▁well ▁as ▁accuracy , ▁must ▁be ▁optimized . ▁In ▁that ▁case ▁it ▁is ▁useful ▁to ▁optimize ▁a ▁regular ized ▁objective ▁function ▁such ▁as ▁ ▁where ▁ ▁and ▁ ▁where ▁optimization ▁of ▁S ▁maxim izes ▁smooth ness ▁and ▁ ▁is ▁known ▁as ▁a ▁regular ization ▁parameter . ▁ ▁A ▁third ▁optional ▁back prop ag ation ▁step ▁can ▁be ▁performed ▁to ▁fine - t une ▁all ▁of ▁the ▁R BF ▁net ' s ▁parameters . ▁ ▁Inter pol ation ▁ ▁R BF ▁networks ▁can ▁be ▁used ▁to ▁interpol ate ▁a ▁function ▁ ▁when ▁the ▁values ▁of ▁that ▁function ▁are ▁known ▁on ▁finite ▁number ▁of ▁points : ▁. ▁T aking ▁the ▁known ▁points ▁ ▁to ▁be ▁the ▁cent ers ▁of ▁the ▁radial ▁basis ▁functions ▁and ▁evalu ating ▁the ▁values ▁of ▁the ▁basis ▁functions ▁at ▁the ▁same ▁points ▁ ▁the ▁weights ▁can ▁be ▁solved ▁from ▁the ▁equation ▁ ▁It ▁can ▁be ▁shown ▁that ▁the ▁interpolation ▁matrix ▁in ▁the ▁above ▁equation ▁is ▁non - sing ular , ▁if ▁the ▁points ▁ ▁are ▁distinct , ▁and ▁thus ▁the ▁weights ▁ ▁can ▁be ▁solved ▁by ▁simple ▁linear ▁algebra : ▁ ▁where ▁. ▁ ▁Function ▁approximation ▁ ▁If ▁the ▁purpose ▁is ▁not ▁to ▁perform ▁strict ▁interpolation ▁but ▁instead ▁more ▁general ▁function ▁approximation ▁or ▁classification ▁the ▁optimization ▁is ▁somewhat ▁more ▁complex ▁because ▁there ▁is ▁no ▁obvious ▁choice ▁for ▁the ▁cent ers . ▁ ▁The ▁training ▁is ▁typically ▁done ▁in ▁two ▁phases ▁first ▁fixing ▁the ▁width ▁and ▁cent ers ▁and ▁then ▁the ▁weights . ▁This ▁can ▁be ▁just ified ▁by ▁considering ▁the ▁different