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arXiv 2404.08069cs.LG
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持久分类:一种研究数据稳定性与对抗样本的新方法

Persistent Classification: A New Approach to Stability of Data and Adversarial Examples

University of Arizona(亚利桑那大学);Los Alamos National Laboratory(洛斯阿拉莫斯国家实验室);University of Texas San Antonio(德克萨斯大学圣安东尼奥分校);University of Texas at Arlington(德克萨斯大学阿灵顿分校)

Brian Bell, Michael Geyer, David Glickenstein, Keaton Hamm, Carlos Scheidegger, Amanda Fernandez, Juston Moore

AI总结:

该研究提出持久分类新框架,通过$(γ,σ)$稳定性定义和插值路径持久化度量分析对抗样本,发现对抗样本持久化更低,还提出流形对齐梯度度量以提升模型鲁棒性。

摘要:

分类问题中对抗样本的存在性基于多种假设,包括数据的高维性、目标数据流形在环境空间中的高余维数,以及机器学习模型的结构可能促使分类器生成靠近数据点的决策边界。本文提出了一种不直接依赖到决策边界距离的对抗样本研究新框架。与平滑分类器相关研究类似,我们将(自然或对抗)数据点定义为$(γ,σ)$-稳定的,当在该点的高斯邻域内以给定标准差$σ$采样的点被分类为同一类别的概率至少为$γ$时。我们重点研究自然样本与对抗样本的插值路径上持久化度量的差异。实验表明,在MNIST和ImageNet数据集上,大型神经网络的对抗样本持久化程度显著低于自然样本。我们通过测量插值路径与决策边界的夹角,将这种持久化缺失与决策边界几何结构关联起来。最后,我们通过提出流形对齐梯度度量,将该方法与鲁棒性联系起来,并证明在训练中加入该度量可提升模型鲁棒性。

英文摘要:

There are a number of hypotheses underlying the existence of adversarial examples for classification problems. These include the high-dimensionality of the data, high codimension in the ambient space of the data manifolds of interest, and that the structure of machine learning models may encourage classifiers to develop decision boundaries close to data points. This article proposes a new framework for studying adversarial examples that does not depend directly on the distance to the decision boundary. Similarly to the smoothed classifier literature, we define a (natural or adversarial) data point to be $(γ,σ)$-stable if the probability of the same classification is at least $γ$ for points sampled in a Gaussian neighborhood of the point with a given standard deviation $σ$. We focus on studying the differences between persistence metrics along interpolants of natural and adversarial points. We show that adversarial examples have significantly lower persistence than natural examples for large neural networks in the context of the MNIST and ImageNet datasets. We connect this lack of persistence with decision boundary geometry by measuring angles of interpolants with respect to decision boundaries. Finally, we connect this approach with robustness by developing a manifold alignment gradient metric and demonstrating the increase in robustness that can be achieved when training with the addition of this metric.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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