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Books > Social sciences > Psychology > Cognition & cognitive psychology
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Mathematical Perspectives on Neural Networks (Paperback)
Loot Price: R1,878
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Mathematical Perspectives on Neural Networks (Paperback)
Series: Developments in Connectionist Theory Series
Expected to ship within 12 - 19 working days
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Recent years have seen an explosion of new mathematical results on
learning and processing in neural networks. This body of results
rests on a breadth of mathematical background which even few
specialists possess. In a format intermediate between a textbook
and a collection of research articles, this book has been assembled
to present a sample of these results, and to fill in the necessary
background, in such areas as computability theory, computational
complexity theory, the theory of analog computation, stochastic
processes, dynamical systems, control theory, time-series analysis,
Bayesian analysis, regularization theory, information theory,
computational learning theory, and mathematical statistics.
Mathematical models of neural networks display an amazing richness
and diversity. Neural networks can be formally modeled as
computational systems, as physical or dynamical systems, and as
statistical analyzers. Within each of these three broad
perspectives, there are a number of particular approaches. For each
of 16 particular mathematical perspectives on neural networks, the
contributing authors provide introductions to the background
mathematics, and address questions such as: * Exactly what
mathematical systems are used to model neural networks from the
given perspective? * What formal questions about neural networks
can then be addressed? * What are typical results that can be
obtained? and * What are the outstanding open problems? A
distinctive feature of this volume is that for each perspective
presented in one of the contributed chapters, the first editor has
provided a moderately detailed summary of the formal results and
the requisite mathematical concepts. These summaries are presented
in four chapters that tie together the 16 contributed chapters:
three develop a coherent view of the three general perspectives --
computational, dynamical, and statistical; the other assembles
these three perspectives into a unified overview of the neural
networks field.
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