EMC$^2$: Efficient MCMC Negative Sampling for Contrastive Learning with Global Convergence
<|reference_start|>EMC$^2$: 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 (EMC$^2$). We follow the global contrastive learning loss as introduced in SogCLR, and propose EMC$^2$ which utilizes an adaptive Metropolis-Hastings subroutine to generate hardness-aware negative samples in an online fashion during the optimization. We prove that EMC$^2$ finds an $\mathcal{O}(1/\sqrt{T})$-stationary point of the global contrastive loss in $T$ iterations. Compared to prior works, EMC$^2$ 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 EMC$^2$ 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.<|reference_end|>
@article{yau2024emc$^2$:,
    title={EMC$^2$: Efficient MCMC Negative Sampling for Contrastive Learning with
  Global Convergence},
    author={Chung-Yiu Yau, Hoi-To Wai, Parameswaran Raman, Soumajyoti Sarkar,
  Mingyi Hong},
    journal={arXiv preprint arXiv:2404.10575},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.10575},
    primaryClass={cs.LG cs.AI cs.CV math.OC}
}