# Deep Neural Networks as Complex Networks

arXiv: https://arxiv.org/abs/2209.05488 · HTML: https://mlsanity.com/paper/2209.05488/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 16 references that are in the map.
- First posted on arXiv 12 Sep 2022.

## Builds on (most cited first, 8 of 8)

- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [The Neural Race Reduction: Dynamics of Abstraction in Gated Networks](https://mlsanity.com/paper/2207.10430/) (2022)
- [How far can we go without convolution: Improving fully-connected networks](https://mlsanity.com/paper/1511.02580/) (2015)
- [Structure and Performance of Fully Connected Neural Networks: Emerging Complex Network Properties](https://mlsanity.com/paper/2107.14062/) (2021)
- [Deep learning systems as complex networks](https://mlsanity.com/paper/1809.10941/) (2018)
- [Emergence of Network Motifs in Deep Neural Networks](https://mlsanity.com/paper/1912.12244/) (2019)
- [Fusion of complex networks and randomized neural networks for texture analysis](https://mlsanity.com/paper/1806.09170/) (2018)
- [Characterizing Learning Dynamics of Deep Neural Networks via Complex Networks](https://mlsanity.com/paper/2110.02628/) (2021)

## Built on by (most cited first, 2 of 2)

- [Dynamical stability and chaos in artificial neural network trajectories along training](https://mlsanity.com/paper/2404.05782/) (2024)
- [Graph-based methods coupled with specific distributional distances for adversarial attack detection](https://mlsanity.com/paper/2306.00042/) (2023)

## Abstract (arXiv)

Deep Neural Networks are, from a physical perspective, graphs whose `links` and `vertices` iteratively process data and solve tasks sub-optimally. We use Complex Network Theory (CNT) to represents Deep Neural Networks (DNNs) as directed weighted graphs: within this framework, we introduce metrics to study DNNs as dynamical systems, with a granularity that spans from weights to layers, including neurons. CNT discriminates networks that differ in the number of parameters and neurons, the type of hidden layers and activations, and the objective task. We further show that our metrics discriminate low vs. high performing networks. CNT is a comprehensive method to reason about DNNs and a complementary approach to explain a model's behavior that is physically grounded to networks theory and goes beyond the well-studied input-output relation.