  We formulate the computational processes of perception in the framework of
the principle of least action by postulating the theoretical action as a time
integral of the free energy in the brain sciences. The free energy principle is
accordingly rephrased as that for autopoietic grounds all viable organisms
attempt to minimize the sensory uncertainty about the unpredictable environment
over a temporal horizon. By varying the informational action, we derive the
brain's recognition dynamics (RD) which conducts Bayesian filtering of the
external causes from noisy sensory inputs. Consequently, we effectively cast
the gradient-descent scheme of minimizing the free energy into Hamiltonian
mechanics by addressing only positions and momenta of the organisms'
representations of the causal environment. To manifest the utility of our
theory, we show how the RD may be implemented in a neuronally based biophysical
model at a single-cell level and subsequently in a coarse-grained, hierarchical
architecture of the brain. We also present formal solutions to the RD for a
model brain in linear regime and analyze the perceptual trajectories around
attractors in neural state space.
