Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines
This work provides a comparative analysis of complexity measures for researchers in theoretical machine learning and complex systems, but it is incremental as it applies existing measures to standard models.
The authors compared various information-theoretic complexity measures in Boltzmann machines to assess their similarities, differences, and limitations, finding that complexity increases with network dynamics and parameters, and applied an extended measure to show that information flow rises during Hebbian learning in Hopfield networks as more patterns are learned.
In the past three decades, many theoretical measures of complexity have been proposed to help understand complex systems. In this work, for the first time, we place these measures on a level playing field, to explore the qualitative similarities and differences between them, and their shortcomings. Specifically, using the Boltzmann machine architecture (a fully connected recurrent neural network) with uniformly distributed weights as our model of study, we numerically measure how complexity changes as a function of network dynamics and network parameters. We apply an extension of one such information-theoretic measure of complexity to understand incremental Hebbian learning in Hopfield networks, a fully recurrent architecture model of autoassociative memory. In the course of Hebbian learning, the total information flow reflects a natural upward trend in complexity as the network attempts to learn more and more patterns.