We develop tools for explicitly constructing categories enriched over generating data and that compose via ordinary scalar and matrix arithmetic arithmetic operations. We characterize meaningful size maps, weightings, and magnitude that reveal features analogous to outliers that these same notions have previously been shown to reveal in the context of metric spaces. Throughout, we provide examples of such "outlier detection" relevant to the analysis of computer programs, neural networks, cyber-physical systems, and networks of communications channels.

翻译：我们开发了用于显式构造生成数据上的丰富范畴的工具，这些范畴通过普通的标量和矩阵算术运算进行组合。我们刻画了有意义的规模映射、加权和量级，这些揭示了类似于异常值的特征——这些概念此前在度量空间背景下已被证明能揭示此类特征。全文提供了与计算机程序、神经网络、信息物理系统及通信信道网络分析相关的此类“异常检测”示例。