Learning from set-structured data is a fundamental problem that has recently attracted increasing attention, where a series of summary networks are introduced to deal with the set input. In fact, many meta-learning problems can be treated as set-input tasks. Most existing summary networks aim to design different architectures for the input set in order to enforce permutation invariance. However, scant attention has been paid to the common cases where different sets in a meta-distribution are closely related and share certain statistical properties. Viewing each set as a distribution over a set of global prototypes, this paper provides a novel prototype-oriented optimal transport (POT) framework to improve existing summary networks. To learn the distribution over the global prototypes, we minimize its regularized optimal transport distance to the set empirical distribution over data points, providing a natural unsupervised way to improve the summary network. Since our plug-and-play framework can be applied to many meta-learning problems, we further instantiate it to the cases of few-shot classification and implicit meta generative modeling. Extensive experiments demonstrate that our framework significantly improves the existing summary networks on learning more powerful summary statistics from sets and can be successfully integrated into metric-based few-shot classification and generative modeling applications, providing a promising tool for addressing set-input and meta-learning problems.

翻译：从集合结构数据中学习是一个基础问题，近年来日益受到关注，其中一系列摘要网络被引入以处理集合输入。事实上，许多元学习问题可视为集合输入任务。现有的大多数摘要网络旨在为输入集合设计不同的架构以强制实现排列不变性。然而，对于元分布中不同集合紧密相关且共享某些统计属性的常见情况，鲜有关注。本文将每个集合视为一组全局原型上的分布，提出了一种新颖的原型导向最优传输（POT）框架来改进现有摘要网络。为了学习全局原型上的分布，我们最小化其与数据点上的集合经验分布之间的正则化最优传输距离，这提供了一种自然的无监督方式来改进摘要网络。由于我们的即插即用框架可应用于许多元学习问题，我们进一步将其实例化为少样本分类和隐式元生成建模的情况。大量实验表明，我们的框架显著改进了现有摘要网络从集合中学习更强大的摘要统计量的能力，并能够成功集成到基于度量的少样本分类和生成建模应用中，为处理集合输入和元学习问题提供了一种有前景的工具。