Textbook in PDF format

This book offers an in-depth exploration of the mathematical foundations underlying Transformer Networks, the cornerstone of modern AI across various domains. Unlike existing literature that focuses primarily on implementation, this work delves into the elegant geometry, symmetry, and mathematical structures that drive the success of Transformers. Through rigorous analysis and theoretical insights, the book unravels the complex relationships and dependencies that these models capture, providing a comprehensive understanding of their capabilities. Designed for researchers, academics, and advanced practitioners, this text bridges the gap between practical application and theoretical exploration. Readers will gain a profound understanding of how Transformers operate in abstract spaces, equipping them with the knowledge to innovate, optimize, and push the boundaries of AI. Whether you seek to deepen your expertise or pioneer the next generation of AI models, this book is an essential resource on the mathematical principles of Transformers. The advent of Transformer networks has not merely advanced the field of Artificial Intelligence; it has redefined the landscape entirely. As the current state-of-the-art across various domains—including natural language processing (NLP), computer vision, time series forecasting, and signal analysis—Transformers have demonstrated an unparalleled ability to model complex patterns, understand intricate relationships, and deliver breakthrough performance. The self-attention mechanism at the heart of these models allows them to capture dependencies within data in ways that traditional architectures could never achieve, making Transformers the backbone of modern AI research and applications. Despite the widespread adoption and success of Transformers, much of the literature remains focused on their practical implementation, often overlooking the deep mathematical structures that enable their effectiveness. This gap presents a significant opportunity for researchers and practitioners alike. Understanding the mathematical foundations of Transformers is essential for those who seek to push the boundaries of what these models can achieve. A solid mathematical understanding equips us to innovate, optimize, and potentially discover the next generation of models that will build on the success of Transformers. The Geometry of Intelligence: Foundations of Transformer Networks in Deep Learning is crafted for those who wish to explore the profound theoretical underpinnings of Transformer networks. This book is intended for researchers, academics, and advanced practitioners who aspire to grasp the elegant mathematical principles that make Transformers work. By focusing exclusively on the theoretical aspects, we aim to provide readers with a deep and thorough understanding of the geometry, symmetry, and intelligence encoded within these models, without the distractions of implementation details, for which a plethora of resources already exist