On the Computational Power of Sigmoid versus Boolean Threshold Circuits

We examine the power of constant depth circuits with sigmoid (i.e. smooth) threshold gates for computing boolean functions. It is shown that, for depth 2, constant size circuits of this type are strictly more powerful than constant size boolean threshold circuits (i.e. circuits with boolean threshold gates). On the other hand it turns out that, for any constant depth d , polynomial size sigmoid threshold circuits with polynomially bounded weights compute exactly the same boolean functions as the corresponding circuits with boolean threshold gates.