Deep networks typically learn concepts via classifiers, which involves
setting up a model and training it via gradient descent to fit the
concept-labeled data. We will argue instead that learning a concept could be
done by looking at its moment statistics matrix to generate a concrete
representation or signature of that concept. These signatures can be used to
discover structure across the set of concepts and could recursively produce
higher-level concepts by learning this structure from those signatures. When
the concepts are `intersected', signatures of the concepts can be used to find
a common theme across a number of related `intersected' concepts. This process
could be used to keep a dictionary of concepts so that inputs could correctly
identify and be routed to the set of concepts involved in the (latent)
generation of the input.

利用深度网络，基于概念分类器通过梯度下降的训练，我们提出通过观察概念的矩阵统计特征来生成其具体表示或特征签名，进而发现概念集合之间的结构，并通过学习这些特征签名的结构递归生成更高级的概念。当概念相交时，利用概念的特征签名可以找到一种共同主题，并可用于建立概念字典，从而使输入正确识别和路由到参与生成输入的概念集合。