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by dual_basis
2621 days ago
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You're correct, the statement of the theorem refers to continuous functions. In practice, however, the input to neural networks is represented by floating point values, which is a discrete set. So pick whatever arbitrary function you would like, there is some continuous approximation to that function which is actually equal to it on every floating point value, and that function can be approximated arbitrarily closely by a neural network. |
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