  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.
