  This paper proposes a probabilistic contrastive loss function for
self-supervised learning. The well-known contrastive loss is deterministic and
involves a temperature hyperparameter that scales the inner product between two
normed feature embeddings. By reinterpreting the temperature hyperparameter as
a quantity related to the radius of the hypersphere, we derive a new loss
function that involves a confidence measure which quantifies uncertainty in a
mathematically grounding manner. Some intriguing properties of the proposed
loss function are empirically demonstrated, which agree with human-like
predictions. We believe the present work brings up a new prospective to the
area of contrastive learning.
