51–60 of 138 posts
Can neural networks solve the halting problem?
No. Neural networks are still computed on Turing machines, which are mathematically proven to not be able to solve the halting problem.
Approximate, not compute. The function also must be continuous. NNs are good for approximation / interpolation / extrapolation, which makes them quite useful for certain domains of problems. But of course, it does not make them a kind of universal computing machine (in the computability sense, like universal Turing machines).
> NNs are good for approximation / interpolation / extrapolation Extrapolation? I was under the impression that generalizability of NNs beyond the training data was one of the major problems faced by NNs.
Approximate, not compute. The function also must be continuous. NNs are good for approximation / interpolation / extrapolation, which makes them quite useful for certain domains of problems. But of course, it does not make them a kind of universal computing machine (in the computability sense, like universal Turing machines).
Wait a minute, isn't it also the case that according to the Weierstrass approximation theorem any continuous function on a closed interval can be approximated by a polynomial function? And isn't that kind of pointless for practical applications because we also need to avoid overfitting? To clarify, I'm not trying to make a snippy remark, I just happened to have used polynomial curve fitting before and looked up the W…
- [1] http://mathworld.wolfram.com/WeierstrassApproximationTheorem...
- [2] http://mathworld.wolfram.com/Stone-WeierstrassTheorem.html
Neural Networks use a different "basis" (sigmoid, ReLU, etc.), but the underlying idea shares the same spirit.
Skimming through the article, I understand that the author... A) was focusing on functions that take a certain amount of input variables and B) that the function (that s/he mirrored using the neural net) computes out of it directly one or more of result(s). C) To do that s/he used a backpropagation network (which is the only model I know very well). Right or wrong? EDIT: when I say "directly" I mean that the function…
Approximate, not compute. The function also must be continuous. NNs are good for approximation / interpolation / extrapolation, which makes them quite useful for certain domains of problems. But of course, it does not make them a kind of universal computing machine (in the computability sense, like universal Turing machines).
Wait a minute, isn't it also the case that according to the Weierstrass approximation theorem any continuous function on a closed interval can be approximated by a polynomial function? And isn't that kind of pointless for practical applications because we also need to avoid overfitting? To clarify, I'm not trying to make a snippy remark, I just happened to have used polynomial curve fitting before and looked up the W…
Any deeplearning expert here. Why Neural network can't compute a linear function Celsius to Fahrenheit 100% accurately. Is it data or is it something can be optimised. ``` celsius_q = np.array([-40, -10, 0, 8, 15, 22, 38], dtype=float) fahrenheit_a = np.array([-40, 14, 32, 46, 59, 72, 100], dtype=float) for i,c in enumerate(celsius_q): print("{} degrees Celsius = {} degrees Fahrenheit".format(c, fahrenheit_a[i])) l0…
*any continuous function