arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1705.09552cs.CVcs.AIcs.LGstat.ML
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深度神经网络的分类区域

Classification regions of deep neural networks

University of California, Los Angeles(加州大学洛杉矶分校);École Polytechnique Fédérale de Lausanne(洛桑联邦理工学院)

Alhussein Fawzi, Seyed-Mohsen Moosavi-Dezfooli, Pascal Frossard, Stefano Soatto

摘要:

本文的目标是分析深度神经网络分类器在输入空间中的几何性质。我们专门研究了由深度网络创建的分类区域的拓扑结构,以及它们相关的决策边界。通过系统的实证调查,我们表明,最先进的深度网络学习连接的分类区域,并且数据点附近的决策边界在大多数方向上是平坦的。我们进一步在深度网络的两个看似无关的属性之间建立了本质联系:它们对输入中的附加扰动的敏感性,以及它们的决策边界的曲率。事实上,决策边界弯曲的方向显著地表征了分类器最易受影响的方向。最后,我们利用深度网络的决策边界曲率的基本不对称性,并提出了一种方法来区分原始图像和被小的对抗性示例扰动的图像。我们证明了这种纯粹的几何方法的有效性,用于检测图像中的小对抗扰动,并恢复扰动图像的标签。

英文摘要:

The goal of this paper is to analyze the geometric properties of deep neural network classifiers in the input space. We specifically study the topology of classification regions created by deep networks, as well as their associated decision boundary. Through a systematic empirical investigation, we show that state-of-the-art deep nets learn connected classification regions, and that the decision boundary in the vicinity of datapoints is flat along most directions. We further draw an essential connection between two seemingly unrelated properties of deep networks: their sensitivity to additive perturbations in the inputs, and the curvature of their decision boundary. The directions where the decision boundary is curved in fact remarkably characterize the directions to which the classifier is the most vulnerable. We finally leverage a fundamental asymmetry in the curvature of the decision boundary of deep nets, and propose a method to discriminate between original images, and images perturbed with small adversarial examples. We show the effectiveness of this purely geometric approach for detecting small adversarial perturbations in images, and for recovering the labels of perturbed images.

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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