Do More Negative Samples Necessarily Hurt In Contrastive Learning?
Pranjal Awasthi,u00a0Nishanth Dikkala,u00a0Pritish Kamath
Recent investigations in noise contrastive estimation suggest, both empirically as well as theoretically, that while having more u201cnegative samplesu201d in the contrastive loss improves downstream classification performance initially, beyond a threshold, it hurts downstream performance due to a u201ccollision-coverageu201d trade-off. But is such a phenomenon inherent in contrastive learning? We show in a simple theoretical setting, where positive pairs are generated by sampling from the underlying latent class (introduced by Saunshi et al. (ICML 2019)), that the downstream performance of the representation optimizing the (population) contrastive loss in fact does not degrade with the number of negative samples. Along the way, we give a structural characterization of the optimal representation in our framework, for noise contrastive estimation. We also provide empirical support for our theoretical results on CIFAR-10 and CIFAR-100 datasets.