{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T06:14:57Z","timestamp":1773468897032,"version":"3.50.1"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1996,12,1]],"date-time":"1996-12-01T00:00:00Z","timestamp":849398400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[1996,12]]},"DOI":"10.1007\/bf02124745","type":"journal-article","created":{"date-parts":[[2005,9,15]],"date-time":"2005-09-15T03:12:16Z","timestamp":1126753936000},"page":"233-243","source":"Crossref","is-referenced-by-count":57,"title":["Limitations of the approximation capabilities of neural networks with one hidden layer"],"prefix":"10.1007","volume":"5","author":[{"given":"C. K.","family":"Chui","sequence":"first","affiliation":[]},{"given":"Xin","family":"Li","sequence":"additional","affiliation":[]},{"given":"H. N.","family":"Mhaskar","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"BF02124745_CR1","doi-asserted-by":"crossref","first-page":"930","DOI":"10.1109\/18.256500","volume":"39","author":"A.R. Barron","year":"1993","unstructured":"A.R. Barron, Universal approximation bounds for superposition of a sigmoidal function, IEEE Trans. Information Theory 39, 1993, 930\u2013945.","journal-title":"IEEE Trans. Information Theory"},{"key":"BF02124745_CR2","unstructured":"A.R. Barron and R.L. Barron, Statistical learning networks: a unified view, in:Symposium on the Interface: Statistics and Computing Science, Reston, Virginia, April, 1988."},{"key":"BF02124745_CR3","first-page":"321","volume":"2","author":"D.S. Broomhead","year":"1988","unstructured":"D.S. Broomhead and D. Lowe, Multivariable functional interpolation and adaptive networks, Complex Systems 2, 1988, 321\u2013355.","journal-title":"Complex Systems"},{"key":"BF02124745_CR4","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1090\/S0025-5718-1994-1240656-2","volume":"63","author":"C.K. Chui","year":"1994","unstructured":"C.K. Chui, X. Li and H.N. Mhaskar, Localized approximation by neural networks, Mathematics of Computation 63, 1994, 607\u2013623.","journal-title":"Mathematics of Computation"},{"key":"BF02124745_CR5","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/BF02551274","volume":"2","author":"G. Cybenko","year":"1989","unstructured":"G. Cybenko, Approximation by superposition of sigmoidal functions, Mathematics of Control, Signal and Systems 2, 1989, 303\u2013314.","journal-title":"Mathematics of Control, Signal and Systems"},{"key":"BF02124745_CR6","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1007\/BF01171759","volume":"63","author":"R. DeVore","year":"1989","unstructured":"R. DeVore, R. Howard and C.A. Micchelli, Optimal nonlinear approximation, Manuscripta Mathematica 63, 1989, 469\u2013478.","journal-title":"Manuscripta Mathematica"},{"key":"BF02124745_CR7","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1162\/neco.1995.7.2.219","volume":"7","author":"F. Girosi","year":"1995","unstructured":"F. Girosi, M. Jones and T. Poggio, Regularization theory and neural networks architectures, Neural Computation 7, 1995, 219\u2013269.","journal-title":"Neural Computation"},{"key":"BF02124745_CR8","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1016\/0893-6080(90)90005-6","volume":"3","author":"K. Hornik","year":"1990","unstructured":"K. Hornik, M. Stinchcombe and H. White, Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks, Neural Networks 3, 1990, 551\u2013560.","journal-title":"Neural Networks"},{"key":"BF02124745_CR9","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1016\/S0893-6080(05)80131-5","volume":"6","author":"M. Leshno","year":"1993","unstructured":"M. Leshno, V. Lin, A. Pinkus and S. Schocken, Multilayer feedforward networks with a non-polynomial activation function can approximate any function, Neural Networks 6, 1993, 861\u2013867.","journal-title":"Neural Networks"},{"key":"BF02124745_CR10","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/BF02070821","volume":"1","author":"H.N. Mhaskar","year":"1993","unstructured":"H.N. Mhaskar, Approximation properties of a multilayered feedforward artificial neural network, Advances in Computational Mathematics 1, 1993, 61\u201380.","journal-title":"Advances in Computational Mathematics"},{"key":"BF02124745_CR11","first-page":"190","volume-title":"Neural Networks for Signal Processing, III","author":"H.N. Mhaskar","year":"1993","unstructured":"H.N. Mhaskar, Neural networks for localized approximation of real functions, in:Neural Networks for Signal Processing, III, eds. C.A. Kamm, G.M. Kuhn, B. Yoon, R. Chellappa and S.Y. Kung, IEEE, New York, 1993, pp. 190\u2013196."