论文标题
大多数Relu网络遭受$ \ ell^2 $对抗性扰动
Most ReLU Networks Suffer from $\ell^2$ Adversarial Perturbations
论文作者
论文摘要
我们考虑具有随机权重的Relu网络，其中尺寸在每一层下降。我们表明，对于大多数这样的网络，大多数示例$ x $在欧几里得的距离为$ o \ left的距离（\ frac {\ | x \ |} {\ sqrt {d}}} \ right）$，其中$ d $是输入点。此外，可以通过梯度流以及足够小的步骤来发现这种扰动。这一结果可以看作是对丰富的对抗性例子的解释，以及通过梯度下降发现它们的事实。
We consider ReLU networks with random weights, in which the dimension decreases at each layer. We show that for most such networks, most examples $x$ admit an adversarial perturbation at an Euclidean distance of $O\left(\frac{\|x\|}{\sqrt{d}}\right)$, where $d$ is the input dimension. Moreover, this perturbation can be found via gradient flow, as well as gradient descent with sufficiently small steps. This result can be seen as an explanation to the abundance of adversarial examples, and to the fact that they are found via gradient descent.
