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Self-supervised representation learning has made significant leaps fueled by progress in contrastive learning, which seeks to learn transformations that embed positive input pairs nearby, while pushing negative pairs far apart. While positive pairs can be generated reliably (e.g., as different views of the same image), it is difficult to accurately establish negative pairs, defined as samples from different images regardless of their semantic content or visual features. A fundamental problem in contrastive learning is mitigating the effects of false negatives. Contrasting false negatives induces two critical issues in representation learning: discarding semantic information and slow convergence. In this paper, we propose novel approaches to identify false negatives, as well as two strategies to mitigate their effect, i.e. false negative elimination and attraction, while systematically performing rigorous evaluations to study this problem in detail. Our method exhibits consistent improvements over existing contrastive learning-based methods. Without labels, we identify false negatives with 40% accuracy among 1000 semantic classes on ImageNet, and achieve 5.8% absolute improvement in top-1 accuracy over the previous state-of-the-art when finetuning with 1% labels. Our code is available at https://github.com/google-research/fnc.