A neuronal least-action principle for real-time learning in cortical circuits

One of the most fundamental laws of physics is the principle of least action. Motivated by its predictive power, we introduce a neuronal least-action principle for cortical processing of sensory streams to produce appropriate behavioural outputs in real time. The principle postulates that the voltage dynamics of cortical pyramidal neurons prospectively minimize the local somato-dendritic mismatch error within individual neurons. For motor output neurons, it implies minimizing an instantaneous behavioural error. For deep network neurons, it implies a prospective firing to overcome integration delays and correct for possible output errors right in time. The neuron-specific errors are extracted in the apical dendrites of pyramidal neurons through a cortical microcircuit that tries to explain away the feedback from the periphery, and correct the trajectory on the fly. Any motor output is in a moving equilibrium with the sensory inputs and the motor feedback during the whole sensory-motor trajectory. Ongoing synaptic plasticity reduces the somato-dendritic mismatch error within each cortical neuron and performs gradient descent on the output cost at any moment in time. The neuronal least-action principle offers an axiomatic framework to derive local neuronal and synaptic dynamics for global real-time computation and learning in the brain and in physical substrates in general. ### Competing Interest Statement The authors have declared no competing interest.