论文标题
基于软马克斯的分类是K-均值聚类：正式证明，对抗攻击的后果以及通过基于Centroid的裁缝改进
Softmax-based Classification is k-means Clustering: Formal Proof, Consequences for Adversarial Attacks, and Improvement through Centroid Based Tailoring
论文作者
论文摘要
我们正式证明了K均值聚类与基于SoftMax激活层的神经网络的预测之间的联系。在现有工作中，这种联系已通过经验进行了分析，但从未有过数学上得出。 SoftMax函数将转换后的输入空间划分为锥体，每个空间都包含一个类。这相当于将许多质心放在与原点相等距离的转换空间中，而K-均值通过与这些质心的接近度聚集了数据点。 SoftMax仅关心锥度数据点的位置，而距离该锥体内的质心有多远。我们正式证明具有小Lipschitz模量的网络（对应于对对抗攻击的低敏感性）地图数据点靠近群集质心，这导致映射到k-means友好的空间。为了利用这些知识，我们建议基于质心的剪裁作为神经网络最后一层中软磁性功能的替代方案。由此产生的高斯网络具有与传统网络相似的预测准确性，但不容易受到单像素攻击的影响。尽管本文的主要贡献本质上是理论上的，但高斯网络贡献了经验辅助利益。
We formally prove the connection between k-means clustering and the predictions of neural networks based on the softmax activation layer. In existing work, this connection has been analyzed empirically, but it has never before been mathematically derived. The softmax function partitions the transformed input space into cones, each of which encompasses a class. This is equivalent to putting a number of centroids in this transformed space at equal distance from the origin, and k-means clustering the data points by proximity to these centroids. Softmax only cares in which cone a data point falls, and not how far from the centroid it is within that cone. We formally prove that networks with a small Lipschitz modulus (which corresponds to a low susceptibility to adversarial attacks) map data points closer to the cluster centroids, which results in a mapping to a k-means-friendly space. To leverage this knowledge, we propose Centroid Based Tailoring as an alternative to the softmax function in the last layer of a neural network. The resulting Gauss network has similar predictive accuracy as traditional networks, but is less susceptible to one-pixel attacks; while the main contribution of this paper is theoretical in nature, the Gauss network contributes empirical auxiliary benefits.
