Excess Capacity and Backdoor Poisoning

TL;DR

This paper provides a formal theoretical framework for understanding backdoor data poisoning attacks, analyzing their statistical vulnerabilities and computational detection methods, and establishing the importance of identifying watermarked examples for robust learning.

Contribution

It introduces a formal framework for backdoor attacks, defines the memorization capacity, and links backdoor detection to robust generalization, advancing understanding of attack robustness and detection.

Findings

The memorization capacity measures vulnerability to backdoors.

Some natural learning problems are inherently robust against backdoor attacks.

Adversarial training can detect backdoors under certain assumptions.

Abstract

A backdoor data poisoning attack is an adversarial attack wherein the attacker injects several watermarked, mislabeled training examples into a training set. The watermark does not impact the test-time performance of the model on typical data; however, the model reliably errs on watermarked examples. To gain a better foundational understanding of backdoor data poisoning attacks, we present a formal theoretical framework within which one can discuss backdoor data poisoning attacks for classification problems. We then use this to analyze important statistical and computational issues surrounding these attacks. On the statistical front, we identify a parameter we call the memorization capacity that captures the intrinsic vulnerability of a learning problem to a backdoor attack. This allows us to argue about the robustness of several natural learning problems to backdoor attacks. Our results favoring the attacker involve presenting explicit constructions of backdoor attacks, and our robustness results show that some natural problem settings cannot yield successful backdoor attacks. From a computational standpoint, we show that under certain assumptions, adversarial training can detect the presence of backdoors in a training set. We then show that under similar assumptions, two closely related problems we call backdoor filtering and robust generalization are nearly equivalent. This implies that it is both asymptotically necessary and sufficient to design algorithms that can identify watermarked examples in the training set in order to obtain a learning algorithm that both generalizes well to unseen data and is robust to backdoors.