Variance-Invariance-Covariance Regularization for Self-Supervised Learning

Labelled data is expensive, which makes benefiting from the current success in supervised learning unfeasible for smaller companies.

However, good representations can be learned without any task-specific information from raw data.

In self-supervised learning, labels are generated artificially. A common approach is to take multiple augmented views from the same source and contrast them to different sources.

Many papers have proven that simply increasing the similarity (decreasing the distance in the embedding space) of such views from the same source can lead to strong representations.

Good representations are expressive and make efficient use of the given dimensionality.

We want the representations to be variant to contextual changes that are essential to a task and invariant to changes related to factors that we cannot control nor care about. 

While these invariances can largely be enforced through task-specific data augmentation, the efficient use of the dimensionality of the representations has to be achieved through clever algorithms.

One way to look at this quality is through the variance of the representations, which shall not collapse for a given class of inputs.