Answers.Body: <p>The claim that Neural Network with a single hidden layer can model any functions is proven in Cybenko's Approximation by superpositions of a sigmoidal function.</p>
  <p><a href="https://link.springer.com/article/10.1007/BF02551274" rel="nofollow noreferrer">https://link.springer.com/article/10.1007/BF02551274</a>
  check also: <a href="https://en.wikipedia.org/wiki/Universal_approximation_theorem" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Universal_approximation_theorem</a></p>
  <p>The thing is that the neural network using sigmoidal functions, which are non-linear functions can.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-11-17T12:55:04.903Z
Answers.LastActivityDate: 2020-11-17T12:55:04.903Z
Answers.UserDisplayName: Jim Kim
Body: <p>I'm currently a student learning about AI Networks. I've came across a statement in one of my Professor's books that a FFBP (Feed-Forward Back-Propagation) Neural Network with a single hidden layer  can model any mathematic function with accuracy dependant on number of hidden layer neurons. Try as I might I cannot find any explanation as to why that occurs - could someone maybe explain the question why that is?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-09-07T13:17:49.357Z
Comments.Text: Possible duplicate of [Where can I find the proof of the universal approximation theorem?](https://ai.stackexchange.com/questions/13317/where-can-i-find-the-proof-of-the-universal-approximation-theorem) You're asking two distinct questions: 1) how does the number of neurons in a hidden layer affect the accuracy of the model and 2) why an NN, with a single hidden layer with an arbitrary number of neurons, can approximate any function. Please, ask just one question per post. The answer to your 2nd question is already implicitly given in the linked post, so I suggest you ask the first question.
Comments.UserDisplayName: nbro
Tags: <neural-networks><backpropagation><hidden-layers><feedforward-neural-networks>
Title: How does a single neuron in hidden layer affect training accuracy
UserDisplayName: Konrad Ł
ThreadText: # How does a single neuron in hidden layer affect training accuracy
  
  (Asked by: username_0 on 2019-09-07)
  
  I'm currently a student learning about AI Networks. I've came across a statement in one of my Professor's books that a FFBP (Feed-Forward Back-Propagation) Neural Network with a single hidden layer can model any mathematic function with accuracy dependant on number of hidden layer neurons. Try as I might I cannot find any explanation as to why that occurs - could someone maybe explain the question why that is?
  
  **Tags:** neural-networks, backpropagation, hidden-layers, feedforward-neural-networks
  
  > **Comments:**
  > **username_1**: Possible duplicate of [Where can I find the proof of the universal approximation theorem?](https://ai.stackexchange.com/questions/13317/where-can-i-find-the-proof-of-the-universal-approximation-theorem) You're asking two distinct questions: 1) how does the number of neurons in a hidden layer affect the accuracy of the model and 2) why an NN, with a single hidden layer with an arbitrary number of neurons, can approximate any function. Please, ask just one question per post. The answer to your 2nd question is already implicitly given in the linked post, so I suggest you ask the first question.  
  
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  ## 1 answers
  
  ### Answer by username_2 on 2020-11-17. Score: 0
  
  The claim that Neural Network with a single hidden layer can model any functions is proven in Cybenko's Approximation by superpositions of a sigmoidal function.
  
  <https://link.springer.com/article/10.1007/BF02551274>
  check also: <https://en.wikipedia.org/wiki/Universal_approximation_theorem>
  
  The thing is that the neural network using sigmoidal functions, which are non-linear functions can.
  
  
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