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.

翻译：我们提出了一种新的学习系统设计框架，该框架通过利用特征空间中的几何结构，基于神经特征提取器实现。首先，我们引入特征几何概念，它统一了统计依赖性与特征在同一函数空间中的几何结构。通过应用特征几何，我们将每个学习问题转化为求解学习设定所指定的依赖分量的最优特征逼近。我们提出了一种嵌套技巧，用于设计从数据样本中学习最优特征的学习算法，该技巧可应用于现成的网络架构和优化器。为了展示嵌套技巧的应用，我们进一步讨论了多变量学习问题，包括条件推理和多模态学习，其中我们提出了最优特征并揭示了它们与经典方法的联系。