A note on computing with Kolmogorov Superpositions without iterations

We extend Kolmogorov’s Superpositions to approximating arbitrary continuous functions with a noniterative approach that can be used by any neural network that uses these superpositions. Our approximation algorithm uses a modified dimension reducing function that allows for an increased number of sum...

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Bibliographic Details
Published in:Neural networks Vol. 144; pp. 438 - 442
Main Authors: Demb, Robert, Sprecher, David
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.12.2021
Subjects:
Approximations
Computational algorithms
Error bound
Function representations
Interpolants
Iterations
Kolmogorov
Köppen’s recursive formula
Parallel computations
Superpositions
Interpolants
Computational algorithms
Parallel computations
Approximations
Kolmogorov
Köppen’s recursive formula
Error bound
Iterations
Superpositions
Function representations
ISSN:0893-6080, 1879-2782, 1879-2782
Online Access:Get full text
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Summary:We extend Kolmogorov’s Superpositions to approximating arbitrary continuous functions with a noniterative approach that can be used by any neural network that uses these superpositions. Our approximation algorithm uses a modified dimension reducing function that allows for an increased number of summands to achieve an error bound commensurate with that of r iterations for any r. This new variant of Kolmogorov’s Superpositions improves upon the original parallelism inherent in them by performing highly distributed parallel computations without synchronization. We note that this approach makes implementation much easier and more efficient on networks of modern parallel hardware, and thus makes it a more practical tool.
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ISSN:0893-6080
1879-2782
1879-2782
DOI:10.1016/j.neunet.2021.07.006