▁three ▁layers : ▁an ▁input ▁layer , ▁a ▁hidden ▁layer ▁with ▁a ▁non - linear ▁R BF ▁activation ▁function ▁and ▁a ▁linear ▁output ▁layer . ▁The ▁input ▁can ▁be ▁mode led ▁as ▁a ▁vector ▁of ▁real ▁numbers ▁. ▁The ▁output ▁of ▁the ▁network ▁is ▁then ▁a ▁scalar ▁function ▁of ▁the ▁input ▁vector , ▁, ▁and ▁is ▁given ▁by ▁ ▁where ▁ ▁is ▁the ▁number ▁of ▁neur ons ▁in ▁the ▁hidden ▁layer , ▁ ▁is ▁the ▁center ▁vector ▁for ▁neur on ▁, ▁and ▁ ▁is ▁the ▁weight ▁of ▁neur on ▁ ▁in ▁the ▁linear ▁output ▁neur on . ▁Function s ▁that ▁depend ▁only ▁on ▁the ▁distance ▁from ▁a ▁center ▁vector ▁are ▁radial ly ▁symmetric ▁about ▁that ▁vector , ▁hence ▁the ▁name ▁radial ▁basis ▁function . ▁In ▁the ▁basic ▁form ▁all ▁inputs ▁are ▁connected ▁to ▁each ▁hidden ▁neur on . ▁The ▁norm ▁is ▁typically ▁taken ▁to ▁be ▁the ▁E uclidean ▁distance ▁( although ▁the ▁Mah al an ob is ▁distance ▁appears ▁to ▁perform ▁better ▁in ▁general ) ▁and ▁the ▁radial ▁basis ▁function ▁is ▁commonly ▁taken ▁to ▁be ▁Gaussian ▁ ▁. ▁ ▁The ▁Gaussian ▁basis ▁functions ▁are ▁local ▁to ▁the ▁center ▁vector ▁in ▁the ▁sense ▁that ▁ ▁i . e . ▁changing ▁parameters ▁of ▁one ▁neur on ▁has ▁only ▁a ▁small ▁effect ▁for ▁input ▁values ▁that ▁are ▁far ▁away ▁from ▁the ▁center ▁of ▁that ▁neur on . ▁ ▁Given ▁certain ▁m ild ▁conditions ▁on ▁the ▁shape ▁of ▁the ▁activation ▁function , ▁R BF ▁networks ▁are ▁universal ▁approxim ators ▁on ▁a ▁compact ▁subset ▁of ▁. ▁This ▁means