Improving Calibration in Deep Metric Learning With Cross-Example Softmax

Modern image retrieval systems increasingly rely on the use of deep neural networks to learn embedding spaces in which distance encodes the relevance between a given query and image. In this setting, existing approaches tend to emphasize one of two properties. Triplet-based methods capture top-$k$ relevancy, where all top-$k$ scoring documents are assumed to be relevant to a given query Pairwise contrastive models capture threshold relevancy, where all documents scoring higher than some threshold are assumed to be relevant. In this paper, we propose Cross-Example Softmax which combines the properties of top-$k$ and threshold relevancy. In each iteration, the proposed loss encourages all queries to be closer to their matching images than all queries are to all non-matching images. This leads to a globally more calibrated similarity metric and makes distance more interpretable as an absolute measure of relevance. We further introduce Cross-Example Negative Mining, in which each pair is compared to the hardest negative comparisons across the entire batch. Empirically, we show in a series of experiments on Conceptual Captions and Flickr30k, that the proposed method effectively improves global calibration and also retrieval performance.