# Active Subspace of Neural Networks: Structural Analysis and Universal Attacks

arXiv: https://arxiv.org/abs/1910.13025 · HTML: https://mlsanity.com/paper/1910.13025/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2019.

## Built on by (most cited first, 12 of 12)

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- [A Proper Orthogonal Decomposition approach for parameters reduction of Single Shot Detector networks](https://mlsanity.com/paper/2207.13551/) (2022)

## Abstract (arXiv)

Active subspace is a model reduction method widely used in the uncertainty quantification community. In this paper, we propose analyzing the internal structure and vulnerability and deep neural networks using active subspace. Firstly, we employ the active subspace to measure the number of "active neurons" at each intermediate layer and reduce the number of neurons from several thousands to several dozens. This motivates us to change the network structure and to develop a new and more compact network, referred to as ASNet, that has significantly fewer model parameters. Secondly, we propose analyzing the vulnerability of a neural network using active subspace and finding an additive universal adversarial attack vector that can misclassify a dataset with a high probability. Our experiments on CIFAR-10 show that ASNet can achieve 23.98× parameter and 7.30× flops reduction. The universal active subspace attack vector can achieve around 20% higher attack ratio compared with the existing approach in all of our numerical experiments. The PyTorch codes for this paper are available online.