We present a novel framework for learning system design based on neural feature extractors. First, we introduce the feature geometry, which unifies statistical dependence and features in the same function 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 applications 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：我们提出了一种基于神经特征提取器的学习系统设计新框架。首先，引入特征几何概念，该概念在具有几何结构的同一函数空间中统一了统计依赖性与特征。通过应用特征几何，我们将每个学习问题转化为求解由学习设定指定的依赖分量的最优特征逼近问题。我们提出一种嵌套技术用于设计从数据样本中学习最优特征的学习算法，该技术可直接应用于现成的网络架构与优化器。为展示嵌套技术的应用，我们进一步讨论了多变量学习问题，包括条件推断与多模态学习，其中给出了最优特征并揭示了其与经典方法的联系。