Geometry and topology of decision regions are closely related with classification performance robustness against adversarial attacks. In this paper, we use differential geometry to theoretically explore the geometrical topological properties produced by deep neural networks (DNNs). The goal is obtain some boundaries for given DNN models, provide principled guidance design regularization DNNs. F...

In this paper a geometric calculator is presented. A language of geometrical expressions, that are evaluated by the calculator, and the design and implementation of its interpreter is also presented. Geometrical expressions correspond to abstract data-types that can be defined dynamically through composition operations. Diagrams can be represented by a set of geometrical expressions, and the ge...