We propose a scheme for defending against adversarial attacks by suppressing the largest eigenvalue of the Fisher information matrix (FIM). Our starting point is one explanation on the rationale of adversarial examples. Based on the idea of the difference between a benign sample and its adversarial example is measured by the Euclidean norm, while the difference between their classification probability densities at the last (softmax) layer of the network could be measured by the Kullback-Leibler (KL) divergence, the explanation shows that the output difference is a quadratic form of the input difference. If the eigenvalue of this quadratic form (a.k.a. FIM) is large, the output difference becomes large even when the input difference is small, which explains the adversarial phenomenon. This makes the adversarial defense possible by controlling the eigenvalues of the FIM. Our solution is adding one term representing the trace of the FIM to the loss function of the original network, as the largest eigenvalue is bounded by the trace. Our defensive scheme is verified by experiments using a variety of common attacking methods on typical deep neural networks, e.g. LeNet, VGG and ResNet, with datasets MNIST, CIFAR-10, and German Traffic Sign Recognition Benchmark (GTSRB). Our new network, after adopting the novel loss function and retraining, has an effective and robust defensive capability, as it decreases the fooling ratio of the generated adversarial examples, and remains the classification accuracy of the original network.

提出一种通过抑制 Fisher 信息矩阵的最大特征值来防御对抗攻击的方案，添加 Fisher 信息矩阵的 trace 值到网络的损失函数中，通过实验验证其有效性和鲁棒性。

通过抑制费舍尔信息矩阵的最大特征值来抵御对抗性攻击