# GradID: Adversarial Detection via Intrinsic Dimensionality of Gradients

arXiv: https://arxiv.org/abs/2512.12827 · HTML: https://mlsanity.com/paper/2512.12827/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 35 references that are in the map.
- First posted on arXiv 14 Dec 2025.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [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)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [DeepFool: a simple and accurate method to fool deep neural networks](https://mlsanity.com/paper/1511.04599/) (2015)
- [Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionality](https://mlsanity.com/paper/1801.02613/) (2018)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Detecting Adversarial Samples from Artifacts](https://mlsanity.com/paper/1703.00410/) (2017)
- [Are adversarial examples inevitable?](https://mlsanity.com/paper/1809.02104/) (2018)
- [Segment and Complete: Defending Object Detectors against Adversarial Patch Attacks with Robust Patch Detection](https://mlsanity.com/paper/2112.04532/) (2021)
- [Multi-head Uncertainty Inference for Adversarial Attack Detection](https://mlsanity.com/paper/2212.10006/) (2022)

## Abstract (arXiv)

Despite their remarkable performance, deep neural networks exhibit a critical vulnerability: small, often imperceptible, adversarial perturbations can lead to drastically altered model predictions. Given the stringent reliability demands of applications such as medical diagnosis and autonomous driving, robust detection of such adversarial attacks is paramount. In this paper, we investigate the geometric properties of a model's input loss landscape. We analyze the Intrinsic Dimensionality (ID) of the model's gradient parameters, which quantifies the minimal number of coordinates required to describe the data points on their underlying manifold. We reveal a distinct and consistent difference in the ID for natural and adversarial data, which forms the basis of our proposed detection method. We validate our approach across two distinct operational scenarios. First, in a batch-wise context for identifying malicious data groups, our method demonstrates high efficacy on datasets like MNIST and SVHN. Second, in the critical individual-sample setting, we establish new state-of-the-art results on challenging benchmarks such as CIFAR-10 and MS COCO. Our detector significantly surpasses existing methods against a wide array of attacks, including CW and AutoAttack, achieving detection rates consistently above 92% on CIFAR-10. The results underscore the robustness of our geometric approach, highlighting that intrinsic dimensionality is a powerful fingerprint for adversarial detection across diverse datasets and attack strategies.