  Contrastive Learning has shown impressive results on natural and medical
images, without requiring annotated data. However, a particularity of medical
images is the availability of meta-data (such as age or sex) that can be
exploited for learning representations. Here, we show that the recently
proposed contrastive y-Aware InfoNCE loss, that integrates multi-dimensional
meta-data, asymptotically optimizes two properties: conditional alignment and
global uniformity. Similarly to [Wang, 2020], conditional alignment means that
similar samples should have similar features, but conditionally on the
meta-data. Instead, global uniformity means that the (normalized) features
should be uniformly distributed on the unit hyper-sphere, independently of the
meta-data. Here, we propose to define conditional uniformity, relying on the
meta-data, that repel only samples with dissimilar meta-data. We show that
direct optimization of both conditional alignment and uniformity improves the
representations, in terms of linear evaluation, on both CIFAR-100 and a brain
MRI dataset.
