Why is sine activation function not used frequently since we know from fourier transforms that sine functions can combine to fit any function?

Pretty much the title. I'm no expert but from what I know, if you add up enough sine functions with proper amplitudes and frequencies you can get any function you want as a result. With that knowledge, wouldn't it make sense to have neuron's activation function be a sine function?

• No it wouldn't. There are many considerations, like computational complexity, monotonicity, multivariate nature of data.
– user9947
Sep 25 '20 at 20:42
• There was once a similar question, which I answered by saying that the sine is periodic, and that may not be desirable. Doesn't the Fourier transform assume that you have like complex coefficients or something? I don't recall anymore.
– nbro
Sep 25 '20 at 20:53