I would like to build a function approaching a ramp function with some parameters defining:

  • the activation threshold
  • the linear slope
  • the 'distance' to the discontinuity, i.e how close we are from the ramp function.

I have started to work on this by combining rational and exponential functions, but I have trouble having isolating the very parameters that control all of this...

  • $\begingroup$ i get linear slope and distance, but what is activation threshold? is it the minimum value? $\endgroup$ – Saketh Malyala Jan 24 at 18:50
  • $\begingroup$ It is the value for which the the function starts to increase. But it just results in translating the function along x, so there was no point to bring this out. $\endgroup$ – Liris Jan 25 at 19:57


As explained in this related post one of the simplest approximations to the ramp function (which is the integral of the Heaviside step) is the following $$ R(x) = {x \over 2}\left( {1 + {x \over {\sqrt {x^{\,2} + \varepsilon ^{\,2} } }}} \right)\quad \left| {\;\varepsilon < < 1} \right. $$

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