Use the Arrhenius Equation as the Activation Function
Image Credit: By Photogravure Meisenbach Riffarth & Co. Leipzig. - Zeitschrift fΓΌr Physikalische Chemie, Band 69, 1909., Public Domain, https://commons.wikimedia.org/w/index.php?curid=96273
Use: e^(-|b|/|x|)
No need for the pre-exponential factor. Let b, the analogue of the activation energy, be adjustable. Like in chemistry, b acts as a barrier to output. Consider, for example, image processing. b can adjust to let different neurons handle different pixel values. It's powerful. You're welcome. Godspeed.