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Learning Sub-Patterns in Piecewise Continuous Functions
[article]
2021
arXiv
pre-print
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a degree of continuity which limits the neural network model's uniform approximation capacity to continuous functions. ...
Most stochastic gradient descent algorithms can optimize neural networks that are sub-differentiable in their parameters; however, this implies that the neural network's activation function must exhibit ...
We first identify approximation-theoretic limitations to commonly deployed feedforward neural networks (FFNNs); i.e.: with continuous activation functions, and then fill this gap with a new deep neural ...
arXiv:2010.15571v4
fatcat:lyn4wu3zvrhyjm7dhwp56x645u
A Canonical Transform for Strengthening the Local L^p-Type Universal Approximation Property
[article]
2021
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Note that this fulltext copy is not of the "primary" version of this work. The version it corresponds to is:
2020 pre-print arXiv:2006.14378v2 fatcat:elghcfx76be23bwepzxuufhpziOther Versions
Applications to feedforward networks, convolutional neural networks, and polynomial bases are explored. ...
In the general case, where ℱ may contain non-analytic functions, we provide an abstract form of these results guaranteeing that there always exists some function space in which ℱ-tope is dense but ℱ is ...
The model class modification, was motivated by the structure approximation problem of learning any composite pattern while preserving its composite pattern structure. ...
arXiv:2006.14378v3
fatcat:442jq46ya5gxjajfqvhfei4ieu