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A relatively small lookup table for the sigmoid function can also work well. Here are the various sigmoid approximations that Theano (a library used for deep learning research among other things) offers: http://deeplearning.net/software/theano/library/tensor/nnet/...

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I usually use an array with a few thousand entries. In C this gives me a 2.5x speedup over the exact function with no important decrease in accuracy.

Very interesting and simple improvement. Definitely will take a look at that.

I wonder though if you might actually do better overall with a smaller lookup table and interpolation (or even just a polynomial approximation, which can be evaluated without branching), since large lookup tables can lead to bad cache behavior.

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