Are there neural networks with very few nodes that decently solve non-trivial problems?How can neural...
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Are there neural networks with very few nodes that decently solve non-trivial problems?
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$begingroup$
I'm interested in knowing whether there exist any neural network, that solves (with >=80% accuracy) any nontrivial problem, that uses very few nodes (where 20 nodes is not a hard limit). I want to develop an intuition on sizes of neural networks.
neural-networks
edited 1 hour ago
nbro
1,418621
asked 3 hours ago
Guillermo MosseGuillermo Mosse
1163
New contributor
Guillermo Mosse is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I'm interested in knowing whether there exist any neural network, that solves (with >=80% accuracy) any nontrivial problem, that uses very few nodes (where 20 nodes is not a hard limit). I want to develop an intuition on sizes of neural networks.
neural-networks
edited 1 hour ago
nbro
1,418621
asked 3 hours ago
Guillermo MosseGuillermo Mosse
1163
New contributor
Guillermo Mosse is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
Universal approximation theorem: a neural network with one hidden layer can approximate any "reasonable" function given a sufficient number of nodes in the hidden layer.
$endgroup$
– nbro
2 hours ago
1
$begingroup$
I think it will not be easy to answer your question. What do you mean by "non-trivial problem"?
$endgroup$
– nbro
2 hours ago
add a comment |
$begingroup$
I'm interested in knowing whether there exist any neural network, that solves (with >=80% accuracy) any nontrivial problem, that uses very few nodes (where 20 nodes is not a hard limit). I want to develop an intuition on sizes of neural networks.
neural-networks
edited 1 hour ago
nbro
1,418621
asked 3 hours ago
Guillermo MosseGuillermo Mosse
1163
New contributor
Guillermo Mosse is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I'm interested in knowing whether there exist any neural network, that solves (with >=80% accuracy) any nontrivial problem, that uses very few nodes (where 20 nodes is not a hard limit). I want to develop an intuition on sizes of neural networks.
neural-networks
neural-networks
edited 1 hour ago
nbro
1,418621
asked 3 hours ago
Guillermo MosseGuillermo Mosse
1163
New contributor
Guillermo Mosse is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 1 hour ago
nbro
1,418621
asked 3 hours ago
Guillermo MosseGuillermo Mosse
1163
New contributor
Guillermo Mosse is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 1 hour ago
nbro
1,418621
edited 1 hour ago
nbro
1,418621
edited 1 hour ago
nbro
1,418621
1,418621
asked 3 hours ago
Guillermo MosseGuillermo Mosse
1163
New contributor
Guillermo Mosse is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 3 hours ago
Guillermo MosseGuillermo Mosse
1163
asked 3 hours ago
Guillermo MosseGuillermo Mosse
1163
1163
New contributor
Guillermo Mosse is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Guillermo Mosse is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Guillermo Mosse is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
Universal approximation theorem: a neural network with one hidden layer can approximate any "reasonable" function given a sufficient number of nodes in the hidden layer.
$endgroup$
– nbro
2 hours ago
1
$begingroup$
I think it will not be easy to answer your question. What do you mean by "non-trivial problem"?
$endgroup$
– nbro
2 hours ago
add a comment |
$begingroup$
Universal approximation theorem: a neural network with one hidden layer can approximate any "reasonable" function given a sufficient number of nodes in the hidden layer.
$endgroup$
– nbro
2 hours ago
1
$begingroup$
I think it will not be easy to answer your question. What do you mean by "non-trivial problem"?
$endgroup$
– nbro
2 hours ago
$begingroup$
Universal approximation theorem: a neural network with one hidden layer can approximate any "reasonable" function given a sufficient number of nodes in the hidden layer.
$endgroup$
– nbro
2 hours ago
$begingroup$
Universal approximation theorem: a neural network with one hidden layer can approximate any "reasonable" function given a sufficient number of nodes in the hidden layer.
$endgroup$
– nbro
2 hours ago
1
1
$begingroup$
I think it will not be easy to answer your question. What do you mean by "non-trivial problem"?
$endgroup$
– nbro
2 hours ago
$begingroup$
I think it will not be easy to answer your question. What do you mean by "non-trivial problem"?
