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Hard sigmoid
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<h2 id="examples">Examples</h2> <p>The most extreme examples are the <a href="/facts/Sign_function/VADy9zQq">sign function</a> or <a href="/facts/Heaviside_step_function/bgsUtxgP">Heaviside step function</a>, which go from −1 to 1 or 0 to 1 (which to use depends on normalization) at 0.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a> </p><p>Other examples include the <a href="/facts/Theano_(software)/Ydap6eEv">Theano</a> library, which provides two approximations: ultra_fast_sigmoid, which is a multi-part piecewise approximation and hard_sigmoid, which is a 3-part piecewise linear approximation (output 0, line with slope 0.2, output 1).<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a><a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> </p> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Curves and Surfaces in Computer Vision and Graphics, Volume 1610, SPIE, 1992, p. 301 <a href="https://books.google.com/books?id=9fpRAQAAIAAJ&q=%22hard+sigmoid%22" target="_blank">https://books.google.com/books?id=9fpRAQAAIAAJ&q=%22hard+sigmoid%22</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>"nnet – Ops for neural networks". Archived from the original on 2018-08-14. Retrieved 2018-09-03. <a href="https://web.archive.org/web/20180814165920/http://deeplearning.net/software/theano/library/tensor/nnet/nnet.html" target="_blank">https://web.archive.org/web/20180814165920/http://deeplearning.net/software/theano/library/tensor/nnet/nnet.html</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Theano/sigm.py at 38a6331ae23250338290e886a72daadb33441bc4 · Theano/Theano · GitHub <a href="https://github.com/Theano/Theano/blob/38a6331ae23250338290e886a72daadb33441bc4/theano/tensor/nnet/sigm.py#L279" target="_blank">https://github.com/Theano/Theano/blob/38a6331ae23250338290e886a72daadb33441bc4/theano/tensor/nnet/sigm.py#L279</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> </ol>