Part of Advances in Neural Information Processing Systems 1 (NIPS 1988)
Jun Zhang, John Miller
Heiligenberg (1987) recently proposed a model to explain how sen(cid:173)
sory maps could enhance resolution through orderly arrangement of
broadly tuned receptors. We have extended this model to the general
case of polynomial weighting schemes and proved that the response
function is also a polynomial of the same order. We further demon(cid:173)
strated that the Hermitian polynomials are eigenfunctions of the sys(cid:173)
tem. Finally we suggested a biologically plausible mechanism for sen(cid:173)
sory representation of external stimuli with resolution far exceeding the
inter-receptor separation.