  Continuous attractor neural networks (CANN) form an appealing conceptual
model for the storage of information in the brain. However a drawback of CANN
is that they require finely tuned interactions. We here study the effect of
quenched noise in the interactions on the coding of positional information
within CANN. Using the replica method we compute the Fisher information for a
network with position-dependent input and recurrent connections composed of a
short-range (in space) and a disordered component. We find that the loss in
positional information is small for not too large disorder strength, indicating
that CANN have a regime in which the advantageous effects of local connectivity
on information storage outweigh the detrimental ones. Furthermore, a
substantial part of this information can be extracted with a simple linear
readout.
