The statistical mechanics of hallucinations and the evolution of the visual cortex

In the normal state of vision, neural excitation patterns are driven by external stimuli. However, accepted models of the visual cortex bear formal similarities to statistical mechanical models describing spatially-extended ecosystems with activation and inhibition. As such, they are subject to fluctuation-induced Turing instabilities, which generically give rise to spatial patterns of neural excitation that would be perceived as hallucinations, masking the true external stimuli. Organisms operating under such conditions would not survive --- for example, they would be easy victims of predators. How is this devastating failure mode finessed by the visual cortex? We analyze the phase diagram of the visual cortex model as a function of its long-range connectivity, and show that the neuronal connections in the visual cortex have evolved precisely the global architecture necessary to mitigate the failure mode: sparse long-range inhibition. These results imply that sparse long-range inhibition plays a previously unrecognized role in stabilizing the normal vision state, and in addition, accounts for the observed regularity of geometric visual hallucinations.