Maximum Caliber can describe neural dynamics and perception

Sensory perception changes spontaneously and repeatedly while sensory scenes remain stable. A recent model (called Clickety Clack) captures this by idealizing cortical columns as bistable on-off units and coupling two-level cortical hierarchy, one receiving input and the other making decision. This model reproduces several qualitative and quantitative features of perception and at the same time makes prediction of microscopic neuronal dynamics. We use this model to understand the details of microscopic neural dynamics. We show the dynamics is out of equilibrium and can be described by a minimal Hamiltonian using the principle of Maximum Caliber (MaxCal). MaxCal is a variational principle in statistical physics that maximizes path entropy — similar to MaxEnt that maximizes state entropy — subject to dynamical constraints and is applicable to thermal and non-thermal complex systems. Application of MaxCal suggests neural dynamics can be described by a variational principle with minimal constraints: birth death of cortical units and their coupling only to the second order. Furthermore, MaxCal integrated with a Bayesian formalism provides an objective way to determine models given trajectory data of cortical columns, providing a new way of modeling neural dynamics.