The Phase Space of Lateral Thought

Abstract

While others prefer to engage in deliberative decision-making, our mind is mostly absorbed in speculative lateral thought. Can it be modeled in a precise mathematical framework? In the attractor network putatively realized in any cortical patch, memory representations are not artificially stored as prescribed binary patterns of activity as in the Hopfield model, but self–organize as continuously graded patterns induced by afferent input. Recordings in macaque indicate that such cortical attractor networks may express retrieval dynamics over cognitively plausible rapid time scales, shorter than those dominated by neuronal fatigue. A cortical network comprised of many local attractor networks, and incorporating a realistic description of adaptation dynamics, may then be captured by a Potts model. This network model has the capacity to engage long-range associations into sustained iterative attractor dynamics at a cortical scale, in what may be regarded as a mathematical model of spontaneous lateral thought. We describe the phase space of the model, which presents a number of phase transitions dependent on a set of critical parameters, which can be related to cortical quantities.