EMC²: Efficient MCMC Negative Sampling for Contrastive Learning with Global Convergence

A key challenge in contrastive learning is to generate negative samples from a large sample set to contrast with positive samples, for learning better encoding of the data. These negative samples often follow a softmax distribution which are dynamically updated during the training process. However, sampling from this distribution is non-trivial due to the high computational costs in computing the partition function. In this paper, we propose an Efficient Markov Chain Monte Carlo negative sampling method for Contrastive learning (EMC²). We follow the global contrastive learning loss as introduced in (Yuan et al., 2022), and propose EMC² which utilizes an adaptive Metropolis-Hastings subroutine to generate hardness-aware negative samples in an online fashion during the optimization. We prove that EMC² finds an O(1/^√T)-stationary point of the global contrastive loss in T iterations. Compared to prior works, EMC² is the first algorithm that exhibits global convergence (to stationarity) regardless of the choice of batch size while exhibiting low computation and memory cost. Numerical experiments validate that EMC² is effective with small batch training and achieves comparable or better performance than baseline algorithms. We report the results for pre-training image encoders on STL-10 and Imagenet-100.