Learning with supervision has achieved remarkable success in numerous artificial intelligence (AI) applications. In the current literature, by referring to the properties of the labels prepared for the training dataset, learning with supervision is categorized as supervised learning (SL) and weakly supervised learning (WSL). SL concerns the situation where the training data set is assigned with ideal (complete, exact and accurate) labels, while WSL concerns the situation where the training data set is assigned with non-ideal (incomplete, inexact or inaccurate) labels. However, various solutions for SL tasks have shown that the given labels are not always easy to learn, and the transformation from the given labels to easy-to-learn targets can significantly affect the performance of the final SL solutions. Without considering the properties of the transformation from the given labels to easy-to-learn targets, the definition of SL conceals some details that can be critical to building the appropriate solutions for specific SL tasks. Thus, for engineers in the AI application field, it is desirable to reveal these details systematically. This article attempts to achieve this goal by expanding the categorization of SL and investigating the sub-type moderately supervised learning (MSL) that concerns the situation where the given labels are ideal, but due to the simplicity in annotation, careful designs are required to transform the given labels into easy-to-learn targets. From the perspectives of the definition, framework and generality, we conceptualize MSL to present a complete fundamental basis to systematically analyse MSL tasks. At meantime, revealing the relation between the conceptualization of MSL and the mathematicians' vision, this paper as well establishes a tutorial for AI application engineers to refer to viewing a problem to be solved from the mathematicians' vision.

翻译：带监督的学习在众多人工智能应用中取得了显著成功。在现有文献中，依据为训练数据集准备的标签属性，带监督的学习被分为监督学习和弱监督学习。监督学习关注训练数据集被赋予理想（完备、确切且准确）标签的情形，而弱监督学习则关注训练数据集被赋予非理想（不完备、不确切或不准确）标签的情形。然而，针对监督学习任务的各种解决方案表明，给定的标签并非总是易于学习，而从给定标签到易学目标的转换会显著影响最终监督学习解决方案的性能。若不考虑从给定标签到易学目标的转换属性，监督学习的定义会隐藏一些对构建特定监督学习任务的适当解决方案至关重要的细节。因此，对于人工智能应用领域的工程师而言，系统地揭示这些细节是值得期望的。本文试图通过扩展监督学习的分类，并研究子类型——适度监督学习（MSL）——来实现这一目标。适度监督学习关注给定标签是理想的，但由于标注方式简单，需要精心设计才能将给定标签转化为易学目标的情形。我们从定义、框架和普适性的角度对MSL进行概念化，为系统分析MSL任务提供一个完整的基础。同时，本文揭示了MSL概念化与数学家视角之间的关系，为AI应用工程师建立了一个参考教程，使其能从数学家的视角审视待解决的问题。