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Ramstead MJD, Sakthivadivel DAR, Heins C, Koudahl M, Millidge B, Da Costa L, Klein B, Friston KJ. On Bayesian mechanics: a physics of and by beliefs. Interface Focus 2023; 13:20220029. [PMID: 37213925 PMCID: PMC10198254 DOI: 10.1098/rsfs.2022.0029] [Citation(s) in RCA: 19] [Impact Index Per Article: 19.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2022] [Accepted: 01/17/2023] [Indexed: 05/23/2023] Open
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.
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Affiliation(s)
- Maxwell J. D. Ramstead
- VERSES Research Lab, Los Angeles, CA 90016, USA
- Wellcome Centre for Human Neuroimaging, University College London, London WC1N 3AR, UK
| | - Dalton A. R. Sakthivadivel
- 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
| | - Conor Heins
- 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
| | - Magnus Koudahl
- VERSES Research Lab, Los Angeles, CA 90016, USA
- Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Beren Millidge
- VERSES Research Lab, Los Angeles, CA 90016, USA
- Brain Network Dynamics Unit, University of Oxford, Oxford, UK
| | - Lancelot Da Costa
- Wellcome Centre for Human Neuroimaging, University College London, London WC1N 3AR, UK
- Department of Mathematics, Imperial College London, London SW7 2AZ, UK
| | - Brennan Klein
- VERSES Research Lab, Los Angeles, CA 90016, USA
- Network Science Institute, Northeastern University, Boston, MA, USA
| | - Karl J. Friston
- VERSES Research Lab, Los Angeles, CA 90016, USA
- Wellcome Centre for Human Neuroimaging, University College London, London WC1N 3AR, UK
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Aguilera M, Millidge B, Tschantz A, Buckley CL. From the free energy principle to a confederation of Bayesian mechanics: Reply to comments on "How particular is the physics of the free energy principle?". Phys Life Rev 2023; 44:270-275. [PMID: 36821891 DOI: 10.1016/j.plrev.2023.01.018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2023] [Accepted: 01/30/2023] [Indexed: 02/10/2023]
Affiliation(s)
- Miguel Aguilera
- BCAM - Basque Center for Applied Mathematics, Bilbao, 480009, Spain; IKERBASQUE, Basque Foundation for Science, Bilbao, 480009, Spain; School of Engineering and Informatics, University of Sussex, Falmer, Brighton, BN1 9QJ, United Kingdom.
| | - Beren Millidge
- VERSES Research Lab, Los Angeles, 2JC7+WX, CA, USA; MRC Brain Network Dynamics Unit, University of Oxford, Oxford, OX1 3TH, United Kingdom
| | | | - Christopher L Buckley
- School of Engineering and Informatics, University of Sussex, Falmer, Brighton, BN1 9QJ, United Kingdom; VERSES Research Lab, Los Angeles, 2JC7+WX, CA, USA
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Aguilera M. The nonequilibrium boundaries of living systems: Comment on "The Markov blanket trick: On the scope of the free energy principle and active inference" by V. Raja et al. Phys Life Rev 2022; 43:23-25. [PMID: 36029603 DOI: 10.1016/j.plrev.2022.08.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2022] [Accepted: 08/15/2022] [Indexed: 12/15/2022]
Affiliation(s)
- Miguel Aguilera
- School of Engineering and Informatics, University of Sussex, Falmer, Brighton, BN1 9QJ, United Kingdom.
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