{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T23:11:28Z","timestamp":1725664288260},"publisher-location":"Berlin, Heidelberg","reference-count":24,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540591191"},{"type":"electronic","value":"9783540491958"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1995]]},"DOI":"10.1007\/3-540-59119-2_189","type":"book-chapter","created":{"date-parts":[[2012,2,26]],"date-time":"2012-02-26T17:03:25Z","timestamp":1330275805000},"page":"337-341","source":"Crossref","is-referenced-by-count":5,"title":["Bounding VC-dimension for neural networks: Progress and prospects"],"prefix":"10.1007","author":[{"given":"Marek","family":"Karpinski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Angus","family":"Macintyre","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2005,6,1]]},"reference":[{"unstructured":"M. Anthony, N. Biggs, Computational Learning Theory: An Introduction, Cambridge University Press, 1992.","key":"25_CR1"},{"key":"25_CR2","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/0166-218X(93)90126-9","volume":"47","author":"M. Anthony","year":"1993","unstructured":"M. Anthony, J. Shawe-Taylor, A Result of Vapnik with Applications, Discrete Applied Math. 47 (1993), pp. 207\u2013217.","journal-title":"Discrete Applied Math."},{"doi-asserted-by":"crossref","unstructured":"A. Borodin, P. Tiwari, On the Decidability of Sparse Univariate Polynomial Interpolation, Proc. 22nd ACM STOC (1990), pp. 535\u2013545.","key":"25_CR3","DOI":"10.1145\/100216.100292"},{"key":"25_CR4","volume-title":"Tame Topology and 0-minimal Structures, preprint","author":"L. Dries van den","year":"1992","unstructured":"L. van den Dries, Tame Topology and 0-minimal Structures, preprint, University of Illinois, Urbana, 1992; to appear as a book."},{"key":"25_CR5","doi-asserted-by":"crossref","first-page":"183","DOI":"10.2307\/2118545","volume":"140","author":"L. Dries van den","year":"1994","unstructured":"L. van den Dries, A.Macintyre and D.Marker, The Elementary Theory of Restricted Analytic Fields with Exponentation, Annuals of Mathematics 140 (1994), pp 183\u2013205.","journal-title":"Annuals of Mathematics"},{"doi-asserted-by":"crossref","unstructured":"P.Goldberg and M.Jerrum, Bounding the Vapnik Chervonenkis Dimension of Concept Classes Parametrized by Real Numbers. Machine Learning, 1994 (to appear). A preliminary version appeared in Proc. 6th ACM Workshop on Computational Learning Theory, pp. 361\u2013369, 1993.","key":"25_CR6","DOI":"10.1145\/168304.168377"},{"key":"25_CR7","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1112\/plms\/s2-10.1.54","volume":"10","author":"G.H. Hardy","year":"1912","unstructured":"G.H. Hardy, Properties of Logarithmic-Exponential Functions, Proc. London Math. Soc. 10 (1912), pp. 54\u201390.","journal-title":"Proc. London Math. Soc."},{"key":"25_CR8","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/0890-5401(92)90010-D","volume":"100","author":"D. Haussler","year":"1992","unstructured":"D. Haussler, Decision Theoretic Generalizations of the PAC Model for Neural Nets and other Learning Applications, Information an Computation 100, (1992), pp. 78\u2013150.","journal-title":"Information an Computation"},{"doi-asserted-by":"crossref","unstructured":"J. Hertz, A. Krogh and R. G. Palmer, Introduction to the Theory of Neural Computation, Addison-Wesley, 1991.","key":"25_CR9","DOI":"10.1063\/1.2810360"},{"doi-asserted-by":"crossref","unstructured":"M. W. Hirsch, Differential Topology, Springer-Verlag, 1976.","key":"25_CR10","DOI":"10.1007\/978-1-4684-9449-5"},{"doi-asserted-by":"crossref","unstructured":"M. Karpinski and A. Macintyre, Quadratic Bounds for VC Dimension at Sigmoidal Neural Networks, Research Report No. 85116-CS, Universit\u00e4t Bonn, 1994; to be submitted.","key":"25_CR11","DOI":"10.1145\/225058.225118"},{"key":"25_CR12","doi-asserted-by":"crossref","first-page":"1276","DOI":"10.1137\/0222076","volume":"22","author":"M. Karpinski","year":"1993","unstructured":"M.Karpinski and T.Werther, VC Dimension and Uniform Learnability of Sparse Polynomials and Rational Functions, SIAM J. Computing 22 (1993), pp 1276\u20131285.","journal-title":"SIAM J. Computing"},{"key":"25_CR13","doi-asserted-by":"crossref","DOI":"10.1090\/mmono\/088","volume-title":"Fewnomials","author":"A.G. Khovanski","year":"1991","unstructured":"A.G.Khovanski, Fewnomials, American Mathematical Society, Providence, R.I., 1991."