Optimal computation with attractor networks.

We investigate the ability of multi-dimensional attractor networks to perform reliable computations with noisy population codes. We show that such networks can perform computations as reliably as possible--meaning they can reach the Cramér-Rao bound--so long as the noise is small enough. "Small enough" depends on the properties of the noise, especially its correlational structure. For many correlational structures, noise in the range of what is observed in the cortex is sufficiently small that biologically plausible networks can compute optimally. We demonstrate that this result applies to computations that involve cues of varying reliability, such as the position of an object on the retina in bright versus dim light.