Friston's FEP — variational inference and prediction error minimization
The Free Energy Principle (Friston 2006) proposes that all self-organizing biological systems minimize variational free energy F = −⟨log p(o,s)⟩_q + ⟨log q(s)⟩_q = KL[q(s) ‖ p(s|o)] − log p(o), which upper-bounds surprise (negative log-evidence). The brain maintains an internal model q(s) — a recognition density — and minimizes F by updating beliefs to reduce prediction error (perception) or by acting to sample predicted sensory data (action). Here: the world (blue) follows a slow random walk; the agent's belief (orange) tracks it by gradient descent on F, weighted by sensory and prior precision.