},{"key":"25_CR14","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1090\/S0002-9947-1986-0833698-1","volume":"295","author":"J. Knight","year":"1986","unstructured":"J.Knight, A.Pillay and C.Steinhorn, Definable Sets and Ordered Structures II, Trans. American Mathematical Society 295 (1986), pp.593\u2013605.","journal-title":"Trans. American Mathematical Society"},{"key":"25_CR15","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1112\/jlms\/s2-45.2.377","volume":"45","author":"M.C. Laskowsky","year":"1992","unstructured":"M.C.Laskowsky, Vapnik-Chervonenkis Classes od Definable Sets, J.London Math. Society 45 (1992), pp 377\u2013384.","journal-title":"J.London Math. Society"},{"unstructured":"W.Maass, On the Complexity of Learning on Feedforward Neural Nets, in Proc. EATCS Advanced School on Computational Learning and Cryptography, Vietri sul Mare, 1993.","key":"25_CR16"},{"unstructured":"W. Maass, G. Schnitger and E. D. Sontag, On the Computational Power of Sigmoidal versus Boolean Threshold Circuits, Proc. 32nd IEEE FOGS (1991), pp. 767\u2013776.","key":"25_CR17"},{"doi-asserted-by":"crossref","unstructured":"A.J.Macintyre and E.D.Sontag, Finiteness results for Sigmoidal Neural Networks, Proc. 25th ACM STOC (1993), pp.325\u2013334.","key":"25_CR18","DOI":"10.1145\/167088.167192"},{"key":"25_CR19","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1090\/S0002-9939-1964-0161339-9","volume":"15","author":"J. Milnor","year":"1964","unstructured":"J.Milnor, On the Betti Numbers of Real Varieties, Proc. of the American Mathematical Society 15 (1964), pp 275\u2013280.","journal-title":"Proc. of the American Mathematical Society"},{"key":"25_CR20","volume-title":"Topology from the Differentiable Viewpoint","author":"J. Milnor","year":"1965","unstructured":"J.Milnor, Topology from the Differentiable Viewpoint, Univ.Press, Virginia, 1965."},{"doi-asserted-by":"crossref","unstructured":"J. Shawe-Taylor, Sample Sizes for Sigmoidal Neural Networks, Preprint, University of London, 1994.","key":"25_CR21","DOI":"10.1145\/225298.225329"},{"doi-asserted-by":"crossref","unstructured":"G. Turan and F. Vatan, On the Computation of Boolean Functions by Analog Circuits of Bounded Fan-in, Proc. 35th IEEE FOCS (1994), pp. 553\u2013564.","key":"25_CR22","DOI":"10.1109\/SFCS.1994.365735"},{"key":"25_CR23","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1090\/S0002-9947-1968-0226281-1","volume":"133","author":"H.E. Warren","year":"1968","unstructured":"H.E.Warren, Lower Bounds for Approximation by Non-linear Manifolds, Trans. of the AMS 133 (1968), pp. 167\u2013178.","journal-title":"Trans. of the AMS"},{"unstructured":"A.J.Wilkie, Model Completeness Results of Restricted Pfaffian Functions and the Exponential Function, to appear in Journal of the AMS, 1994.","key":"25_CR24"}],"container-title":["Lecture Notes in Computer Science","Computational Learning Theory"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-59119-2_189.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,28]],"date-time":"2021-04-28T01:22:52Z","timestamp":1619572972000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-59119-2_189"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995]]},"ISBN":["9783540591191","9783540491958"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/3-540-59119-2_189","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[1995]]}}}