4(3):381–383.

Paper doi abstract bibtex

Paper doi abstract bibtex

It is proved that if we have neurons implementing arbitrary linear functions and a neuron implementing one (arbitrary but smooth) nonlinear function g(x), then for every continuous function f(x1, …, xm) of arbitrarily many variables and for arbitrary e $>$ 0 we can construct a network that consists of g-neurons and linear neurons and computes f with precision e.

@article{kreinovichArbitraryNonlinearitySufficient1991, title = {Arbitrary Nonlinearity Is Sufficient to Represent All Functions by Neural Networks: A Theorem}, author = {Kreinovich, Vladik Y.}, date = {1991-01}, journaltitle = {Neural Networks}, volume = {4}, pages = {381--383}, issn = {0893-6080}, doi = {10.1016/0893-6080(91)90074-f}, url = {https://doi.org/10.1016/0893-6080(91)90074-f}, abstract = {It is proved that if we have neurons implementing arbitrary linear functions and a neuron implementing one (arbitrary but smooth) nonlinear function g(x), then for every continuous function f(x1, …, xm) of arbitrarily many variables and for arbitrary e {$>$} 0 we can construct a network that consists of g-neurons and linear neurons and computes f with precision e.}, keywords = {*imported-from-citeulike-INRMM,~INRMM-MiD:c-10833268,artificial-neural-networks,back-propagation-networks,mapping-networks,network-representation-capability,nonideal-neurons,universal-approximation}, number = {3} }

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