深度欺骗：精确计算深度神经网络鲁棒性的简单方法

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DeepFool算法是一种针对深度神经网络的简单而精确的方法，旨在识别并计算深度模型对图像输入的敏感性，即它们对微小、精心设计的扰动的不稳定性。随着深度学习在图像分类任务中的显著成就，研究人员已经发现这些复杂的网络结构对于输入的细微变化非常敏感，这被称为对抗性攻击。当前，尽管深度神经网络的脆弱性是一个重要的研究领域，但缺乏一种有效且准确的方法来量化大规模数据集上现代深度分类器的鲁棒性。DeepFool算法填补了这一空白，它提供了一种高效的方式来生成那些能够欺骗深度网络的扰动，从而评估模型的防御能力。这种方法的主要目标是生成最小的扰动，使得原本被正确分类的样本在经过这种扰动后被误分类。论文的核心内容包括以下几个关键点： 1. **背景与动机**：深度学习模型的广泛应用伴随着对其鲁棒性的关注。由于深度网络对微小扰动的敏感性，确保其在实际环境中的稳健性成为亟待解决的问题。 2. **算法介绍**： DeepFool基于优化理论，通过线性化逼近方法找到一个最小的扰动向量，这个向量使网络决策边界与原始样本之间的距离最小，从而导致预测错误。算法流程简洁，不需要大量的计算资源。 3. **优势与比较**：相比于现有的对抗性攻击方法，如Fast Gradient Sign Method (FGSM)或Iterative Fast Gradient Sign Method (I-FGSM)，DeepFool具有更高的准确性和效率。实验结果显示，DeepFool能更准确地生成对抗样本，并提高模型的鲁棒性评估的可靠性。 4. **实验结果**：通过一系列详细的实验，DeepFool在计算对抗性扰动任务上表现出色，不仅能够在较小的扰动下诱导误分类，而且在大规模数据集上也展示出稳定性和准确性。 5. **实际应用与影响**：这项工作不仅有助于理解和改进深度学习模型的防御机制，也为安全相关的领域（如网络安全、自动驾驶等）提供了评估模型鲁棒性的实用工具。 DeepFool算法作为深度学习领域的一个里程碑，它不仅揭示了深度模型的内在弱点，还提出了一种强大的工具来衡量和提升模型的抗攻击能力，这对于保护深度学习系统免受恶意攻击具有重要意义。

DeepFool: a simple and accurate method to fool deep neural networks

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

Ecole Polytechnique F

erale de Lausanne

{seyed.moosavi,alhussein.fawzi,pascal.frossard} at epfl.ch

Abstract

State-of-the-art deep neural networks have achieved im-

pressive results on many image classiﬁcation tasks. How-

ever, these same architectures have been shown to be un-

stable to small, well sought, perturbations of the images.

Despite the importance of this phenomenon, no effective

methods have been proposed to accurately compute the ro-

bustness of state-of-the-art deep classiﬁers to such pertur-

bations on large-scale datasets. In this paper, we ﬁll this

gap and propose the DeepFool algorithm to efﬁciently com-

pute perturbations that fool deep networks, and thus reli-

ably quantify the robustness of these classiﬁers. Extensive

experimental results show that our approach outperforms

recent methods in the task of computing adversarial pertur-

bations and making classiﬁers more robust.

1. Introduction

Deep neural networks are powerful learning models that

achieve state-of-the-art pattern recognition performance in

many research areas such as bioinformatics [1, 16], speech

[12, 6], and computer vision [10, 8]. Though deep net-

works have exhibited very good performance in classiﬁca-

tion tasks, they have recently been shown to be particularly

unstable to adversarial perturbations of the data [18]. In

fact, very small and often imperceptible perturbations of the

data samples are sufﬁcient to fool state-of-the-art classiﬁers

and result in incorrect classiﬁcation. (e.g., Figure 1). For-

mally, for a given classiﬁer, we deﬁne an adversarial per-

turbation as the minimal perturbation r that is sufﬁcient to

change the estimated label

k(x):

∆(x;

k) := min

krk

subject to

k(x + r) 6=

k(x), (1)

where x is an image and

k(x) is the estimated label. We

call ∆(x;

k) the robustness of

k at point x. The robustness

of classiﬁer

k is then deﬁned as

To encourage reproducible research, the code of DeepFool is made

available at http://github.com/lts4/deepfool

Figure 1: An example of adversarial perturbations.

First row: the original image x that is classiﬁed as

k(x)=“whale”. Second row: the image x + r classiﬁed

k(x + r)=“turtle” and the corresponding perturbation r

computed by DeepFool. Third row: the image classiﬁed

as “turtle” and the corresponding perturbation computed

by the fast gradient sign method [4]. DeepFool leads to a

smaller perturbation.

arXiv:1511.04599v3 [cs.LG] 4 Jul 2016

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