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Radial Basis Function Neural Networks Have Superlinear VC Dimension [chapter]

Michael Schmitt
2001 Lecture Notes in Computer Science  
As the main result we show that every reasonably sized standard network of radial basis function (RBF) neurons has VC dimension (W log k), where W is the number of parameters and k the number of nodes.  ...  We establish superlinear lower bounds on the Vapnik-Chervonenkis (VC) dimension of neural networks with one hidden layer and local receptive eld neurons.  ...  Acknowledgment This work has been supported in part by the ESPRIT Working Group in Neural and Computational Learning II, NeuroCOLT2, No. 27150.  ... 
doi:10.1007/3-540-44581-1_2 fatcat:ji2r6x2s4fabrmu7lckky6fpv4

Lower Bounds on the VC Dimension of Smoothly Parameterized Function Classes

Wee Sun Lee, Peter L. Bartlett, Robert C. Williamson
1995 Neural Computation  
Neural nets with superlinear VC-dimension. Neural Comp. 6, 877-884. VC Dimension of Parameterized Function Classes 1053 Powell, M. J. D. 1987.  ...  Certain two- and three-layer feedforward neural networks with tanh(x) activation function are known to have VC dimension at least 2(W log W).  ... 
doi:10.1162/neco.1995.7.5.1040 fatcat:hv5ybwmotbfrtmvm77ebgzirvi

RBF Neural Networks and Descartes' Rule of Signs [chapter]

Michael Schmitt
2002 Lecture Notes in Computer Science  
We establish versions of Descartes' rule of signs for radial basis function (RBF) neural networks.  ...  This result contrasts with previous work showing that RBF neural networks with two and more input nodes have superlinear VC dimension.  ...  In this contribution we show that versions of Descartes' rule of signs can be established for radial basis function (RBF) neural networks.  ... 
doi:10.1007/3-540-36169-3_26 fatcat:x5yclcltivez5fywlky2ezvbui

On the Complexity of Computing and Learning with Multiplicative Neural Networks

Michael Schmitt
2002 Neural Computation  
As to lower bounds, we construct product unit networks of fixed depth with superlinear VC dimension.  ...  In particular, we derive upper and lower bounds on the Vapnik-Chervonenkis (VC) dimension and the pseudodimension for various types of networks with multiplicative units.  ...  Some of the results have been presented at the NeuroCOLT Workshop "New Perspectives in the Theory of Neural Nets" in Graz, Austria, on May 3, 2000.  ... 
doi:10.1162/08997660252741121 pmid:11802913 fatcat:qivw7gldfvf33ndge4s66robcy

Learning pattern classification-a survey

S.R. Kulkarni, G. Lugosi, S.S. Venkatesh
1998 IEEE Transactions on Information Theory  
Topics discussed include nearest neighbor, kernel, and histogram methods, Vapnik-Chervonenkis theory, and neural networks.  ...  Radial Basis Function Classifiers: These classifiers have a "neural" flavor and base their decision upon the sign of functions of the form where is a kernel function (such as or ), is an integer, and the  ...  However, typical radial basis function classifiers choose , and tune the rest of the parameters according to some criterion.  ... 
doi:10.1109/18.720536 fatcat:pboyft5ze5gwphln5bpglatbam

An Improved Harris's Hawks Optimization for SAR Target Recognition and Stock Market Index Prediction

Hongping Hu, Yan Ao, Yanping Bai, Rong Cheng, Ting Xu
2020 IEEE Access  
INDEX TERMS Extreme learning machine, function optimization, Harris's hawk optimization, stock prediction, support vector machine, synthetic aperture radar target recognition.  ...  An Improved exponential decreasing inertia weight-particle swarm optimization algorithm [14] is combined with a radial basis function neural network and is applied to perform the air quality index prediction  ...  In this paper, the penalty parameter C and kernel function parameter γ in radial basis function (RBF) are two parameters of SVM that need to be optimized.  ... 
doi:10.1109/access.2020.2985596 fatcat:arih4dvnz5etrmat4vvcffslru

Page 2342 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
(English summary) 2004j:68156 Schmitt, Michael Radial basis function neural networks have superlinear VC dimension.  ...  (English summary) (see 2004j:68005) — RBF neural networks and Descartes’ rule of signs.  ... 

