Tensors, Non Convexity, and High Dimensional Phenomena
Tensors, Non Convexity, and High Dimensional Phenomena
Foundations of Scalable Learning Systems and a Rigorous Mathematical Framework for Building Advanced AI Systems
About the Book
This book connects advanced mathematics with modern machine learning, focusing on tensors, non-convex optimization, and high-dimensional statistics. It combines theories from random matrices, algebraic geometry, and statistical mechanics to provide both researchers and students with the mathematical tools needed for developing better AI algorithms.
The book explores tensor decomposition, high-dimensional geometry, and the structure of neural network optimization landscapes. Each chapter builds from core concepts to current research challenges, balancing theory with practical applications.
Designed for machine learning researchers, computer scientists, and mathematicians working on AI systems, this book creates a unified framework for understanding deep learning mathematics, optimization, and generalization in high dimensions.
About the Author
Table of Contents
- Concentration of Measure and the Advantages of High Dimensionality
- The Spectral Anatomy of Random Matrices
- Algebraic Foundations of Tensor Methods
- Representation Theory for Machine Learning
- Statistical Mechanics of Non-Convex Optimization
- Morse Theory and Gradient Flow Topology
- Global Convergence via Tensor Decomposition
- Hamiltonian Dynamics in Optimization
- Mean-Field Limits of Learning Systems
- Parallel and Distributed Tensor Algorithms
- Large-Deviation Principles for Generalization
- Open Problems at the Interface
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