1D CVM Resources

Here are the important resources that you need to work with the 1D CVM (Cluster Variation Method).

Downloads from Themesis:

Cite the Technical Report as: 

  • Maren, Alianna J. 2014. “The Cluster Variation Method I: 1-D Single Zigzag Chain. Basic Theory, Analytic Solution and Free Energy Variable Distributions at Midpoint (x1 = x2 = 0.5).” Themesis Technical Report THM 2014 002(ajm). (Available online at pdf, also at www.aliannajmaren.com ; access via Patents and Publications page.)   

Journal Papers – Key Tutorials / Background

This is a collection of five papers that you might want to access regarding the CVM. They include:

  • The tutorial-style 2016 paper that discusses the 1D CVM in some depth,
  • The two originating papers – Kikuchi (1951) and Kikuchi and Brush (1967), and
  • The ONLY OTHER paper within recent time that uses the CVM method to solve a problem – the authors were not able to develop the general-purpose methods that we’ll introduce, but just for well-roundedness, you can add this to your collection. 

Primary Reference on the 1D CVM

  • Maren, A.J. (2016). The Cluster Variation Method: A Primer for Neuroscientists. Brain Sci. 6(4), 44, https://doi.org/10.3390/brainsci6040044; online access, pdf; accessed 2018/09/19.

2-D Cluster Variation Method: The Earliest Works (Theory Only)

  • Kikuchi, R. (1951). A theory of cooperative phenomena. Phys. Rev. 81, 988-1003, pdf, accessed 2018/09/17.
  • Kikuchi, R., & Brush, S.G. (1967), “Improvement of the Cluster‐Variation Method,” J. Chem. Phys. 47, 195; online as: online – for purchase through American Inst. Physics. Costs $30.00 for non-members.

CVM Work by Others

Sajid et al. on using the 2-D cluster variation method to model cancer niches.

  • Sajid, Noor, Laura Convertino, and Karl Friston. 2021. “Cancer Niches and Their Kikuchi Free Energy.” Entropy (Basel) (May 2021) 23(5): 609. doi:10.3390/e23050609 (Accessed Sept. 11, 2023; pdf.)

GitHub for the 1D CVM

This is the code repository for everything that we’re discussing regarding the 1D CVM – you will be able to follow along completely using the code here. 

Important Blogposts

The Dec. 23, 2023 blogpost takes the next step – you are now able to (approximately) identify an h-value that corresponds to the free energy minimum most closely matching your “node-swapped” system. 

  • Maren, Alianna J. 2023. “CORTECONs and AGI: Reaching Latent Layer Equilibrium.” Themesis Inc. Blogpost Series (Dec. 23, 2023). (Accessed Dec. 23, 2023; available at blogpost page.)
  • Maren, Alianna J. 2023. “AGI Notation: Friston’s Use of ‘Psi.'” Themesis Inc. Blogpost Series (Dec. 14, 2023). (Accessed Dec. 23, 2023; available at blogpost page.)
  • Maren, Alianna J. 2023. “The 1D CVM (Cluster Variation Method): Complete Interactive Code (Part 2)” Themesis Inc. Blogpost Series (Dec. 14, 2023). (Accessed Dec. 23, 2023; available at blogpost page.)
  • Maren, Alianna J. 2023. “1-D Cluster Variation Method: Simple Text String Worked Example (Part 1)” Themesis Inc. Blogpost Series (Sept. 9, 2023). (Accessed Accessed Dec. 23, 2023; blogpost page.)
  • Maren, Alianna J. 2023. “1D CVM Object Instance Attributes: wLeft Details” Themesis Inc. Blogpost Series (Aug. 6, 2023). (Accessed Accessed Dec. 23, 2023; blogpost page.) 

Prior Related Blogposts – Variational Free Energy

AJM’s Note: This is the “Mega-Resource Compendium.”

AJM’s Note: This is the immediate predecessor blogpost, which is also a “mega-resource compendium.”