On the Structure of Continuous Functions of Several Variables

Sprecher, David A.

doi:10.2307/1994273

Cited by 57 publications

(54 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The proof is similar in spirit to the Kolmogorov superposition existence theorem [34][35][36]. & This conclude that three-layered perceptrons, including n(2n+1) of neurons, can compute any continuous function of n variables, exactly using nonlinear continuous and strictly increasing activation functions [37].…”

Section: Feed Forward Artificial Neural Networkmentioning

confidence: 52%

Solving initial-boundary value problems for systems of partial differential equations using neural networks and optimization techniques

Beidokhti

Malek

2009

Journal of the Franklin Institute

View full text Add to dashboard Cite

Section: Feed Forward Artificial Neural Networkmentioning

confidence: 52%

Solving initial-boundary value problems for systems of partial differential equations using neural networks and optimization techniques

Beidokhti

Malek

2009

Journal of the Franklin Institute

View full text Add to dashboard Cite

“…This result was originated by Kolmogorov [5], and was later used by Sprecher [6] in his solution of Hilbert's thirteenth problem (see references [1] and [2] for more details). However, the universality of these networks is based on an "in-principle" result, which contains no hint as to how the representation is to be obtained.…”

Section: Discussionmentioning

confidence: 89%

Non‐linear Processing in Artificial Synapses

Engel

1992

Kybernetes

View full text Add to dashboard Cite

Analyses the possibility of allowing non‐linear synaptic processing in Artificial Neural Networks (ANN) both theoretically and practically. The simple computer simulations described strongly suggest that this is a viable alternative, and preferable to ANN with just linear synapses, because of the savings in hardware (fewer components are needed) and software (reduction in training time) when dealing with similar problems. Derives some considerations regarding a possible relationship between the parallel processor proposed and living nerve cells.

show abstract

“…9) where xl, xi, x: is the ith training example, dt is the corresponding desired output, for i = 1, 2, 3, 4, 5 and w,,, w,,, w,,, w,, are the connected weight values between the input cells and the output cells. Since, if the rank r of the coefficient matrix X is equal to the rank r' of augmented matrix [XI Y], there exists a solution (Hoffman and Kunze 1971, Albert 1972, Lorentz 1976, Sprecher 1965, Werbis 1974, i.e. there is a solution for the connected weight matrix W. We know that expression (3), consisting of five linear equations in four unknown variables, may not be solved.…”

Section: An Improved Methods To Reduce the Number Of Functional-link Cmentioning

confidence: 99%

A neural-based boolean function generator

Chu

1993

International Journal of Electronics

View full text Add to dashboard Cite

A neural technique is used to implement a positive logic boolean function. The neural technique is a modified perceptron learning algorithm by which a boolean function can be generated. The connected weight values in the neural network represents the sum of product terms of a boolean function. The paper is divided into four parts. First, a neural network technique to generate functional-link cells for successful learning is provided. Second, an improved method is described to decrease the required number of functional-link cells for successful learning. Third, the algorithm is described and proved. Finally, a functional hardware diagram is proposed to illustrate the overall structure and an example is taken to validate its effectiveness.

show abstract

On the Structure of Continuous Functions of Several Variables

Cited by 57 publications

References 3 publications

Solving initial-boundary value problems for systems of partial differential equations using neural networks and optimization techniques

Solving initial-boundary value problems for systems of partial differential equations using neural networks and optimization techniques

Non‐linear Processing in Artificial Synapses

A neural-based boolean function generator

Contact Info

Product

Resources

About