  Noise contrastive learning is a popular technique for unsupervised
representation learning. In this approach, a representation is obtained via
reduction to supervised learning, where given a notion of semantic similarity,
the learner tries to distinguish a similar (positive) example from a collection
of random (negative) examples. The success of modern contrastive learning
pipelines relies on many parameters such as the choice of data augmentation,
the number of negative examples, and the batch size; however, there is limited
understanding as to how these parameters interact and affect downstream
performance. We focus on disambiguating the role of one of these parameters:
the number of negative examples. Theoretically, we show the existence of a
collision-coverage trade-off suggesting that the optimal number of negative
examples should scale with the number of underlying concepts in the data.
Empirically, we scrutinize the role of the number of negatives in both NLP and
vision tasks. In the NLP task, we find that the results broadly agree with our
theory, while our vision experiments are murkier with performance sometimes
even being insensitive to the number of negatives. We discuss plausible
explanations for this behavior and suggest future directions to better align
theory and practice.
