The Variational Principles of Action

This chapter provides a theoretical perspective on action and the control of movement from the point of view of the free-energy principle. This variational principle offers an explanation for neuronal activity and ensuing behavior that is formulated in terms of dynamical systems and attracting sets. We will see that the free-energy principle emerges when considering the ensemble dynamics of biological systems like ourselves. When we look closely what this principle implies for the behavior of systems like the brain, one finds a fairly straightforward explanation for many aspects of action and perception; in particular, their (approximately Bayesian) optimality. Within the Bayesian brain framework, the ensuing dynamics can be separated into those serving perceptual inference, learning and behavior. Variational principles play a key role in what follows; both in understanding the nature of self-organizing systems but also in explaining the adaptive nature of neuronal dynamics and plasticity in terms of optimization—and the process theories that mediate optimal inference and motor control. A special focus of this chapter is the pre-eminent role of heteroclinic cycles in providing deep and dynamic (generative) models of the sensorium; particularly the sensations that we generate ourselves through action. In what follows, we will briefly rehearse the basic theory and illustrate its implications using simulations of action (handwriting)—and its observation.