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Brain Sci. 2016 Sep 30;6(4). pii: E44.

The Cluster Variation Method: A Primer for Neuroscientists.

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Northwestern University School of Professional Studies, Master of Science in Predictive Analytics Program, 405 Church St, Evanston, IL 60201, USA.


Effective Brain-Computer Interfaces (BCIs) require that the time-varying activation patterns of 2-D neural ensembles be modelled. The cluster variation method (CVM) offers a means for the characterization of 2-D local pattern distributions. This paper provides neuroscientists and BCI researchers with a CVM tutorial that will help them to understand how the CVM statistical thermodynamics formulation can model 2-D pattern distributions expressing structural and functional dynamics in the brain. The premise is that local-in-time free energy minimization works alongside neural connectivity adaptation, supporting the development and stabilization of consistent stimulus-specific responsive activation patterns. The equilibrium distribution of local patterns, or configuration variables, is defined in terms of a single interaction enthalpy parameter (h) for the case of an equiprobable distribution of bistate (neural/neural ensemble) units. Thus, either one enthalpy parameter (or two, for the case of non-equiprobable distribution) yields equilibrium configuration variable values. Modeling 2-D neural activation distribution patterns with the representational layer of a computational engine, we can thus correlate variational free energy minimization with specific configuration variable distributions. The CVM triplet configuration variables also map well to the notion of a M = 3 functional motif. This paper addresses the special case of an equiprobable unit distribution, for which an analytic solution can be found.


Cluster Variation Method; brain networks; brain–computer interfaces; deep learning; entropy; functional motifs; neural activation patterns; pattern recognition; statistical thermodynamics; variational free energy

Conflict of interest statement

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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