# Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines

arXiv: https://arxiv.org/abs/1706.09667 · HTML: https://mlsanity.com/paper/1706.09667/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2017.

## Built on by (most cited first, 1 of 1)

- [An AI Theory of Mind Will Enhance Our Collective Intelligence](https://mlsanity.com/paper/2411.09168/) (2024)

## Abstract (arXiv)

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.