A linear relation between input and first layer in neural networks

Artificial neural networks grow on the number of applications and complexity, which require a minimization on the number of units for some practical implementations. A particular problem is the minimum number of units that a feed forward neural network needs on its first layer. In order to study thi...

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Bibliographic Details
Published in:Annals of mathematics and artificial intelligence 2019-12, Vol.87 (4), p.361-372
Main Author: Grillo, Sebastián A.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Artificial Intelligence
Artificial neural networks
Classification
Complex Systems
Computer Science
Hypotheses
Machine learning
Mathematics
Neural networks
Optimization
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Summary:Artificial neural networks grow on the number of applications and complexity, which require a minimization on the number of units for some practical implementations. A particular problem is the minimum number of units that a feed forward neural network needs on its first layer. In order to study this problem, it is defined a family of classification problems following a continuity hypothesis, where inputs that are close to some set of points may share the same category. Given a set S of k −dimensional inputs and let N be a feed forward neural network that classifies any input in S within a fixed error, there is proved that N requires Θ k units in the first layer, if N can solve any instance from the given family of classification problems. Furthermore, this asymptotic result is optimal.
ISSN:1012-2443
1573-7470
DOI:10.1007/s10472-019-09657-3