Название: Deep Learning Through the Prism of Tensors Автор: Pradeep Singh, Balasubramanian Raman Издательство: Springer Год: 2025 Страниц: 627 Язык: английский Формат: pdf (true) Размер: 10.1 MB
In the rapidly evolving field of Artificial Intelligence (AI), 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.
The interdisciplinary nature of this book reflects the reality of modern Deep Learning research, where insights from mathematics, Computer Science, and engineering converge to drive innovation. By emphasizing the tensorial perspective, this book not only provides a robust understanding of existing models but also equips readers with the conceptual tools to explore and develop new architectures. In writing this book, we have drawn from our own experiences in research and teaching, striving to present complex ideas in a clear and accessible manner. The examples and exercises are designed to bridge the gap between theory and practice, helping readers to apply what they have learned to real-world challenges. The mathematical formalism in this book is rich and rigorous, reflecting the complex nature of the subject matter, yet it is presented with clarity and coherence to ensure that readers are not lost in abstraction.
One of the hallmarks of Deep Learning is its broad applicability across various domains. From image and sequence processing to the geometric understanding of data, the versatility of Deep Learning models continues to expand. This book not only covers the theoretical underpinnings but also showcases practical implementations using popular frameworks such as TensorFlow and PyTorch. I believe that this hands-on approach will equip readers with the skills necessary to tackle real-world problems.
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.
1. A Tensorial Perspective to Deep Learning 2. The Algebra and Geometry of Deep Learning 3. Building Blocks 4. Journey into Convolutions 5. Modeling Temporal Data 6. Transformer Architectures 7. Attention Mechanisms Beyond Transformers 8. Graph Neural Networks: Extending Deep Learning to Graphs 9. Self-supervised and Unsupervised Learning in Deep Learning 10. Learning Representations via Autoencoders and Generative Models 11. Recent Advances and Future Perspectives
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Deep Learning Through the Prism of Tensors 
