In self-supervised contrastive learning, negative pairs are typically constructed using an anchor image and a sample drawn from the entire dataset, excluding the anchor. However, this approach can result in the creation of negative pairs with similar semantics, referred to as "false negatives", leading to their embeddings being falsely pushed apart. To address this issue, we introduce GloFND, an optimization-based approach that automatically learns on the fly the threshold for each anchor data to identify its false negatives during training. In contrast to previous methods for false negative discovery, our approach globally detects false negatives across the entire dataset rather than locally within the mini-batch. Moreover, its per-iteration computation cost remains independent of the dataset size. Experimental results on image and image-text data demonstrate the effectiveness of the proposed method. Our implementation is available at https://github.com/vibalcam/GloFND.

We study the performance of optimal mass transport-based methods applied to point-set matching problems. The present study, which is based on the L2 mass transport cost, states that perfect matches always occur when the product of the point-set cardinality and the norm of the curl of the non-rigid deformation field does not exceed some constant. This analytic result is justified by a numerical study of matching two sets of pulmonary vascular tree branch points whose displacement is caused by the lung volume changes in the same human subject. The nearly perfect match performance verifies the effectiveness of this mass transport-based approach.