# A Geometrical Approach to Evaluate the Adversarial Robustness of Deep Neural Networks

arXiv: https://arxiv.org/abs/2310.06468 · HTML: https://mlsanity.com/paper/2310.06468/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 59 references that are in the map.
- First posted on arXiv 10 Oct 2023.

## Builds on (most cited first, 30 of 45)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [DeepFool: a simple and accurate method to fool deep neural networks](https://mlsanity.com/paper/1511.04599/) (2015)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Practical Black-Box Attacks against Machine Learning](https://mlsanity.com/paper/1602.02697/) (2016)
- [The Limitations of Deep Learning in Adversarial Settings](https://mlsanity.com/paper/1511.07528/) (2015)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Distillation as a Defense to Adversarial Perturbations against Deep Neural Networks](https://mlsanity.com/paper/1511.04508/) (2015)
- [ZOO: Zeroth Order Optimization based Black-box Attacks to Deep Neural Networks without Training Substitute Models](https://mlsanity.com/paper/1708.03999/) (2017)
- [Improving Transferability of Adversarial Examples with Input Diversity](https://mlsanity.com/paper/1803.06978/) (2018)
- [Black-box Adversarial Attacks with Limited Queries and Information](https://mlsanity.com/paper/1804.08598/) (2018)
- [Decision-Based Adversarial Attacks: Reliable Attacks Against Black-Box Machine Learning Models](https://mlsanity.com/paper/1712.04248/) (2017)
- [Threat of Adversarial Attacks on Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/1801.00553/) (2018)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Evading Defenses to Transferable Adversarial Examples by Translation-Invariant Attacks](https://mlsanity.com/paper/1904.02884/) (2019)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Towards Fast Computation of Certified Robustness for ReLU Networks](https://mlsanity.com/paper/1804.09699/) (2018)
- [Adversarial Logit Pairing](https://mlsanity.com/paper/1803.06373/) (2018)
- [Improving Adversarial Robustness via Promoting Ensemble Diversity](https://mlsanity.com/paper/1901.08846/) (2019)
- [Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach](https://mlsanity.com/paper/1801.10578/) (2018)
- [Efficient Decision-based Black-box Adversarial Attacks on Face Recognition](https://mlsanity.com/paper/1904.04433/) (2019)

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

- [Model Inversion Attacks Through Target-Specific Conditional Diffusion Models](https://mlsanity.com/paper/2407.11424/) (2024)
- [Rethinking Robustness in Machine Learning: A Posterior Agreement Approach](https://mlsanity.com/paper/2503.16271/) (2025)

## Abstract (arXiv)

Deep Neural Networks (DNNs) are widely used for computer vision tasks. However, it has been shown that deep models are vulnerable to adversarial attacks, i.e., their performances drop when imperceptible perturbations are made to the original inputs, which may further degrade the following visual tasks or introduce new problems such as data and privacy security. Hence, metrics for evaluating the robustness of deep models against adversarial attacks are desired. However, previous metrics are mainly proposed for evaluating the adversarial robustness of shallow networks on the small-scale datasets. Although the Cross Lipschitz Extreme Value for nEtwork Robustness (CLEVER) metric has been proposed for large-scale datasets (e.g., the ImageNet dataset), it is computationally expensive and its performance relies on a tractable number of samples. In this paper, we propose the Adversarial Converging Time Score (ACTS), an attack-dependent metric that quantifies the adversarial robustness of a DNN on a specific input. Our key observation is that local neighborhoods on a DNN's output surface would have different shapes given different inputs. Hence, given different inputs, it requires different time for converging to an adversarial sample. Based on this geometry meaning, ACTS measures the converging time as an adversarial robustness metric. We validate the effectiveness and generalization of the proposed ACTS metric against different adversarial attacks on the large-scale ImageNet dataset using state-of-the-art deep networks. Extensive experiments show that our ACTS metric is an efficient and effective adversarial metric over the previous CLEVER metric.