Deep Learning Through the Prism of Tensors

Dr. Pradeep Singh earned his Ph.D. and Master’s degrees from the Indian Institute of Technology (IIT) Delhi, specializing in Dynamical Systems, and an undergraduate degree in Data Science from IIT Madras. Currently, he is a Post-Doctoral Researcher and Principal Investigator at the Machine Intelligence Lab within the Department of Computer Science and Engineering at IIT Roorkee, where he is actively engaged in research at the intersection of Geometric Deep Learning, Neuro-symbolic AI, and Dynamical Systems. His research is supported by the National Post Doctoral Fellowship (N-PDF) from the Science and Engineering Research Board (SERB), Department of Science and Technology. Dr. Singh has earned multiple accolades, including All India Rank 1 in IIT GATE 2020, IIT JAM 2015, and CSIR NET 2019, along with prestigious fellowships such as the National Board for Higher Mathematics (NBHM) Masters, Doctoral, and Post Doctoral Fellowships from the Department of Atomic Energy, and the SPM Doctoral Fellowship from the Council of Scientific and Industrial 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.

• 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.