It is a known phenomenon that adversarial robustness comes at a cost to natural accuracy. To improve this trade-off, this paper proposes an ensemble approach that divides a complex robust-classification task into simpler subtasks. Specifically, fractal divide derives multiple training sets from the training data, and fractal aggregation combines inference outputs from multiple classifiers that are trained on those sets. The resulting ensemble classifiers have a unique property that ensures robustness for an input if certain don't-care conditions are met. The new techniques are evaluated on MNIST and Fashion-MNIST, with no adversarial training. The MNIST classifier has 99% natural accuracy, 70% measured robustness and 36.9% provable robustness, within L2 distance of 2. The Fashion-MNIST classifier has 90% natural accuracy, 54.5% measured robustness and 28.2% provable robustness, within L2 distance of 1.5. Both results are new state of the art, and we also present new state-of-the-art binary results on challenging label-pairs.
翻译:已知的现象是, 对抗性稳健性会以自然准确性为代价。 为了改进这一权衡, 本文件建议采用混合方法, 将复杂的强势分类任务分成更简单的子任务。 具体地说, 分形分解从培训数据中产生多种培训组合, 分形汇总结合了用这些组合培训的多个分类者的推断结果。 结果的混合分类者具有独特的属性, 如果某些不看病的条件得到满足, 可以确保输入的稳健性。 新技术在MNIST和时装- MNIST上进行了评价, 没有经过任何培训。 MNIST 分类者有99% 的自然精度、 70% 的测量稳健性和 36.9% 的可辨识性, 在 2 的L2 距离内, 时装- MNIST 分类者有90% 的自然精度、 54.5% 的测量稳健性和28.2% 的可辨识强性, 在1.5 的L2 距离内。 这两种结果都是艺术的新状态, 我们还展示了具有挑战性标签的新型的状态二进制结果。