000			a
999			_c30973 _d30973
008			220610b xxu||||| |||| 00| 0 eng d
020			_a9789811660450
082			_a006.31 _bYEJ
100			_aYe, Jong Chul
245			_aGeometry of deep learning : a signal processing perspective
260			_bSpringer, _c2022 _aSingapore :
300			_axvi, 330 p. ; _bill., _c25 cm
365			_b74.99 _cEUR _d86.00
490			_aMathematics in industry, 1612-3956 _vv.37
504			_aIncludes bibliographical references and index.
520			_aThe focus of this book is on providing students with insights into geometry that can help them understand deep learning from a unified perspective. Rather than describing deep learning as an implementation technique, as is usually the case in many existing deep learning books, here, deep learning is explained as an ultimate form of signal processing techniques that can be imagined. To support this claim, an overview of classical kernel machine learning approaches is presented, and their advantages and limitations are explained. Following a detailed explanation of the basic building blocks of deep neural networks from a biological and algorithmic point of view, the latest tools such as attention, normalization, Transformer, BERT, GPT-3, and others are described. Here, too, the focus is on the fact that in these heuristic approaches, there is an important, beautiful geometric structure behind the intuition that enables a systematic understanding. A unified geometric analysis to understand the working mechanism of deep learning from high-dimensional geometry is offered. Then, different forms of generative models like GAN, VAE, normalizing flows, optimal transport, and so on are described from a unified geometric perspective, showing that they actually come from statistical distance-minimization problems. Because this book contains up-to-date information from both a practical and theoretical point of view, it can be used as an advanced deep learning textbook in universities or as a reference source for researchers interested in acquiring the latest deep learning algorithms and their underlying principles. In addition, the book has been prepared for a codeshare course for both engineering and mathematics students, thus much of the content is interdisciplinary and will appeal to students from both disciplines.
650			_aFunctional Analysis
650			_aDifferential Geometry
650			_aArtificial Intelligence
650			_aMathematical Models
650			_aCognitive Processes
650			_aNeural Networks
650			_aMathematical and Computational Biology
650			_aActivation function
650			_a Algorithmic robutness
650			_aBias-variance trade-off
650			_aConvex optimization
650			_aDeep convolutional framelets
650			_aEncoder-decoder CNN
650			_aFeature space
650			_a Gradient descent method
650			_aKernel SVM
650			_aLoss surfaces
650			_aNeural tangent Kernel (NTK)
650			_aPositive definite
650			_aRepresenter theorem
650			_aSigmoid function
650			_aTraining data
650			_a Universal approximation theorem
650			_a Vanishing gradient problem
650			_aWeight clipping
942			_2ddc _cBK