations via Autoencoders and Generative Models.- Chapter 11: Recent Advances and Future Perspectives.