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Networks of Spiking Neurons: The Third Generation of Neural Network Models
, 1996
"... The computational power of formal models for networks of spiking neurons is compared with that of other neural network models based on McCulloch Pitts neurons (i.e. threshold gates) respectively sigmoidal gates. In particular it is shown that networks of spiking neurons are computationally more powe ..."
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Cited by 192 (14 self)
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The computational power of formal models for networks of spiking neurons is compared with that of other neural network models based on McCulloch Pitts neurons (i.e. threshold gates) respectively sigmoidal gates. In particular it is shown that networks of spiking neurons are computationally more
On the computational power of sigmoid versus boolean threshold circuits
 In: Proc. of the 32nd Annual IEEE Symposium on Foundations of Computer Science
, 1991
"... We examine the power of constant depth circuits with sigmoid (i.e. smooth) threshold gates for computing boolean functions. It is shown that, for depth 2, constant size circuits of this type are strictly more powerful than constant size boolean threshold circuits (i.e. circuits with boolean thresho ..."
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Cited by 63 (26 self)
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We examine the power of constant depth circuits with sigmoid (i.e. smooth) threshold gates for computing boolean functions. It is shown that, for depth 2, constant size circuits of this type are strictly more powerful than constant size boolean threshold circuits (i.e. circuits with boolean
Deviation Theorems For Pfaffian Sigmoids
 St. Petersburg Math. J
, 1994
"... . By a Pfaffian sigmoid with a depth d we mean a circuit with d layers in which rational operations are admitted at each layer, and to jump to the next layer one solves an ordinary differential equation of the type v 0 = p(v) where p is a polynomial with the coefficients being the functions comput ..."
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Cited by 2 (1 self)
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. By a Pfaffian sigmoid with a depth d we mean a circuit with d layers in which rational operations are admitted at each layer, and to jump to the next layer one solves an ordinary differential equation of the type v 0 = p(v) where p is a polynomial with the coefficients being the functions
Finiteness Results for Sigmoidal "Neural" Networks
 In Proceedings of 25th Annual ACM Symposium on the Theory of Computing
, 1993
"... ) Angus Macintyre Mathematical Inst., University of Oxford Oxford OX1 3LB, England, UK Email: ajm@maths.ox.ac.uk Eduardo D. Sontag 3 Dept. of Mathematics, Rutgers University New Brunswick, NJ 08903 Email: sontag@hilbert.rutgers.edu Abstract Proc. 25th Annual Symp. Theory Computing , San Diego, ..."
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Cited by 47 (12 self)
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a widely believed conjecture in number theory. The results, the first ones that are independent of weight size, apply when the gate function is the "standard sigmoid" commonly used in neural networks research. The proofs rely on very recent developments in the elementary theory of real
On the Computational Power of Sigmoidal Neural Networks
"... Nine months ago, when I first started to work on this project, I kept thinking “Will I be able to do anything good? ” I looked into the future and felt troubled by the possibility of spending months investigating without reaching any significant conclusion. Now, that the work is done, I look back an ..."
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of this work is a fruit of Felix. First of all, the idea to clarify the question of the computational power of sigmoidal networks was his. He taught me almost everything I know about neural networks. During this year, not only he kept providing me with the necessary material (every time I entered his office, I
Unifying sigmoid univariate growth equations [online
 For. Biometry Model. Inf. Sci
"... ABSTRACT. An equation depending on two shape parameters includes many of the sigmoids found in the literature as special cases. The formulation facilitates the analysis and description of model properties, and can be used to enhance the generality of software and statistical procedures. Some of the ..."
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Cited by 7 (0 self)
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ABSTRACT. An equation depending on two shape parameters includes many of the sigmoids found in the literature as special cases. The formulation facilitates the analysis and description of model properties, and can be used to enhance the generality of software and statistical procedures. Some
Training a Single Sigmoidal Neuron Is Hard
"... We first present a brief survey of hardness results for training feedforward neural networks. These results are then completed by the proof that the simplest architecture containing only a single neuron that applies a sigmoidal activation function : < ! [; ], satisfying certain natural axio ..."
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Cited by 4 (0 self)
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We first present a brief survey of hardness results for training feedforward neural networks. These results are then completed by the proof that the simplest architecture containing only a single neuron that applies a sigmoidal activation function : < ! [; ], satisfying certain natural
4 A COMPARISON OF THE COMPUTATIONAL POWER OF SIGMOID AND BOOLEAN THRESHOLD CIRCUITS
"... Research on neural networks has led to the investigation of massively parallel computational models that consist of analog computational elements. Usually these analog computational elements are assumed to be smooth threshold gates, i.e:ygates for some nondecreasing differentiable function " ( ..."
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Research on neural networks has led to the investigation of massively parallel computational models that consist of analog computational elements. Usually these analog computational elements are assumed to be smooth threshold gates, i.e:ygates for some nondecreasing differentiable function "
An Algorithm for Qualitative Simulation of Gene Regulatory Networks with Steep Sigmoidal Response Functions
, 2008
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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Cited by 2 (2 self)
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Results 1  10
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11,115