The first Dagstuhl Seminar on Neural Computing had been organized by

Wolfgang Maass
unpublished
Tutorials were given by Christoph von der Malsburg ("The binding problem of neural networks"), Wulfram Gerstner ("Models of spiking neurons"), Angus Mac-intyre ("The VC-dimension of neural networks"),  ...  computing and learning on biological and artificial neural networks.  ...  For supervised learning the described incremental models can be coupled with the radial basis function (RBF) approach. This leads to incremental RBF networks.  ... 
fatcat:hw6zmihh3jestkyhrjgswc7igu

Spatial networks

Marc Barthélemy
2011 Physics reports  
Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, neural networks, are all examples where space is relevant and where topology alone does  ...  An important consequence of space on networks is that there is a cost associated to the length of edges which in turn has dramatic effects on the topological structure of these networks.  ...  connections exist between regions with no direct structural connections, demonstrating that the structural and functional properties of neural networks are entangled in a complex way and that future studies  ... 
doi:10.1016/j.physrep.2010.11.002 fatcat:mp77spbw2jewvijlttu7y3bktq

Page 2222 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
(Bastien Fernandez) 2004m:37154 37L60 (37A25, 37C30) Schmitt, Michael Radial basis function neural networks have superlinear VC dimension.  ...  (see 2004j:68005) 68T05 (68Q32) — RBF neural networks and Descartes’ rule of signs. (English summary) Algorithmic learning theory, 321-335, Lecture Notes in Comput.  ... 

Neural network modeling of a dolphin's sonar discrimination capabilities

Lars N. Andersen, A. René Rasmussen, Whitlow W. L. Au, Paul E. Nachtigall, Herbert Roitblat
1994 Journal of the Acoustical Society of America  
Processing of continuous speech by a hierarchical neural network.  ...  The speech vectors are then quantized into a determined number of categories using a self-organizing neural network.  ...  This is the basis of the IPA problem.  ... 
doi:10.1121/1.410770 fatcat:ioiiov6bmjdi7kiflait5dhdfe

Neural network modeling of a dolphin's sonar discrimination capabilities

Whitlow W. L. Au, Lars N. Andersen, A. René Rasmussen, Herbert L. Roitblat, Paul E. Nachtigall
1995 Journal of the Acoustical Society of America  
Processing of continuous speech by a hierarchical neural network.  ...  The speech vectors are then quantized into a determined number of categories using a self-organizing neural network.  ...  This is the basis of the IPA problem.  ... 
doi:10.1121/1.413700 pmid:7608403 fatcat:m3nunzs4wfflhfl27n4shdn2n4

Influence of statistical surface models on dynamic scattering of high‐frequency signals from the ocean surface

Christian Bjerrum‐Niese, Leif Bjo/rno/
1994 Journal of the Acoustical Society of America  
Processing of continuous speech by a hierarchical neural network.  ...  The speech vectors are then quantized into a determined number of categories using a self-organizing neural network.  ...  This is the basis of the IPA problem.  ... 
doi:10.1121/1.411137 fatcat:ajwj7bozxzg6fd27v4xe57drgm

Radiology diagnostics at the stages of extracorporal resection of a single kidney in the treatment of renal cell cancer

Yulia Stepanova, Vlada Raguzina, Tatiana Baitman, Aleksandr Gritskevich
2021 Book of Abstracts   unpublished
Acknowledgments Having used equation of mass transfer equation and numerical methods, we improved this technique and determined distribution coefficients, heights of theoretical plates and influence of  ...  The intensity of the lower-energy VIS emission shows the superlinear dependence on the Bi 3+ content.  ...  Good properties which both of those two materials have in common are strain in compression, tensile strength, good accuracy and precision, very solid dimensional stability, fine elastic recovery and minimal  ... 
doi:10.21175/rad.abstr.book.2021.17.7 fatcat:ltnqghblr5e6blnq6zimmsdyxu