  In this paper, we explore the application of mean field theory, a technique
from statistical physics, to deep metric learning and address the high training
complexity commonly associated with conventional metric learning loss
functions. By adapting mean field theory for deep metric learning, we develop
an approach to design classification-based loss functions from pair-based ones,
which can be considered complementary to the proxy-based approach. Applying the
mean field theory to two pair-based loss functions, we derive two new loss
functions, MeanFieldContrastive and MeanFieldClassWiseMultiSimilarity losses,
with reduced training complexity. We extensively evaluate these derived loss
functions on three image-retrieval datasets and demonstrate that our loss
functions outperform baseline methods in two out of the three datasets.
