The Graphical Brain: Belief Propagation and Active Inference

Overview

Journal Netw Neurosci

Publisher MIT Press

Specialty Neurology

Date 2018 Feb 9

PMID 29417960

Citations 146

Authors

Karl J Friston

Thomas Parr

Bert de Vries

Affiliations

Soon will be listed here.

Abstract

Author Summary: This paper considers functional integration in the brain from a computational perspective. We ask what sort of neuronal message passing is mandated by active inference-and what implications this has for context-sensitive connectivity at microscopic and macroscopic levels. In particular, we formulate neuronal processing as belief propagation under deep generative models that can entertain both discrete and continuous states. This leads to distinct schemes for belief updating that play out on the same (neuronal) architecture. Technically, we use Forney (normal) factor graphs to characterize the requisite message passing, and link this formal characterization to canonical microcircuits and extrinsic connectivity in the brain.

Citing Articles

Counteracting uncertainty: exploring the impact of anxiety on updating predictions about environmental states.

Harris D, Arthur T, Wilson M, Le Gallais B, Parsons T, Dill A Biol Cybern. 2025; 119(2-3):8.

PMID: 39976741 PMC: 11842521. DOI: 10.1007/s00422-025-01006-4.

FrAMBI: A Software Framework for Auditory Modeling Based on Bayesian Inference.

Barumerli R, Majdak P Neuroinformatics. 2025; 23(2):20.

PMID: 39928214 DOI: 10.1007/s12021-024-09702-5.

A detailed theory of thalamic and cortical microcircuits for predictive visual inference.

George D, Lazaro-Gredilla M, Lehrach W, Dedieu A, Zhou G, Marino J Sci Adv. 2025; 11(6):eadr6698.

PMID: 39908384 PMC: 11800772. DOI: 10.1126/sciadv.adr6698.

Adaptation, not prediction, drives neuronal spiking responses in mammalian sensory cortex.

Westerberg J, Xiong Y, Nejat H, Sennesh E, Durand S, Hardcastle B bioRxiv. 2025; .

PMID: 39829871 PMC: 11741236. DOI: 10.1101/2024.10.02.616378.

Generative models for sequential dynamics in active inference.

Parr T, Friston K, Pezzulo G Cogn Neurodyn. 2024; 18(6):3259-3272.

PMID: 39712086 PMC: 11655747. DOI: 10.1007/s11571-023-09963-x.

References

Friston K, Fitzgerald T, Rigoli F, Schwartenbeck P, Pezzulo G . Active Inference: A Process Theory. Neural Comput. 2016; 29(1):1-49. DOI: 10.1162/NECO_a_00912. View

Friston K . Hierarchical models in the brain. PLoS Comput Biol. 2008; 4(11):e1000211. PMC: 2570625. DOI: 10.1371/journal.pcbi.1000211. View

Shipp S . The importance of being agranular: a comparative account of visual and motor cortex. Philos Trans R Soc Lond B Biol Sci. 2005; 360(1456):797-814. PMC: 1569485. DOI: 10.1098/rstb.2005.1630. View

Bak , Tang , Wiesenfeld . Self-organized criticality: An explanation of the 1/f noise. Phys Rev Lett. 1987; 59(4):381-384. DOI: 10.1103/PhysRevLett.59.381. View

Friston K, Penny W . Post hoc Bayesian model selection. Neuroimage. 2011; 56(4):2089-99. PMC: 3112494. DOI: 10.1016/j.neuroimage.2011.03.062. View

Breakspear M, Stam C . Dynamics of a neural system with a multiscale architecture. Philos Trans R Soc Lond B Biol Sci. 2005; 360(1457):1051-74. PMC: 1854927. DOI: 10.1098/rstb.2005.1643. View

Murray J, Bernacchia A, Freedman D, Romo R, Wallis J, Cai X . A hierarchy of intrinsic timescales across primate cortex. Nat Neurosci. 2014; 17(12):1661-3. PMC: 4241138. DOI: 10.1038/nn.3862. View

Auksztulewicz R, Friston K . Attentional Enhancement of Auditory Mismatch Responses: a DCM/MEG Study. Cereb Cortex. 2015; 25(11):4273-83. PMC: 4816780. DOI: 10.1093/cercor/bhu323. View

Rayner K . Eye movements in reading and information processing. Psychol Bull. 1978; 85(3):618-60. View

10.

Heinzle J, Hepp K, Martin K . A microcircuit model of the frontal eye fields. J Neurosci. 2007; 27(35):9341-53. PMC: 6673112. DOI: 10.1523/JNEUROSCI.0974-07.2007. View

11.

Friston K, Parr T, de Vries B . The graphical brain: Belief propagation and active inference. Netw Neurosci. 2018; 1(4):381-414. PMC: 5798592. DOI: 10.1162/NETN_a_00018. View

12.

Bender D . Retinotopic organization of macaque pulvinar. J Neurophysiol. 1981; 46(3):672-93. DOI: 10.1152/jn.1981.46.3.672. View

13.

Lee J, Whittington M, Kopell N . Top-down beta rhythms support selective attention via interlaminar interaction: a model. PLoS Comput Biol. 2013; 9(8):e1003164. PMC: 3738471. DOI: 10.1371/journal.pcbi.1003164. View

14.

Friston K . Life as we know it. J R Soc Interface. 2013; 10(86):20130475. PMC: 3730701. DOI: 10.1098/rsif.2013.0475. View

15.

Fries P . A mechanism for cognitive dynamics: neuronal communication through neuronal coherence. Trends Cogn Sci. 2005; 9(10):474-80. DOI: 10.1016/j.tics.2005.08.011. View

16.

Srinivasan M, Laughlin S, Dubs A . Predictive coding: a fresh view of inhibition in the retina. Proc R Soc Lond B Biol Sci. 1982; 216(1205):427-59. DOI: 10.1098/rspb.1982.0085. View

17.

Friston K, Kahan J, Razi A, Stephan K, Sporns O . On nodes and modes in resting state fMRI. Neuroimage. 2014; 99:533-47. PMC: 4121089. DOI: 10.1016/j.neuroimage.2014.05.056. View

18.

Zelinsky G, Bisley J . The what, where, and why of priority maps and their interactions with visual working memory. Ann N Y Acad Sci. 2015; 1339:154-64. PMC: 4376606. DOI: 10.1111/nyas.12606. View

19.

Deco G, Jirsa V . Ongoing cortical activity at rest: criticality, multistability, and ghost attractors. J Neurosci. 2012; 32(10):3366-75. PMC: 6621046. DOI: 10.1523/JNEUROSCI.2523-11.2012. View

20.

de Lafuente V, Jazayeri M, Shadlen M . Representation of accumulating evidence for a decision in two parietal areas. J Neurosci. 2015; 35(10):4306-18. PMC: 4355201. DOI: 10.1523/JNEUROSCI.2451-14.2015. View