Single hidden layer with finite #neurons limitations
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I need to prove that MNN with one hidden layer, and finite number of neurons does not have compact support, i.e. the integral of the normal of f (network function) upon all R^d equal to infinity.
It possible to show that finite taylor series does not have compact support and show that you can represent finite such network with finite taylor series.
The question is if a more simpler proof exist?
approximation-theory neural-networks
asked Nov 18 at 11:35
tnt1674
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up vote
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down vote
favorite
I need to prove that MNN with one hidden layer, and finite number of neurons does not have compact support, i.e. the integral of the normal of f (network function) upon all R^d equal to infinity.
It possible to show that finite taylor series does not have compact support and show that you can represent finite such network with finite taylor series.
The question is if a more simpler proof exist?
approximation-theory neural-networks
asked Nov 18 at 11:35
tnt1674
1
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 18 at 11:36
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I need to prove that MNN with one hidden layer, and finite number of neurons does not have compact support, i.e. the integral of the normal of f (network function) upon all R^d equal to infinity.
It possible to show that finite taylor series does not have compact support and show that you can represent finite such network with finite taylor series.
The question is if a more simpler proof exist?
approximation-theory neural-networks
asked Nov 18 at 11:35
tnt1674
1
I need to prove that MNN with one hidden layer, and finite number of neurons does not have compact support, i.e. the integral of the normal of f (network function) upon all R^d equal to infinity.
It possible to show that finite taylor series does not have compact support and show that you can represent finite such network with finite taylor series.
The question is if a more simpler proof exist?
approximation-theory neural-networks
approximation-theory neural-networks
asked Nov 18 at 11:35
tnt1674
1
asked Nov 18 at 11:35
tnt1674
1
asked Nov 18 at 11:35
tnt1674
1
asked Nov 18 at 11:35
tnt1674
1
asked Nov 18 at 11:35
tnt1674
1
1
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 18 at 11:36
add a comment |
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 18 at 11:36
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 18 at 11:36
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 18 at 11:36
add a comment |
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Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 18 at 11:36