$endgroup$
– nbro
2 hours ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Even if it’s impossible to answer this question properly, as non trivial is not well defined (maybe the author will edit this questions later, to specify it better), I take the opportunity to point this paper which looks interesting to me
Smallest Neural Network to Learn the Ising Criticality
Assuming you have a general idea of the Ising Model I think the problem of identifying the critical temperature from a data driver perspective can be considered as non trivial and the paper shows how the authors have improved the performance related to solve this task with NN passing from 100 Hidden Neurons, as performed in this paper Machine learning phases of matter from 2017, to only 2 Hidden Neurons
Just my cents:
- reducing the neurons, while keeping good performance, should help in terms of neural processing interpretability which is notoriously obscure and its complexity grows (exponentially) with the number of neurons
answered 1 hour ago
Nicola BerniniNicola Bernini
511
$endgroup$
add a comment |
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1 Answer
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$begingroup$
Even if it’s impossible to answer this question properly, as non trivial is not well defined (maybe the author will edit this questions later, to specify it better), I take the opportunity to point this paper which looks interesting to me
Smallest Neural Network to Learn the Ising Criticality
Assuming you have a general idea of the Ising Model I think the problem of identifying the critical temperature from a data driver perspective can be considered as non trivial and the paper shows how the authors have improved the performance related to solve this task with NN passing from 100 Hidden Neurons, as performed in this paper Machine learning phases of matter from 2017, to only 2 Hidden Neurons
Just my cents:
- reducing the neurons, while keeping good performance, should help in terms of neural processing interpretability which is notoriously obscure and its complexity grows (exponentially) with the number of neurons
answered 1 hour ago
Nicola BerniniNicola Bernini
511
$endgroup$
add a comment |
$begingroup$
Even if it’s impossible to answer this question properly, as non trivial is not well defined (maybe the author will edit this questions later, to specify it better), I take the opportunity to point this paper which looks interesting to me
Smallest Neural Network to Learn the Ising Criticality
Assuming you have a general idea of the Ising Model I think the problem of identifying the critical temperature from a data driver perspective can be considered as non trivial and the paper shows how the authors have improved the performance related to solve this task with NN passing from 100 Hidden Neurons, as performed in this paper Machine learning phases of matter from 2017, to only 2 Hidden Neurons
Just my cents:
- reducing the neurons, while keeping good performance, should help in terms of neural processing interpretability which is notoriously obscure and its complexity grows (exponentially) with the number of neurons
answered 1 hour ago
Nicola BerniniNicola Bernini
511
$endgroup$
add a comment |
$begingroup$
Even if it’s impossible to answer this question properly, as non trivial is not well defined (maybe the author will edit this questions later, to specify it better), I take the opportunity to point this paper which looks interesting to me
Smallest Neural Network to Learn the Ising Criticality
Assuming you have a general idea of the Ising Model I think the problem of identifying the critical temperature from a data driver perspective can be considered as non trivial and the paper shows how the authors have improved the performance related to solve this task with NN passing from 100 Hidden Neurons, as performed in this paper Machine learning phases of matter from 2017, to only 2 Hidden Neurons
Just my cents:
- reducing the neurons, while keeping good performance, should help in terms of neural processing interpretability which is notoriously obscure and its complexity grows (exponentially) with the number of neurons
answered 1 hour ago
Nicola BerniniNicola Bernini
511
$endgroup$
Even if it’s impossible to answer this question properly, as non trivial is not well defined (maybe the author will edit this questions later, to specify it better), I take the opportunity to point this paper which looks interesting to me
Smallest Neural Network to Learn the Ising Criticality
Assuming you have a general idea of the Ising Model I think the problem of identifying the critical temperature from a data driver perspective can be considered as non trivial and the paper shows how the authors have improved the performance related to solve this task with NN passing from 100 Hidden Neurons, as performed in this paper Machine learning phases of matter from 2017, to only 2 Hidden Neurons
Just my cents:
- reducing the neurons, while keeping good performance, should help in terms of neural processing interpretability which is notoriously obscure and its complexity grows (exponentially) with the number of neurons
answered 1 hour ago
Nicola BerniniNicola Bernini
511
answered 1 hour ago
Nicola BerniniNicola Bernini
511
answered 1 hour ago
Nicola BerniniNicola Bernini
511
answered 1 hour ago
Nicola BerniniNicola Bernini
511
511
add a comment |
add a comment |
Guillermo Mosse is a new contributor. Be nice, and check out our Code of Conduct.
Guillermo Mosse is a new contributor. Be nice, and check out our Code of Conduct.
Guillermo Mosse is a new contributor. Be nice, and check out our Code of Conduct.
Guillermo Mosse is a new contributor. Be nice, and check out our Code of Conduct.
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$begingroup$
Universal approximation theorem: a neural network with one hidden layer can approximate any "reasonable" function given a sufficient number of nodes in the hidden layer.
$endgroup$
– nbro
2 hours ago
1
$begingroup$
I think it will not be easy to answer your question. What do you mean by "non-trivial problem"?
$endgroup$
– nbro
2 hours ago