Mathematical Foundations of Deep Learning Models and Algorithms by Konstantinos Spiliopoulos
Deep learning uses multi-layer neural networks to model complex data patterns. Large models-with millions or even billions of parameters-are trained on massive datasets. This approach has produced revolutionary advances in image, text, and speech recognition and also has potential applications in a range of other fields such as engineering, finance, mathematics, and medicine. This book provides an introduction to the mathematical theory underpinning the recent advances in deep learning. Detailed derivations as well as mathematical proofs are presented for many of the models and optimization methods which are commonly used in machine learning and deep learning. Applications, code, and practical approaches to training models are also included. The book is designed for advanced undergraduates, graduate students, practitioners, and researchers. Divided into two parts, it begins with mathematical foundations before tackling advanced topics in approximation, optimization, and neural network training. Part 1 is written for a general audience, including students in mathematics, statistics, computer science, data science, or engineering, while select chapters in Part 2 present more advanced mathematical theory requiring familiarity with analysis, probability, and stochastic processes. Together, they form an ideal foundation for an introductory course on the mathematics of deep learning. Thoughtfully designed exercises and a companion website with code examples enhance both theoretical understanding and practical skills, preparing readers to engage more deeply with this fast-evolving field.-
Analysis
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Options Pricing and Portfolio Optimization
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Scrapbook of Complex Curve Theory
- Partial Differential Equations
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Algebra
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A Course on the Web Graph
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Global Analysis
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Invitation to Nonlinear Algebra
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Applied Asymptotic Analysis
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Advanced Modern Algebra
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A Course in Operator Theory
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Representations of Finite and Compact Groups
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Classical and Quantum Computation
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Toric Varieties
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Introduction to Analytic and Probabilistic Number Theory
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Mathematical Methods in Quantum Mechanics
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Discovering Modern Set Theory, Part 1
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Differential Geometry, Lie Groups, and Symmetric Spaces
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Lectures on Elliptic and Parabolic Equations in Sobolev Spaces
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Riemann Surfaces by Way of Complex Analytic Geometry
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Advanced Modern Algebra, Parts 1 and 2
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Introduction to Quantum Groups and Crystal Bases
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Introduction to the H-Principle
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A Course in Differential Geometry
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Measure Theory and Integration
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Algebraic Number Fields
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Inequalities in Matrix Algebras
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Algebraic Curves and Riemann Surfaces
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$\textrm {C}^*$-Algebras and Finite-Dimensional Approximations
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The Calderon Problem
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Several Complex Variables with Connections to Algebraic Geometry and Lie Groups
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Function Theory of One Complex Variable
Konstantinos Spiliopoulos, Boston University, MA.
Richard B. Sowers, University of Illinois at Urbana Champaign, Illinois.
Justin Sirignano, University of Oxford, United Kingdom
Richard B. Sowers, University of Illinois at Urbana Champaign, Illinois.
Justin Sirignano, University of Oxford, United Kingdom
| SKU | Unavailable |
| ISBN 13 | 9781470483999 |
| ISBN 10 | 1470483998 |
| Title | Mathematical Foundations of Deep Learning Models and Algorithms |
| Author | Konstantinos Spiliopoulos |
| Series | Graduate Studies In Mathematics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | American Mathematical Society |
| Year published | 2025-12-31 |
| Number of pages | 550 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |