Body: <p>Are there a finite set of computable functions constructing deep neural network which can form or implement any c.e. function or computable function? </p>
  
  <p>Or does there exist a finite set of computable function by which every c.e. function can be implemented by combination and connection(like connection in DNN)?</p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-01-23T00:43:24.113Z
Comments.Text: @DuttaA you know the connection and the combination of neurons of DNN, for example, like ReLu or some other finite set of neurons, I ask whether there is a finite set of neurons which can implement such a DNN that given a c.e. function or Turing Machine ,we can simulate the c.e. function or Turing Machine by the DNN?
Comments.UserDisplayName: XL _At_Here_There
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-01-23T01:55:46.313Z
Comments.Text: https://web.archive.org/web/20130502094857/http://www.math.rutgers.edu/~sontag/FTP_DIR/aml-turing.pdf
Comments.UserDisplayName: XL _At_Here_There
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-01-23T02:03:21.447Z
Comments.Text: http://people.cs.georgetown.edu/~cnewport/teaching/cosc844-spring17/pubs/nn-tm.pdf
Comments.UserDisplayName: XL _At_Here_There
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-01-23T02:05:37.413Z
Comments.Text: https://www.cs.montana.edu/~elser/turing%20papers/Schoolboy%20Ideas.pdf
Comments.UserDisplayName: XL _At_Here_There
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-01-23T02:44:17.000Z
Comments.Text: https://www.dartmouth.edu/~gvc/Cybenko_MCSS.pdf
Comments.UserDisplayName: XL _At_Here_There
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-01-23T02:44:39.377Z
Comments.Text: It seems that the question has been settled by the works above, but I have not read them through
Comments.UserDisplayName: XL _At_Here_There
Tags: <deep-neural-networks><reference-request>
Title: Are there a finite set of computable functions constructing deep neural network which can form or implement any c.e. function or computable function?
UserDisplayName: XL _At_Here_There
ThreadText: # Are there a finite set of computable functions constructing deep neural network which can form or implement any c.e. function or computable function?
  
  (Asked by: username_0 on 2018-01-21)
  
  Are there a finite set of computable functions constructing deep neural network which can form or implement any c.e. function or computable function?
  
  Or does there exist a finite set of computable function by which every c.e. function can be implemented by combination and connection(like connection in DNN)?
  
  **Tags:** deep-neural-networks, reference-request
  > **Comments:**
  > **username_0**: @DuttaA you know the connection and the combination of neurons of DNN, for example, like ReLu or some other finite set of neurons, I ask whether there is a finite set of neurons which can implement such a DNN that given a c.e. function or Turing Machine ,we can simulate the c.e. function or Turing Machine by the DNN?  
  > **username_0**: https://web.archive.org/web/20130502094857/http://www.math.rutgers.edu/~sontag/FTP_DIR/aml-turing.pdf  
  > **username_0**: http://people.cs.georgetown.edu/~cnewport/teaching/cosc844-spring17/pubs/nn-tm.pdf  
  > **username_0**: https://www.cs.montana.edu/~elser/turing%20papers/Schoolboy%20Ideas.pdf  
  > **username_0**: https://www.dartmouth.edu/~gvc/Cybenko_MCSS.pdf  
  > **username_0**: It seems that the question has been settled by the works above, but I have not read them through  
  
  ---
  
  ## 0 answers
  
  