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fengxiang h foundations deep learning 2025

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Textbook in PDF format Deep Learning has significantly reshaped a variety of technologies, such as image processing, natural language processing (NLP), and audio processing. The excellent generalizability of Deep Learning is like a “cloud” to conventional complexity-based learning theory: the over-parameterization of Deep Learning makes almost all existing tools vacuous. This irreconciliation considerably undermines the confidence of deploying Deep Learning to security-critical areas, including autonomous vehicles and medical diagnosis, where small algorithmic mistakes can lead to fatal disasters. This book seeks to explaining the excellent generalizability, including generalization analysis via the size-independent complexity measures, the role of optimization in understanding the generalizability, and the relationship between generalizability and ethical/security issues. The efforts to understand the excellent generalizability are following two major paths: (1) developing size-independent complexity measures, which can evaluate the “effective” hypothesis complexity that can be learned, instead of the whole hypothesis space; and (2) modelling the learned hypothesis through stochastic gradient methods, the dominant optimizers in Deep Learning, via stochastic differential functions and the geometry of the associated loss functions. Related works discover that over-parameterization surprisingly bring many good properties to the loss functions. Rising concerns of Deep Learning are seen on the ethical and security issues, including privacy preservation and adversarial robustness. Related works also reveal an interplay between them and generalizability: a good generalizability usually means a good privacy-preserving ability; and more robust algorithms might have a worse generalizability. Deep Learning refers to a subset of Machine Learning techniques that employ artificial neural networks characterized by multiple layers of interconnected nodes (or neurons) followed by nonlinear activation functions. Such networks are of significant size. These deep neural networks are designed to process and learn from experience, extracting complex patterns and features through successive layers of computation. Such experience can be obtained either from human-annotated electronic records such as datasets or from the learner’s own interactions with its perceived environment. By leveraging these layered architectures, Deep Learning models can autonomously discover and represent intricate relationships within the data, enabling them to make sophisticated predictions and informed decisions based on learned knowledge. We expect readers can have a big picture of the current knowledge in Deep Learning theory, understand how the Deep Learning theory can guide new algorithm designing, and identify future research directions. Readers need knowledge of calculus, linear algebra, probability, statistics, and statistical learning theory. - The first comprehensive overview book on the foundations of Deep Learning - Written by leading experts in the field - Explicates excellent generalizability of Deep Learning, including generalization analysis

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fengxiang h foundations deep learning 2025