# Deep learning systems as complex networks

arXiv: https://arxiv.org/abs/1809.10941 · HTML: https://mlsanity.com/paper/1809.10941/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2018.

## Built on by (most cited first, 9 of 9)

- [The Neural Race Reduction: Dynamics of Abstraction in Gated Networks](https://mlsanity.com/paper/2207.10430/) (2022)
- [Structure and Performance of Fully Connected Neural Networks: Emerging Complex Network Properties](https://mlsanity.com/paper/2107.14062/) (2021)
- [Quantifying Local Specialization in Deep Neural Networks](https://mlsanity.com/paper/2110.08058/) (2021)
- [Characterizing Learning Dynamics of Deep Neural Networks via Complex Networks](https://mlsanity.com/paper/2110.02628/) (2021)
- [Improving Deep Neural Network Random Initialization Through Neuronal Rewiring](https://mlsanity.com/paper/2207.08148/) (2022)
- [Deep Neural Networks as Complex Networks](https://mlsanity.com/paper/2209.05488/) (2022)
- [Deep Neural Networks via Complex Network Theory: a Perspective](https://mlsanity.com/paper/2404.11172/) (2024)
- [A developmental approach for training deep belief networks](https://mlsanity.com/paper/2207.05473/) (2022)
- [Self-similarity Analysis in Deep Neural Networks](https://mlsanity.com/paper/2507.17785/) (2025)

## Abstract (arXiv)

Thanks to the availability of large scale digital datasets and massive amounts of computational power, deep learning algorithms can learn representations of data by exploiting multiple levels of abstraction. These machine learning methods have greatly improved the state-of-the-art in many challenging cognitive tasks, such as visual object recognition, speech processing, natural language understanding and automatic translation. In particular, one class of deep learning models, known as deep belief networks, can discover intricate statistical structure in large data sets in a completely unsupervised fashion, by learning a generative model of the data using Hebbian-like learning mechanisms. Although these self-organizing systems can be conveniently formalized within the framework of statistical mechanics, their internal functioning remains opaque, because their emergent dynamics cannot be solved analytically. In this article we propose to study deep belief networks using techniques commonly employed in the study of complex networks, in order to gain some insights into the structural and functional properties of the computational graph resulting from the learning process.