Download or read book Banach Space Valued Neural Network written by George A. Anastassiou and published by Springer Nature. This book was released on 2022-10-01 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the generalization and modernization of approximation by neural network operators. Functions under approximation and the neural networks are Banach space valued. These are induced by a great variety of activation functions deriving from the arctangent, algebraic, Gudermannian, and generalized symmetric sigmoid functions. Ordinary, fractional, fuzzy, and stochastic approximations are exhibited at the univariate, fractional, and multivariate levels. Iterated-sequential approximations are also covered. The book’s results are expected to find applications in the many areas of applied mathematics, computer science and engineering, especially in artificial intelligence and machine learning. Other possible applications can be in applied sciences like statistics, economics, etc. Therefore, this book is suitable for researchers, graduate students, practitioners, and seminars of the above disciplines, also to be in all science and engineering libraries.

Download or read book Parametrized Deformed and General Neural Networks written by George A. Anastassiou and published by Springer Nature. This book was released on 2023-09-29 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we introduce the parametrized, deformed and general activation function of neural networks. The parametrized activation function kills much less neurons than the original one. The asymmetry of the brain is best expressed by deformed activation functions. Along with a great variety of activation functions, general activation functions are also engaged. Thus, in this book, all presented is original work by the author given at a very general level to cover a maximum number of different kinds of neural networks: giving ordinary, fractional, fuzzy and stochastic approximations. It presents here univariate, fractional and multivariate approximations. Iterated sequential multi-layer approximations are also studied. The functions under approximation and neural networks are Banach space valued.

Download or read book Intelligent Computations Abstract Fractional Calculus Inequalities Approximations written by George A. Anastassiou and published by Springer. This book was released on 2017-09-02 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief book presents the strong fractional analysis of Banach space valued functions of a real domain. The book’s results are abstract in nature: analytic inequalities, Korovkin approximation of functions and neural network approximation. The chapters are self-contained and can be read independently. This concise book is suitable for use in related graduate classes and many research projects. An extensive list of references is provided for each chapter. The book’s results are relevant for many areas of pure and applied mathematics. As such, it offers a unique resource for researchers, and a valuable addition to all science and engineering libraries.

Download or read book Neural Networks and Qualitative Physics written by Jean-Pierre Aubin and published by Cambridge University Press. This book was released on 1996-03-29 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics. Professor Aubin makes use of control and viability theory in neural networks and cognitive systems, regarded as dynamical systems controlled by synaptic matrices, and set-valued analysis that plays a natural and crucial role in qualitative analysis and simulation. This allows many examples of neural networks to be presented in a unified way. In addition, several results on the control of linear and nonlinear systems are used to obtain a "learning algorithm" of pattern classification problems, such as the back-propagation formula, as well as learning algorithms of feedback regulation laws of solutions to control systems subject to state constraints.

Download or read book Advances in Mathematical Modelling Applied Analysis and Computation written by Jagdev Singh and published by Springer Nature. This book was released on with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Handbook on Neural Information Processing written by Monica Bianchini and published by Springer Science & Business Media. This book was released on 2013-04-12 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook presents some of the most recent topics in neural information processing, covering both theoretical concepts and practical applications. The contributions include: Deep architectures Recurrent, recursive, and graph neural networks Cellular neural networks Bayesian networks Approximation capabilities of neural networks Semi-supervised learning Statistical relational learning Kernel methods for structured data Multiple classifier systems Self organisation and modal learning Applications to content-based image retrieval, text mining in large document collections, and bioinformatics This book is thought particularly for graduate students, researchers and practitioners, willing to deepen their knowledge on more advanced connectionist models and related learning paradigms.

Download or read book The Multipliers of Banach Space Valued Functions written by 何達諭 and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The 1994 IEEE International Conference on Neural Networks written by and published by IEEE Computer Society Press. This book was released on 1994 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Extension of Banach Space Valued Lipschitz Fubctions written by Mark Kozdoba and published by . This book was released on 2005 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book AI Magazine written by and published by . This book was released on 1993 with total page 826 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Asymptotic Properties of Recursive M estimators in an Infinite dimensional Hilbert Space written by Xiaohong Chen and published by . This book was released on 1993 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Norm Estimates of Banach Space Valued Random Series and Their Applications in Harmonic Analysis written by Niandi Xiang and published by . This book was released on 1997 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Complex valued Neural Networks written by Akira Hirose and published by World Scientific. This book was released on 2003 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, complex-valued neural networks have widened the scope of application in optoelectronics, imaging, remote sensing, quantum neural devices and systems, spatiotemporal analysis of physiological neural systems, and artificial neural information processing. In this first-ever book on complex-valued neural networks, the most active scientists at the forefront of the field describe theories and applications from various points of view to provide academic and industrial researchers with a comprehensive understanding of the fundamentals, features and prospects of the powerful complex-valued networks.

Download or read book On the Integration of Set valued Mappings in a Nonreflexive Banach Space written by M. Ali Khan and published by . This book was released on 1982 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Integral Geometry and Radon Transforms written by Sigurdur Helgason and published by Springer Science & Business Media. This book was released on 2010-11-17 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, integral geometry deals with Radon’s problem of representing a function on a manifold in terms of its integrals over certain submanifolds—hence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial di erential equations and group representations). For the case of the plane, the inversion theorem and the support theorem have had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroom use or self-study. A number of exercises point to further results with documentation. From the reviews: “Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. the contents of the book is concentrated around the duality and double vibration, which is realized through the masterful treatment of a variety of examples. the book is written by an expert, who has made fundamental contributions to the area.” —Boris Rubin, Louisiana State University

Download or read book On Ridge Splines Neural Networks and Variational Problems in Radon domain BV Spaces written by Rahul Parhi (Ph.D.) and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deep neural networks are not well understood mathematically and their success in many science and engineering applications is usually only backed by empirical evidence. In this dissertation, we study neural networks from first principles, beginning with the simplest architecture of shallow feedforward neural networks. We use tools from variational spline theory to mathematically understand neural networks. In particular, we view neural networks as a type of spline. We propose and study a new family of Banach spaces, which are bounded variation (BV) spaces defined via the Radon transform. These are the "native spaces" for neural networks. We show that finite-width neural networks are solutions to data-fitting variational problems over these spaces. Moreover, these variational problems can be recast as finite-dimensional neural network training problems with regularization schemes related to weight decay and path-norm regularization, giving theoretical insight into these common regularization schemes as well as providing several new, principled forms of regularization for (deep) neural networks. The Radon-domain BV spaces are also interesting from the perspective of functional analysis and statistical estimation. The best approximation and estimation error rates of these spaces are (essentially) independent of the input dimension, while the best linear approximation and estimation error rates suffer the curse of dimensionality. The Radon-domain BV spaces contain functions that are very smooth in all directions except (perhaps) a few directions. The anisotropic nature of these spaces distinguishes them from classical function spaces. This dissertation provides a first step towards a mathematical theory of neural networks through the lens of spline theory and functional analysis.

Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 980 pages. Available in PDF, EPUB and Kindle. Book excerpt: