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This "proof" is pretty sketchy. I think he means every differentiable function? Because I fail to see how you can make a neural network evaluate the indicator f
by voldacar 5y ago
This "proof" is pretty sketchy. I think he means every differentiable function? Because I fail to see how you can make a neural network evaluate the indicator function of the rationals
- bjourne 5y ago"The second caveat is that the class of functions which can be approximated in the way described are the continuous functions. If a function is discontinuous, i.e., makes sudden, sharp jumps, then it won't in general be possible to approximate using a neural net. This is not surprising, since our neural networks compute continuous functions of their input. However, even if the function we'd really like to compute is discontinuous, it's often the case that a continuous approximation is good enough. If that's so, then we can use a neural network. In practice, this is not usually an important limitation."
- voldacar 5y agoI guess I didn't see that. But he's still using continuous where the correct term would be differentiable
- kevinventullo 5y agoYou can uniformly approximate any continuous function on a compact domain with a differentiable/smooth function.
- bjourne 5y agoContinuous functions aren't necessarily differentiable.
- voldacar 5y agoyes, that's my point