# Empirical Perturbation Analysis of Linear System Solvers from a Data Poisoning Perspective

arXiv: https://arxiv.org/abs/2410.00878 · HTML: https://mlsanity.com/paper/2410.00878/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Backdoor and data poisoning attacks, one of 12 directions in LLM safety and security.
- Builds on 21 of its 48 references that are in the map.
- First posted on arXiv 1 Oct 2024.

## Placed in

- LLM safety and security / [Backdoor and data poisoning attacks](https://mlsanity.com/safety/backdoor-and-data-poisoning-attacks/)

## Builds on (most cited first, 21 of 21)

- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Manipulating Machine Learning: Poisoning Attacks and Countermeasures for Regression Learning](https://mlsanity.com/paper/1804.00308/) (2018)
- [Unlearnable Examples: Making Personal Data Unexploitable](https://mlsanity.com/paper/2101.04898/) (2021)
- [MetaPoison: Practical General-purpose Clean-label Data Poisoning](https://mlsanity.com/paper/2004.00225/) (2020)
- [Anti-DreamBooth: Protecting users from personalized text-to-image synthesis](https://mlsanity.com/paper/2303.15433/) (2023)
- [Adversarial Examples Make Strong Poisons](https://mlsanity.com/paper/2106.10807/) (2021)
- [Just How Toxic is Data Poisoning? A Unified Benchmark for Backdoor and Data Poisoning Attacks](https://mlsanity.com/paper/2006.12557/) (2020)
- [Learning to Confuse: Generating Training Time Adversarial Data with Auto-Encoder](https://mlsanity.com/paper/1905.09027/) (2019)
- [Availability Attacks Create Shortcuts](https://mlsanity.com/paper/2111.00898/) (2021)
- [Better Safe Than Sorry: Preventing Delusive Adversaries with Adversarial Training](https://mlsanity.com/paper/2102.04716/) (2021)
- [MetaCloak: Preventing Unauthorized Subject-driven Text-to-image Diffusion-based Synthesis via Meta-learning](https://mlsanity.com/paper/2311.13127/) (2023)
- [Transferable Unlearnable Examples](https://mlsanity.com/paper/2210.10114/) (2022)
- [Unlearnable Clusters: Towards Label-agnostic Unlearnable Examples](https://mlsanity.com/paper/2301.01217/) (2022)
- [Indiscriminate Poisoning Attacks on Unsupervised Contrastive Learning](https://mlsanity.com/paper/2202.11202/) (2022)
- [Stable Unlearnable Example: Enhancing the Robustness of Unlearnable Examples via Stable Error-Minimizing Noise](https://mlsanity.com/paper/2311.13091/) (2023)
- [A Survey of Defenses Against AI-Generated Visual Media: Detection,Disruption, and Authentication](https://mlsanity.com/paper/2407.10575/) (2024)
- [Efficient Availability Attacks against Supervised and Contrastive Learning Simultaneously](https://mlsanity.com/paper/2402.04010/) (2024)
- [The Hammer and the Nut: Is Bilevel Optimization Really Needed to Poison Linear Classifiers?](https://mlsanity.com/paper/2103.12399/) (2021)
- [Ungeneralizable Examples](https://mlsanity.com/paper/2404.14016/) (2024)
- [U Can't Gen This? A Survey of Intellectual Property Protection Methods for Data in Generative AI](https://mlsanity.com/paper/2406.15386/) (2024)
- [Analysis and Detectability of Offline Data Poisoning Attacks on Linear Dynamical Systems](https://mlsanity.com/paper/2211.08804/) (2022)

## Abstract (arXiv)

The perturbation analysis of linear solvers applied to systems arising broadly in machine learning settings -- for instance, when using linear regression models -- establishes an important perspective when reframing these analyses through the lens of a data poisoning attack. By analyzing solvers' responses to such attacks, this work aims to contribute to the development of more robust linear solvers and provide insights into poisoning attacks on linear solvers. In particular, we investigate how the errors in the input data will affect the fitting error and accuracy of the solution from a linear system-solving algorithm under perturbations common in adversarial attacks. We propose data perturbation through two distinct knowledge levels, developing a poisoning optimization and studying two methods of perturbation: Label-guided Perturbation (LP) and Unconditioning Perturbation (UP). Existing works mainly focus on deriving the worst-case perturbation bound from a theoretical perspective, and the analysis is often limited to specific kinds of linear system solvers. Under the circumstance that the data is intentionally perturbed -- as is the case with data poisoning -- we seek to understand how different kinds of solvers react to these perturbations, identifying those algorithms most impacted by different types of adversarial attacks.