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Abstract: . It is shown that high-order feedforward neural nets of constant depth with piecewisepolynomial activation functions and arbitrary real weights can be simulated for Boolean inputs and outputs by neural nets of a somewhat larger size and depth with Heaviside gates and weights from {-1, 0, 1}. This provides the first known upper bound for the computational power of the former type of neural nets. It is also shown that in the case of first-order nets with piecewise-linear activation functions... (Update)
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.... size, having arbitrary real weights and employing the saturated linear activation function (4) have been shown to belong to the class TC 0 [72]. Finally, the trade o lower bounds concerning the n variable parity function have also been generalized for analog feedforward...
...the vc dimensions of feedforward linear threshold networks. The rst part is due to Baum and Haussler [6] and the second part to Maass [16,17]. Theorem 6.2 There is a constant c 1 0 such that, if N is any feedforward linear threshold network with one output node and whose...
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BibTeX entry: (Update)
W. Maass. Bounds for the computational power and learning complexity of analog neural nets. In Proc. 25th Annu. ACM Sympos. Theory Comput., pages 335--344. ACM Press, New York, NY, 1993. http://citeseer.ist.psu.edu/maass97bounds.html More
@inproceedings{ maass93bounds,
author = "Wolfgang Maass",
title = "Bounds for the computational power and learning complexity of analog neural nets",
pages = "335--344",
year = "1993",
url = "citeseer.ist.psu.edu/maass97bounds.html" }
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550 Parallel Distributed Processing (context) - McClelland, Rumelhart - 1986
537 A theory of the learnable (context) - Valiant - 1984
481 Algorithms in Combinatorial Geometry (context) - Edelsbrunner - 1987
465 Learnability and the Vapnik-Chervonenkis dimension (context) - Blumer, Ehrenfeucht et al. - 1989
422 Networks for approximation and learning (context) - Poggio, Girosi - 1990
398 Fast learning in networks of locally tuned processing units (context) - Moody, Darken - 1989
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268 Decision theoretic generalizations of the PAC model for neur.. (context) - Haussler - 1992
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174 Principles of Neurodynamics (context) - Rosenblatt - 1988
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67 Bounding the Vapnik-Chervonenkis dimension of concept classe.. (context) - Goldberg, Jerrum - 1993
64 Feedforward nets for interpolation and classification (context) - Sontag - 1992
45 Product units: A computationally powerful and biologically p.. (context) - Durbin, Rumelhart - 1989
44 Bounds for the computational power and learning complexity o.. - Maass - 1993
44 Bounds for the computational power and learning complexity o.. - Maass - 1992
37 general weighted threshold gates (context) - Goldmann, astad et al. - 1992
36 the computational power of sigmoid versus boolean threshold .. (context) - Maass, Schnitger et al. - 1991
32 the size of weights for threshold gates - astad - 1994
31 Parallel computation with threshold functions (context) - Parberry, Schnitger - 1986
29 The Vapnik-Chervonenkis dimension: Information versus comple.. (context) - Abu-Mostafa - 1989
26 How fast can a threshold gate learn (context) - Maass, Turan - 1994
25 On Optimal Depth Threshold Circuits for Multiplication and R.. (context) - Siu, Roychowdhury - 1992
23 Neural nets with superlinear VC-dimension - Maass - 1994
23 The power of approximating: A comparison of activation funct.. - DasGupta, Schnitger - 1993
20 Agnostic PAC-learning of functions on analog neural nets - Maass - 1995
13 A weak version of the Blum (context) - Koiran - 1993
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