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> Neural networks are universal function approximators, Do we have tight error bounds proofs for neural networks as approximators ?

• ska 5y ago
  https://en.wikipedia.org/wiki/Universal_approximation_theorem https://en.wikipedia.org/wiki/Universal_approximation_theore...
  • volta83 5y ago
    That just says that it is possible to approximate functions well with neural networks of "sufficient depth" and "suitable weights". It doesn't tell you whether for a particular function f: - a particular network structure is suitable, - a trained network with particular weight value is suitable, and it obviously doesn't answer the most useful question: - given this network with this weights, what's the largest approximation error for this function f? There are many approximation methods in approximation theory that can answer this last question. Do we have these answers for neural networks?
    • ska 5y ago
      > Do we have these answers for neural networks? Not in general that I'm aware of. I agree the result is not practical, but you asked what is known. There have been some refinements (the citations on that page give a reasonable flavor, fwiw).