This was a really cool-to-me paper that asked whether contrastive losses, of the kind that have found widespread success in semi-supervised domains, can add value in a supervised setting as well. In a semi-supervised context, contrastive loss works by pushing together the representations of an "anchor" data example with an augmented version of itself (which is taken as a positive or target, because the image is understood to not be substantively changed by being augmented), and pushing the representation of that example away from other examples in the batch, which are negatives in the sense that they are assumed to not be related to the anchor image. 

This paper investigates whether this same structure - of training representations of positives to be close relative to negatives - could be expanded to the supervised setting, where "positives" wouldn't just mean augmented versions of a single image, but augmented versions of other images belonging to the same class. This would ideally combine the advantages of self-supervised contrastive loss - that explicitly incentivizes invariance to augmentation-based changes - with the advantages of a supervised signal, which allows the representation to learn that it should also see instances of the same class as close to one another. 

https://i.imgur.com/pzKXEkQ.png

To evaluate the performance of this as a loss function, the authors first train the representation - either with their novel supervised contrastive loss SupCon, or with a control cross-entropy loss - and then train a linear regression with cross-entropy on top of that learned representation. (Just because, structurally, a contrastive loss doesn't lead to assigning probabilities to particular classes, even if it is supervised in the sense of capturing information relevant to classification in the representation) 

The authors investigate two versions of this contrastive loss, which differ, as shown below, in terms of the relative position of the sum and the log operation, and show that the L_out version dramatically outperforms (and I mean dramatically, with a top-one accuracy of 78.7 vs 67.4%). 

https://i.imgur.com/X5F1DDV.png

The authors suggest that the L_out version is superior in terms of training dynamics, and while I didn't fully follow their explanation, I believe it had to do with L_out version doing its normalization outside of the log, which meant it actually functioned as a multiplicative normalizer, as opposed to happening inside the log, where it would have just become an additive (or, really, subtractive) constant in the gradient term. Due to this stronger normalization, the authors positive the L_out loss was less noisy and more stable. 

Overall, the authors show that SupCon consistently (if not dramatically) outperforms cross-entropy when it comes to final accuracy. They also show that it is comparable in transfer performance to a self-supervised contrastive loss. One interesting extension to this work, which I'd enjoy seeing more explored in the future, is how the performance of this sort of loss scales with the number of different augmentations that performed of each element in the batch (this work uses two different augmentations, but there's no reason this number couldn't be higher, which would presumably give additional useful signal and robustness?)