# Adversarial Attacks, Regression, and Numerical Stability Regularization

arXiv: https://arxiv.org/abs/1812.02885 · HTML: https://mlsanity.com/paper/1812.02885/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2018.

## Built on by (most cited first, 14 of 14)

- [Adversarial Driving: Attacking End-to-End Autonomous Driving](https://mlsanity.com/paper/2103.09151/) (2021)
- [Targeted Adversarial Attacks on Wind Power Forecasts](https://mlsanity.com/paper/2303.16633/) (2023)
- [Cauchy-Schwarz Divergence Information Bottleneck for Regression](https://mlsanity.com/paper/2404.17951/) (2024)
- [Adversarial Transfer Attacks With Unknown Data and Class Overlap](https://mlsanity.com/paper/2109.11125/) (2021)
- [Physical Passive Patch Adversarial Attacks on Visual Odometry Systems](https://mlsanity.com/paper/2207.05729/) (2022)
- [Downlink Power Allocation in Massive MIMO via Deep Learning: Adversarial Attacks and Training](https://mlsanity.com/paper/2206.06592/) (2022)
- [Physics-Guided Adversarial Machine Learning for Aircraft Systems Simulation](https://mlsanity.com/paper/2209.03431/) (2022)
- [Fooling Neural Networks for Motion Forecasting via Adversarial Attacks](https://mlsanity.com/paper/2403.04954/) (2024)
- [Adversarial Machine Learning Attacks on Financial Reporting via Maximum Violated Multi-Objective Attack](https://mlsanity.com/paper/2507.05441/) (2025)
- [Enhancing Accuracy and Robustness of Steering Angle Prediction with Attention Mechanism](https://mlsanity.com/paper/2211.11133/) (2022)
- [On the Robustness of Decision-Focused Learning](https://mlsanity.com/paper/2311.16487/) (2023)
- [What is Adversarial Training for Diffusion Models?](https://mlsanity.com/paper/2505.21742/) (2025)
- [Are Inherently Interpretable Models More Robust? A Study In Music Emotion Recognition](https://mlsanity.com/paper/2508.03780/) (2025)
- [Adversarial Samples Are Not Created Equal](https://mlsanity.com/paper/2601.00577/) (2026)

## Abstract (arXiv)

Adversarial attacks against neural networks in a regression setting are a critical yet understudied problem. In this work, we advance the state of the art by investigating adversarial attacks against regression networks and by formulating a more effective defense against these attacks. In particular, we take the perspective that adversarial attacks are likely caused by numerical instability in learned functions. We introduce a stability inducing, regularization based defense against adversarial attacks in the regression setting. Our new and easy to implement defense is shown to outperform prior approaches and to improve the numerical stability of learned functions.