Chaos in discrete learning systems |
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| Institution: | 1. Department of Mathematics, University of Colorado, Boulder, CO 80309-0395, USA;2. International Solvay Institute for Physics and Chemistry, CP 231 ULB, 1050 Brussels, Belgium;1. Texas Tech University School of Music, Lubbock, TX;2. Department of Mechanical Engineering, Texas Tech University, Lubbock, TX;3. Department of Educational Psychology and Leadership, Texas Tech University, Lubbock, TX;1. Department of Mathematics, Dalian Nationalities University, 116600, China;2. Department of Mathematics, Jilin Normal University, 136000, China;3. Department of Mathematics, Liaoning Normal University, 116029, China;4. Department of Basics, Dalian Naval Academy, 116018, China;1. Department of Electrical and Computer Engineering, University of Auckland, New Zealand;2. Department of Engineering Science, University of Auckland, New Zealand;1. Division of Epidemiology, School of Public Health, University of California, 140 Warren Hall, Berkeley, CA 94720, USA;2. Department of International Health, Johns Hopkins School of Public Health, USA;3. Population Council, Brazil |
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| Abstract: | Departing from the customary view of the sigmoid thresholding functions as smooth nonlinearities introduced into multilayer perceptron networks to enable continuously differentiable gradient descents toward optimal solutions minimizing some error norm, here a different more fundamental point of view is advanced: the intrinsic local dynamics of the network become that of the quadratic map of the chaos theory. This new insight aids understanding of important supervised learning algorithms such as the widely used Backpropagation scheme. |
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