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Graphical methods provide an intuitive and visual means of solving equations by representing functions on the coordinate plane. These methods are especially helpful for estimating solutions, analyzing complex expressions, or understanding the behavior of functions.To solve an equation graphically, it must first be expressed in the form y = f(x). The solution to the original equation corresponds to the x-values where the graph intersects the x-axis, meaning where f(x) = 0.For example, the linear...
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Related Experiment Video

Updated: Feb 14, 2026

Neural Activity Propagation in an Unfolded Hippocampal Preparation with a Penetrating Micro-electrode Array
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The graphical brain: Belief propagation and active inference.

Karl J Friston1, Thomas Parr1, Bert de Vries2,3

  • 1Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, United Kingdom.

Network Neuroscience (Cambridge, Mass.)
|February 9, 2018
PubMed
Summary

This study explores brain function using active inference and deep generative models. It reveals how neuronal message passing supports context-sensitive brain connectivity for integrating discrete and continuous information.

Keywords:
BayesianBelief propagationConnectivityFactor graphsFree energyMessage passingNeuronal

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Area of Science:

  • Computational neuroscience
  • Neuroscience
  • Artificial Intelligence

Background:

  • Functional integration in the brain is crucial for complex cognitive processes.
  • Understanding neuronal message passing is key to deciphering brain computation.
  • Active inference provides a framework for modeling brain function.

Purpose of the Study:

  • To investigate neuronal message passing within the framework of active inference.
  • To explore the implications for context-sensitive neural connectivity at various scales.
  • To formulate neuronal processing using belief propagation under deep generative models.

Main Methods:

  • Formulated neuronal processing as belief propagation under deep generative models.
  • Utilized Forney (normal) factor graphs to characterize message passing.
  • Developed methods to accommodate mixed generative models with discrete and continuous states.

Main Results:

  • Identified distinct belief updating schemes for discrete and continuous states on a shared neuronal architecture.
  • Demonstrated how Bayesian model averaging and comparison can be implemented in thalamocortical loops.
  • Showcased state-dependent and self-organizing computational connectome.

Conclusions:

  • Neuronal message passing, as dictated by active inference, enables context-sensitive brain connectivity.
  • Deep generative models offer a unified framework for discrete and continuous information processing in the brain.
  • Simulations of reading illustrate the integration of semantic and visual information processing.