We present a novel framework for learning system design based on neural
feature extractors by exploiting geometric structures in feature spaces. First,
we introduce the feature geometry, which unifies statistical dependence and
features in the same functional space with geometric structures. By applying
the feature geometry, we formulate each learning problem as solving the optimal
feature approximation of the dependence component specified by the learning
setting. We propose a nesting technique for designing learning algorithms to
learn the optimal features from data samples, which can be applied to
off-the-shelf network architectures and optimizers. To demonstrate the
application of the nesting technique, we further discuss multivariate learning
problems, including conditioned inference and multimodal learning, where we
present the optimal features and reveal their connections to classical
approaches.

基于神经特征提取器和图形结构，我们提出了一个新颖的学习系统设计框架，并使用特征空间中的几何结构进行学习问题的建模。我们通过嵌套技术设计学习算法，从数据样本中学习最佳特征，进而应用于现成的网络架构和优化器，同时我们还探讨了多元学习问题，包括条件推理和多模态学习，以及它们与经典方法的联系。