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In the past three decades, many theoretical measures of complexity have beenproposed to help understand complex systems. In this work, for the first time,we place these measures on a level playing field, to explore the qualitativesimilarities and differences between them, and their shortcomings.Specifically, using the Boltzmann machine architecture (a fully connectedrecurrent neural network) with uniformly distributed weights as our model ofstudy, we numerically measure how complexity changes as a function of networkdynamics and network parameters. We apply an extension of one suchinformation-theoretic measure of complexity to understand incremental Hebbianlearning in Hopfield networks, a fully recurrent architecture model ofautoassociative memory. In the course of Hebbian learning, the totalinformation flow reflects a natural upward trend in complexity as the networkattempts to learn more and more patterns.

Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines