Body: <p>Gold showed that a language can be learned only if it contains a finite set of sentences.</p>
  
  <p>We know that deep neural networks can implement any function. Does this contradict the Gold's result? </p>
  
  <p>What is the relation or difference between the definition of learnability of Vapnik and Gold and the definition of learnability of neural networks?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2018-10-07T13:10:34.580Z
Comments.Text: That's a problem about expressivity v.s. learnability.
Comments.UserDisplayName: Kexin Wang
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-01-22T14:41:27.200Z
Comments.Text: This is an old question, but I suggest that you provide references where we can find the definitions that you were talking about.
Comments.UserDisplayName: nbro
Tags: <neural-networks><machine-learning><deep-learning><computational-learning-theory><comparison>
Title: What is the relation between the definition of learnability of Vapnik and Gold and learnability of neural networks?
UserDisplayName: XL _At_Here_There
ThreadText: # What is the relation between the definition of learnability of Vapnik and Gold and learnability of neural networks?
  
  (Asked by: username_0 on 2018-02-01)
  
  Gold showed that a language can be learned only if it contains a finite set of sentences.
  
  We know that deep neural networks can implement any function. Does this contradict the Gold's result?
  
  What is the relation or difference between the definition of learnability of Vapnik and Gold and the definition of learnability of neural networks?
  
  **Tags:** neural-networks, machine-learning, deep-learning, computational-learning-theory, comparison
  > **Comments:**
  > **username_1**: That's a problem about expressivity v.s. learnability.  
  > **username_2**: This is an old question, but I suggest that you provide references where we can find the definitions that you were talking about.  
  
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  ## 0 answers
  
  