  Contrastive learning has emerged as a cornerstone in recent achievements of
unsupervised representation learning. Its primary paradigm involves an instance
discrimination task with a mutual information loss. The loss is known as
InfoNCE and it has yielded vital insights into contrastive learning through the
lens of mutual information analysis. However, the estimation of mutual
information can prove challenging, creating a gap between the elegance of its
mathematical foundation and the complexity of its estimation. As a result,
drawing rigorous insights or conclusions from mutual information analysis
becomes intricate. In this study, we introduce three novel methods and a few
related theorems, aimed at enhancing the rigor of mutual information analysis.
Despite their simplicity, these methods can carry substantial utility.
Leveraging these approaches, we reassess three instances of contrastive
learning analysis, illustrating their capacity to facilitate deeper
comprehension or to rectify pre-existing misconceptions. Specifically, we
investigate small batch size, mutual information as a measure, and the InfoMin
principle.
