On Bayesian mechanics: a physics of and by beliefs

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 sta...

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Published inInterface focus Vol. 13; no. 3; p. 20220029
Main Authors Ramstead, Maxwell J. D., Sakthivadivel, Dalton A. R., Heins, Conor, Koudahl, Magnus, Millidge, Beren, Da Costa, Lancelot, Klein, Brennan, Friston, Karl J.
Format Journal Article
LanguageEnglish
Published England The Royal Society 14.04.2023
Subjects
gauge theory
maximum entropy
free energy principle
active inference
information geometry
Bayesian mechanics
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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 external states (or their trajectories). 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. This provides a formal language for modelling the constraints, forces, potentials and other quantities determining the dynamics of such systems, especially as they entail dynamics on 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 go on to examine a duality between the free energy principle and the constrained maximum entropy principle, both of which lie at the heart of Bayesian mechanics, and discuss its implications.
AbstractList 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 external states (or their trajectories). 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. This provides a formal language for modelling the constraints, forces, potentials and other quantities determining the dynamics of such systems, especially as they entail dynamics on 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 go on to examine a duality between the free energy principle and the constrained maximum entropy principle, both of which lie at the heart of Bayesian mechanics, and discuss its implications.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 external states (or their trajectories). 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. This provides a formal language for modelling the constraints, forces, potentials and other quantities determining the dynamics of such systems, especially as they entail dynamics on 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 go on to examine a duality between the free energy principle and the constrained maximum entropy principle, both of which lie at the heart of Bayesian mechanics, and discuss its implications.
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 external states (or their trajectories). 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. This provides a formal language for modelling the constraints, forces, potentials and other quantities determining the dynamics of such systems, especially as they entail dynamics on 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 go on to examine a duality between the free energy principle and the constrained maximum entropy principle, both of which lie at the heart of Bayesian mechanics, and discuss its implications.
Author Heins, Conor
Koudahl, Magnus
Ramstead, Maxwell J. D.
Millidge, Beren
Da Costa, Lancelot
Klein, Brennan
Sakthivadivel, Dalton A. R.
Friston, Karl J.
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  organization: VERSES Research Lab, Los Angeles, CA 90016, USA, Department of Mathematics, Stony Brook University, Stony Brook, NY, USA, Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY, USA, Department of Biomedical Engineering, Stony Brook University, Stony Brook, NY, USA
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  givenname: Conor
  surname: Heins
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  organization: VERSES Research Lab, Los Angeles, CA 90016, USA, Department of Collective Behaviour, Max Planck Institute of Animal Behavior, 78464 Konstanz, Germany, Department of Biology, University of Konstanz, 78464 Konstanz, Germany, Centre for the Advanced Study of Collective Behaviour, University of Konstanz, 78464 Konstanz, Germany
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  givenname: Lancelot
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  surname: Da Costa
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  surname: Friston
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  organization: VERSES Research Lab, Los Angeles, CA 90016, USA, Wellcome Centre for Human Neuroimaging, University College London, London WC1N 3AR, UK
BackLink https://www.ncbi.nlm.nih.gov/pubmed/37213925$$D View this record in MEDLINE/PubMed
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Issue 3
Keywords gauge theory
maximum entropy
free energy principle
active inference
information geometry
Bayesian mechanics
Language English
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These authors contributed equally to this study.
One contribution of 15 to a theme issue ‘Making and breaking symmetries in mind and life’.
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Snippet 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...
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Title On Bayesian mechanics: a physics of and by beliefs
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