# Correlation Analysis between the Robustness of Sparse Neural Networks and their Random Hidden Structural Priors

arXiv: https://arxiv.org/abs/2107.06158 · HTML: https://mlsanity.com/paper/2107.06158/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 25 references that are in the map.
- First posted on arXiv 13 Jul 2021.

## Builds on (most cited first, 11 of 11)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [One pixel attack for fooling deep neural networks](https://mlsanity.com/paper/1710.08864/) (2017)
- [Threat of Adversarial Attacks on Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/1801.00553/) (2018)
- [Exploring Randomly Wired Neural Networks for Image Recognition](https://mlsanity.com/paper/1904.01569/) (2019)
- [Analysis of classifiers' robustness to adversarial perturbations](https://mlsanity.com/paper/1502.02590/) (2015)
- [Structural Analysis of Sparse Neural Networks](https://mlsanity.com/paper/1910.07225/) (2019)

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

- [Experiments on Properties of Hidden Structures of Sparse Neural Networks](https://mlsanity.com/paper/2107.12917/) (2021)

## Abstract (arXiv)

Deep learning models have been shown to be vulnerable to adversarial attacks. This perception led to analyzing deep learning models not only from the perspective of their performance measures but also their robustness to certain types of adversarial attacks. We take another step forward in relating the architectural structure of neural networks from a graph theoretic perspective to their robustness. We aim to investigate any existing correlations between graph theoretic properties and the robustness of Sparse Neural Networks. Our hypothesis is, that graph theoretic properties as a prior of neural network structures are related to their robustness. To answer to this hypothesis, we designed an empirical study with neural network models obtained through random graphs used as sparse structural priors for the networks. We additionally investigated the evaluation of a randomly pruned fully connected network as a point of reference. We found that robustness measures are independent of initialization methods but show weak correlations with graph properties: higher graph densities correlate with lower robustness, but higher average path lengths and average node eccentricities show negative correlations with robustness measures. We hope to motivate further empirical and analytical research to tightening an answer to our hypothesis.