# Nonlinear Projection Based Gradient Estimation for Query Efficient Blackbox Attacks

arXiv: https://arxiv.org/abs/2102.13184 · HTML: https://mlsanity.com/paper/2102.13184/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 40 references that are in the map.
- First posted on arXiv 25 Feb 2021.

## Builds on (most cited first, 24 of 24)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [ZOO: Zeroth Order Optimization based Black-box Attacks to Deep Neural Networks without Training Substitute Models](https://mlsanity.com/paper/1708.03999/) (2017)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Delving into Transferable Adversarial Examples and Black-box Attacks](https://mlsanity.com/paper/1611.02770/) (2016)
- [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)
- [Transferability in Machine Learning: from Phenomena to Black-Box Attacks using Adversarial Samples](https://mlsanity.com/paper/1605.07277/) (2016)
- [HopSkipJumpAttack: A Query-Efficient Decision-Based Attack](https://mlsanity.com/paper/1904.02144/) (2019)
- [Gradient Sparsification for Communication-Efficient Distributed Optimization](https://mlsanity.com/paper/1710.09854/) (2017)
- [The Space of Transferable Adversarial Examples](https://mlsanity.com/paper/1704.03453/) (2017)
- [AutoZOOM: Autoencoder-based Zeroth Order Optimization Method for Attacking Black-box Neural Networks](https://mlsanity.com/paper/1805.11770/) (2018)
- [Improving Black-box Adversarial Attacks with a Transfer-based Prior](https://mlsanity.com/paper/1906.06919/) (2019)
- [Sign-OPT: A Query-Efficient Hard-label Adversarial Attack](https://mlsanity.com/paper/1909.10773/) (2019)
- [QEBA: Query-Efficient Boundary-Based Blackbox Attack](https://mlsanity.com/paper/2005.14137/) (2020)
- [RecurJac: An Efficient Recursive Algorithm for Bounding Jacobian Matrix of Neural Networks and Its Applications](https://mlsanity.com/paper/1810.11783/) (2018)

## Built on by (most cited first, 9 of 9)

- [TRS: Transferability Reduced Ensemble via Encouraging Gradient Diversity and Model Smoothness](https://mlsanity.com/paper/2104.00671/) (2021)
- [Back in Black: A Comparative Evaluation of Recent State-Of-The-Art Black-Box Attacks](https://mlsanity.com/paper/2109.15031/) (2021)
- [Query Efficient Decision Based Sparse Attacks Against Black-Box Deep Learning Models](https://mlsanity.com/paper/2202.00091/) (2022)
- [3DHacker: Spectrum-based Decision Boundary Generation for Hard-label 3D Point Cloud Attack](https://mlsanity.com/paper/2308.07546/) (2023)
- [Rethinking Image-Scaling Attacks: The Interplay Between Vulnerabilities in Machine Learning Systems](https://mlsanity.com/paper/2104.08690/) (2021)
- [SoK: Pitfalls in Evaluating Black-Box Attacks](https://mlsanity.com/paper/2310.17534/) (2023)
- [On the Robustness of Deep Clustering Models: Adversarial Attacks and Defenses](https://mlsanity.com/paper/2210.01940/) (2022)
- [NoPain: No-box Point Cloud Attack via Optimal Transport Singular Boundary](https://mlsanity.com/paper/2503.00063/) (2025)
- [Hard-Label Black-Box Attacks on 3D Point Clouds](https://mlsanity.com/paper/2412.00404/) (2024)

## Abstract (arXiv)

Gradient estimation and vector space projection have been studied as two distinct topics. We aim to bridge the gap between the two by investigating how to efficiently estimate gradient based on a projected low-dimensional space. We first provide lower and upper bounds for gradient estimation under both linear and nonlinear projections, and outline checkable sufficient conditions under which one is better than the other. Moreover, we analyze the query complexity for the projection-based gradient estimation and present a sufficient condition for query-efficient estimators. Built upon our theoretic analysis, we propose a novel query-efficient Nonlinear Gradient Projection-based Boundary Blackbox Attack (NonLinear-BA). We conduct extensive experiments on four image datasets: ImageNet, CelebA, CIFAR-10, and MNIST, and show the superiority of the proposed methods compared with the state-of-the-art baselines. In particular, we show that the projection-based boundary blackbox attacks are able to achieve much smaller magnitude of perturbations with 100% attack success rate based on efficient queries. Both linear and nonlinear projections demonstrate their advantages under different conditions. We also evaluate NonLinear-BA against the commercial online API MEGVII Face++, and demonstrate the high blackbox attack performance both quantitatively and qualitatively. The code is publicly available at https://github.com/AI-secure/NonLinear-BA.