On Bayesian Mechanics: A Physics of and by Beliefs

Abstract

The aim of this paper is to introduce a field of study that has emerged over the last decade, called Bayesian mechanics. Bayesian mechanics is a probabilistic mechanics, comprising tools that enable us to model systems endowed with a particular partition (i.e., into particles), where the internal states (or the trajectories of internal states) of a particular system encode the parameters of beliefs about quantities that characterise the system. These tools allow us to write down mechanical theories for systems that look as if they are estimating posterior probability distributions over the causes of their sensory states, providing a formal language to model the constraints, forces, fields, and potentials that determine how the internal states of such systems move in a space of beliefs (i.e., on a statistical manifold). Here we will review the state of the art in the literature on the free energy principle, distinguishing between three ways in which Bayesian mechanics has been applied to particular systems (i.e., path-tracking, mode-tracking, and mode-matching). We will go on to examine the duality of the free 1

The nature of beliefs and believing

“…Depending on how well their beliefs enable them to predict the world, agents can update their (Bayesian) beliefs about of the world. This can be read as a Bayesian mechanics in which, agents acuminate and assimilate new evidence, and re-calibrate what they believe to be the cause of their sensory experiences (Ramstead et al, 2022). This process is generally read as minimizing surprise (technically, the negative logarithm of model evidence of observations).…”

Resilience and Active Inference

“…This process theory allows us to model and understand the dynamics of adaptive systems at different scales of self-organization, from the cellular to the societal. The FEP provides a first-principles account of adaptive, belief-driven behavior, by providing a general formalism to model the representational capacities of living tissues (and physical systems more generally) [42,43]. One of the central innovations of active inference is the re-conceptualization of living systems generally, such as bodies, brains, and even ecosystems, as machines driven by probabilistic prediction.…”

“…Finally, we have structure learning; namely learning the structure and architecture of generative models per se [42,52]. Figure 1: An example of generative model taken from [49] We use the tools of active inference to formalize the structure of the agentenvironment system as a generative model [43,44], which contain states, directed edges between states, and parameters associated with those edges. The structure of these models is usually described in an easy-to-remember ABC.…”

Regulative development as a model for origin of life and artificial life studies

“…systems that have MBs. Since its introduction as a theory of brain function (Friston, 2005;Friston, Kilner, and Harrison, 2006;Friston, 2010), the FEP has developed into a general theory of living systems (Friston, 2013;Friston et al, 2017;Ramstead, Badcock and Friston, 2018;Ramstead, Constant, Badcock and Friston, 2019;Kuchling, Friston, Georgiev and Levin, 2020), and has more recently been formulated as a general theory of classical (Friston, 2019;Ramstead et al, 2022) and quantum (Fields, Friston, Glazebrook, and Levin, 2022) physical systems. Key to this generality is that the FEP does not specify how a system minimizes its detected VFE, consistent with the general idea that "competence" involves not just an ability to solve problems, but an ability to solve the same problem in different ways or by different means in different contexts.…”