We present BadGD, a unified theoretical framework that exposes the vulnerabilities of gradient descent algorithms through strategic backdoor attacks. Backdoor attacks involve embedding malicious triggers into a training dataset to disrupt the model's learning process. Our framework introduces three novel constructs: Max RiskWarp Trigger, Max GradWarp Trigger, and Max GradDistWarp Trigger, each designed to exploit specific aspects of gradient descent by distorting empirical risk, deterministic gradients, and stochastic gradients respectively. We rigorously define clean and backdoored datasets and provide mathematical formulations for assessing the distortions caused by these malicious backdoor triggers. By measuring the impact of these triggers on the model training procedure, our framework bridges existing empirical findings with theoretical insights, demonstrating how a malicious party can exploit gradient descent hyperparameters to maximize attack effectiveness. In particular, we show that these exploitations can significantly alter the loss landscape and gradient calculations, leading to compromised model integrity and performance. This research underscores the severe threats posed by such data-centric attacks and highlights the urgent need for robust defenses in machine learning. BadGD sets a new standard for understanding and mitigating adversarial manipulations, ensuring the reliability and security of AI systems.

翻译：本文提出BadGD，一个统一的理论框架，通过战略性后门攻击揭示梯度下降算法的脆弱性。后门攻击涉及将恶意触发器嵌入训练数据集以破坏模型的学习过程。我们的框架引入了三种新颖构造：最大风险扭曲触发器、最大梯度扭曲触发器和最大梯度距离扭曲触发器，分别通过扭曲经验风险、确定性梯度和随机梯度来利用梯度下降的特定方面。我们严格定义了干净数据集与后门数据集，并提供了评估这些恶意后门触发器所引发扭曲的数学公式。通过测量这些触发器对模型训练过程的影响，本框架将现有实证发现与理论洞见相连接，论证了恶意方如何利用梯度下降超参数来最大化攻击效果。特别地，我们证明这些利用手段能显著改变损失景观和梯度计算，导致模型完整性与性能受损。本研究揭示了此类数据驱动攻击构成的严重威胁，并强调了机器学习领域对鲁棒防御机制的迫切需求。BadGD为理解和缓解对抗性操纵设立了新标准，为保障人工智能系统的可靠性与安全性提供了理论基础。