Precise statistical analysis of classification accuracies for adversarial training
对抗训练分类准确率的精确统计分析AI 解读 ↓
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对抗训练分类准确率的精确统计分析
- 研究问题
- 在二元分类中，对抗训练如何影响未扰动输入的标准准确率与受扰动输入的稳健准确率，哪些模型和数据参数决定这种关系？
- 方法与思路
- 作者在具有一般各向异性协方差的双高斯混合模型中，分析一类极小极大对抗训练方法，允许任意 p≥1 的有界 ℓp 扰动。
- 材料陈述的贡献
- 摘要称精确刻画标准与稳健准确率，并据此解释若干经验现象及问题参数的作用，具体表达式和适用条件未给出。
- 阅读关注点
- 应核对高斯混合设定、训练目标、分析所处的样本与维度范围，以及不同扰动范数下准确率刻画的条件。
- 阅读边界
- 所给为版本未注明的 OpenAlex 摘要；结论针对特定生成模型与训练方法，不能推广到任意真实分类数据或所有对抗训练程序。
原文摘要
Despite the wide empirical success of modern machine learning algorithms and models in a multitude of applications, they are known to be highly susceptible to seemingly small indiscernible perturbations to the input data known as adversarial attacks. A variety of recent adversarial training procedures have been proposed to remedy this issue. Despite the success of such procedures at increasing accuracy on adversarially perturbed inputs or robust accuracy, these techniques often reduce accuracy on natural unperturbed inputs or standard accuracy. Complicating matters further, the effect and trend of adversarial training procedures on standard and robust accuracy is rather counter intuitive and radically dependent on a variety of factors including the perceived form of the perturbation during training, size/quality of data, model overparameterization, etc. In this paper, we focus on binary classification problems where the data is generated according to the mixture of two Gaussians with general anisotropic covariance matrices and derive a precise characterization of the standard and robust accuracy for a class of minimax adversarially trained models. We consider a general norm-based adversarial model, where the adversary can add perturbations of bounded ℓp norm to each input data, for an arbitrary p≥1. Our comprehensive analysis allows us to theoretically explain several intriguing empirical phenomena and provide a precise understanding of the role of different problem parameters on standard and robust accuracies.