标题： 面向鲁棒的深度神经网络 显示英文标题

标题： Towards Robust Deep Neural Networks

摘要： 我们研究前馈和卷积神经网络中的敏感性和鲁棒性问题。 结合计算化学中开发的能量景观技术以及来自形式方法的工具，我们提供了实证证据，表明在学习目标的优化景观中处于较低极小值的网络往往更鲁棒。 使用的鲁棒性估计是所提出的敏感性度量的倒数，我们将其定义为在所有加法$l_{\infty}$-有界扰动下的网络输出可达集的超近似体积。 我们提出了一种新颖的损失函数，除了传统的任务导向项和正则化项外，还包括一个敏感性项。 在标准机器学习和计算机视觉数据集上的实验中，我们展示了所提出的损失函数能够使网络可靠地优化鲁棒性度量以及其他相关的对抗鲁棒性指标，而不会显著降低分类误差。 实验结果表明，与基于敏感性的最新学习方法相比，所提出的方法在对抗攻击的鲁棒性方面表现更好。 我们还证明了尽管引入的框架并未显式强制对抗损失，但它相对于那些包含对抗损失的方法表现出具有竞争力的整体性能。 显示英文摘要

摘要： We investigate the topics of sensitivity and robustness in feedforward and convolutional neural networks. Combining energy landscape techniques developed in computational chemistry with tools drawn from formal methods, we produce empirical evidence indicating that networks corresponding to lower-lying minima in the optimization landscape of the learning objective tend to be more robust. The robustness estimate used is the inverse of a proposed sensitivity measure, which we define as the volume of an over-approximation of the reachable set of network outputs under all additive $l_{\infty}$-bounded perturbations on the input data. We present a novel loss function which includes a sensitivity term in addition to the traditional task-oriented and regularization terms. In our experiments on standard machine learning and computer vision datasets, we show that the proposed loss function leads to networks which reliably optimize the robustness measure as well as other related metrics of adversarial robustness without significant degradation in the classification error. Experimental results indicate that the proposed method outperforms state-of-the-art sensitivity-based learning approaches with regards to robustness to adversarial attacks. We also show that although the introduced framework does not explicitly enforce an adversarial loss, it achieves competitive overall performance relative to methods that do.