},{"key":"BF02124745_CR12","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1162\/neco.1996.8.1.164","volume":"8","author":"H.N. Mhaskar","year":"1996","unstructured":"H.N. Mhaskar, Neural networks for optimal approximation of smooth and analytic functions, Neural Computation 8, 1996, 164\u2013177.","journal-title":"Neural Computation"},{"key":"BF02124745_CR13","unstructured":"H.N. Mhaskar, Approximation of real functions using neural networks, in:Proc. of Int. Conf. on Computational Mathematics, New Delhi, India, 1993, eds. H.P. Dikshit and C.A. Micchelli, World Scientific Press, 1994, pp. 267\u2013278."},{"key":"BF02124745_CR14","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/0196-8858(92)90016-P","volume":"13","author":"H.N. Mhaskar","year":"1992","unstructured":"H.N. Mhaskar and C.A. Micchelli, Approximation by superposition of a sigmoidal function and radial basis functions, Advances in Applied Mathematics 13, 1992, 350\u2013373.","journal-title":"Advances in Applied Mathematics"},{"key":"BF02124745_CR15","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1147\/rd.383.0277","volume":"38","author":"H.N. Mhaskar","year":"1994","unstructured":"H.N. Mhaskar and C.A. Micchelli, Dimension independent bounds on the degree of approximation by neural networks, IBM Journal of Research and Development 38, 1994, 277\u2013284.","journal-title":"IBM Journal of Research and Development"},{"key":"BF02124745_CR16","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1006\/aama.1995.1008","volume":"16","author":"H.N. Mhaskar","year":"1995","unstructured":"H.N. Mhaskar and C.A. Micchelli, Degree of approximation by neural and translation networks with a single hidden layer, Advances in Applied Mathematics 16, 1995, 151\u2013183.","journal-title":"Advances in Applied Mathematics"},{"key":"BF02124745_CR17","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1162\/neco.1989.1.2.281","volume":"1","author":"J. Moody","year":"1989","unstructured":"J. Moody and C. Darken, Fast learning in networks of locally tuned processing units, Neural Computations 1, 1989, 282\u2013294.","journal-title":"Neural Computations"},{"key":"BF02124745_CR18","doi-asserted-by":"crossref","unstructured":"T. Poggio and F. Girosi, Networks for approximation and learning, Proceedings of the IEEE 78, 1990.","DOI":"10.1109\/5.58326"},{"key":"BF02124745_CR19","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1109\/NNSP.1993.471890","volume-title":"Neural Networks for Signal Processing, III, 1993","author":"T. Poggio","year":"1993","unstructured":"T. Poggio, F. Girosi and M. Jones, From regularization to radial, tensor and additive splines, in:Neural Networks for Signal Processing, III, 1993, eds. C.A. Kamm, G.M. Buhn, B. Yoon, R. Chellappa and S.Y. Kung, IEEE, New York, 1993, pp. 3\u201310."},{"key":"BF02124745_CR20","volume-title":"Spline Functions: Basic Theory","author":"L.L. Schumaker","year":"1981","unstructured":"L.L. Schumaker,Spline Functions: Basic Theory, Wiley, New York, 1981."},{"key":"BF02124745_CR21","volume-title":"Singular Integrals and Differentiability Properties of Functions","author":"E.M. Stein","year":"1970","unstructured":"E.M. Stein,Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, 1970."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02124745.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02124745\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02124745","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,14]],"date-time":"2019-05-14T01:31:09Z","timestamp":1557797469000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02124745"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,12]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1996,12]]}},"alternative-id":["BF02124745"],"URL":"https:\/\/doi.org\/10.1007\/bf02124745","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,12]]}}}