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Category: Cluster Variation Method

Figuring Out the Puzzle (in a 2-D CVM Grid)

Figuring Out the Puzzle (in a 2-D CVM Grid)

The Conundrum – and How to Solve It: We left off last week with a bit of a cliff-hanger; a puzzle with the 2-D CVM. (CVM stands for Cluster Variation Method; it’s a more complex form of a free energy equation that I discussed two weeks ago in this blogpost on The Big, Bad, Scary Free Energy Equation (and New Experimental Results); while not entirely unknown, it’s still not very common yet.) We asked ourselves: which of the two grids…

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2-D Cluster Variation Method: Code V&V

2-D Cluster Variation Method: Code V&V

New Code (Not Released Yet): V&V the Code Before We Play:   Well, my darling, as you gathered from last week’s post, the world has shifted. Up until now, when we were talking about having a new free energy function to use inside a neural network, we had to do “Gedankenexperiments” (German for “thought experiments”). Now, though, there’s working code – and I so LOVE seeing the numbers and graphs come out; teasing it, playing with it … stroking it…

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The Big, Bad, Scary Free Energy Equation (and New Experimental Results)

The Big, Bad, Scary Free Energy Equation (and New Experimental Results)

The 2-D Cluster Variation Method Free Energy Equation – in All Its Scary Glory:   You know, my dear, that we’ve been leading up to this moment for a while now. I’ve hinted. I’ve teased and been coy. But now, it’s time to be full frontal. We’re going to look at a new form of a free energy equation; a cluster variation method (CVM) equation. It deals not only with how many units are in state A or state B,…

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A “First Principles” Approach to General AI

A “First Principles” Approach to General AI

What We Need to Take the Next Tiny, Incremental Little Step: The “next big thing” is likely to be the next small thing – a tiny step, an incremental shift in perspective. However, a perspective shift is all that we need in order to make some real advances towards general artificial intelligence (GAI). In the second chapter of the ongoing book , I share the following figure (and sorry, the chapter itself is not released yet): Now, we’ve actually been…

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Brain Networks and the Cluster Variation Method: Testing a Scale-Free Model

Brain Networks and the Cluster Variation Method: Testing a Scale-Free Model

Surprising Result Modeling a Simple Scale-Free Brain Network Using the Cluster Variation Method One of the primary research thrusts that I suggested in my recent paper, The Cluster Variation Method: A Primer for Neuroscientists, was that we could use the 2-D Cluster Variation Method (CVM) to model distribution of configuration variables in different brain network topologies. Specifically, I was expecting that the h-value (which measures the interaction enthalpy strength between nodes in a 2-D CVM grid) would change in a…

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The Cluster Variation Method: A Primer for Neuroscientists

The Cluster Variation Method: A Primer for Neuroscientists

Single-Parameter Analytic Solution for Modeling Local Pattern Distributions The cluster variation method (CVM) offers a means for the characterization of both 1-D and 2-D local pattern distributions. The paper referenced at the end of this post provides neuroscientists and BCI researchers with a CVM tutorial that will help them to understand how the CVM statistical thermodynamics formulation can model 1-D and 2-D pattern distributions expressing structural and functional dynamics in the brain. The equilibrium distribution of local patterns, or configuration…

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The 1-D Cluster Variation Method (CVM) – Simple Application

The 1-D Cluster Variation Method (CVM) – Simple Application

The 1-D Cluster Variation Method – Application to Text Mining and Data Mining There are three particularly good reasons for us to look at the Cluster Variation Method (CVM) as an alternative means of understanding the information in a system: The CVM captures local pattern distributions (for an equilibrium state), When the system is made up of equal numbers of units in each of two states, and the enthalpy for each state is the same (the simple unit activation energy…

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Statistical Mechanics, Neural Domains, and Big Data

Statistical Mechanics, Neural Domains, and Big Data

How Neural Domain Activation and Statistical Mechanics Model Interactions in Large Data Corpora (Big Data) I was enthralled. I could read for only a few pages at a time, I was so overwhelmed with the insights that this book provided. And I was about twenty-five years old at the time. I had just discovered this book while browsing the stacks as a graduate student at Arizona State (ASU). The book was The Mindful Brain: Cortical Organization and the Group-Selective Theory…

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Visualizing Variables with the 2-D Cluster Variation Method

Visualizing Variables with the 2-D Cluster Variation Method

Cluster Variation Method – 2-D Case – Configuration Variables, Entropy and Free Energy Following the previous blog on the 1-D Cluster Variation Method, I illustrate here a micro-ensemble for the 2-D Cluster Variation Method, consisting of the original single zigzag chain of only ten units (see previous post), with three additional layers added, as shown in the following Figure 1. In Figure 1, we again have an equilibrium distribution of fraction variables z(i). Note that, as with the 1-D case,…

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Visualizing Configuration Variables with the 1-D Cluster Variation Method

Visualizing Configuration Variables with the 1-D Cluster Variation Method

Cluster Variation Method – 1-D Case – Configuration Variables, Entropy and Free Energy We construct a micro-system consisting of a single zigzag chain of only eight units, as shown in the following Figure 1. (Note that the additional textured units, with a dashed border, to the right illustrate a wrap-around effect, giving full horizontal nearest-neighbor connectivity.) In Figure 1, we have the equilibrium distribution of fraction variables z(i). Note that the weighting coefficients for z(2) = z(5) = 2, whereas…

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