论文标题
当地鲁棒性认证的快速几何预测
Fast Geometric Projections for Local Robustness Certification
论文作者
论文摘要
局部鲁棒性可确保模型一致地将$ \ ell_2 $ - 球中的所有输入分类，这排除了各种形式的对抗输入。在本文中，我们提出了一个快速的程序，用于检查具有分段线性激活函数的前馈神经网络中的局部鲁棒性。这样的网络将输入空间分配到网络行为是线性的一组凸的多面体区域中；因此，在给定输入周围区域内对决策边界进行系统的搜索足以评估鲁棒性。至关重要的是，我们展示了如何使用简单的几何预测来分析某个点周围的区域，从而承认有效的高度平行的GPU实现，特别是对于$ \ ell_2 $ norm，在先前的工作效果较低的情况下，尤其是对$ \ ell_2 $ norm的表现。从经验上讲，我们发现这种方法比许多近似验证方法要精确得多，而同时执行多个数量级的速度比完整的验证仪更快，并扩展到更深的网络。
Local robustness ensures that a model classifies all inputs within an $\ell_2$-ball consistently, which precludes various forms of adversarial inputs. In this paper, we present a fast procedure for checking local robustness in feed-forward neural networks with piecewise-linear activation functions. Such networks partition the input space into a set of convex polyhedral regions in which the network's behavior is linear; hence, a systematic search for decision boundaries within the regions around a given input is sufficient for assessing robustness. Crucially, we show how the regions around a point can be analyzed using simple geometric projections, thus admitting an efficient, highly-parallel GPU implementation that excels particularly for the $\ell_2$ norm, where previous work has been less effective. Empirically we find this approach to be far more precise than many approximate verification approaches, while at the same time performing multiple orders of magnitude faster than complete verifiers, and scaling to much deeper networks.
