Many recent efforts have been devoted to designing sophisticated deep
learning structures, obtaining revolutionary results on benchmark datasets. The
success of these deep learning methods mostly relies on an enormous volume of
labeled training samples to learn a huge number of parameters in a network;
therefore, understanding the generalization ability of a learned deep network
cannot be overlooked, especially when restricted to a small training set, which
is the case for many applications. In this paper, we propose a novel deep
learning objective formulation that unifies both the classification and metric
learning criteria. We then introduce a geometry-aware deep transform to enable
a non-linear discriminative and robust feature transform, which shows
competitive performance on small training sets for both synthetic and
real-world data. We further support the proposed framework with a formal
$(K,\epsilon)$-robustness analysis.

该文章提出了一种新的深度学习目标公式，在小训练集合的情况下能够使得其学习到的深层网络具有较好的泛化能力，同时介绍了一种基于几何感知的深度转换技术，从而实现了非线性、具有鲁棒性的特征转换，该方法在合成和真实数据方面表现良好，并支持所提出的框架使用 (K,ε)- 鲁棒性分析。