  Similarity learning is a general problem to elicit useful representations by
predicting the relationship between a pair of patterns. This problem is related
to various important preprocessing tasks such as metric learning, kernel
learning, and contrastive learning. A classifier built upon the representations
is expected to perform well in downstream classification; however, little
theory has been given in literature so far and thereby the relationship between
similarity and classification has remained elusive. Therefore, we tackle a
fundamental question: can similarity information provably leads a model to
perform well in downstream classification? In this paper, we reveal that a
product-type formulation of similarity learning is strongly related to an
objective of binary classification. We further show that these two different
problems are explicitly connected by an excess risk bound. Consequently, our
results elucidate that similarity learning is capable of solving binary
classification by directly eliciting a decision boundary.
