Paper:
Many recent methods for unsupervised or self-supervised representation learning train feature extractors by maximizing an estimate of the mutual information (MI) between different views of the data. This comes with several immediate problems: For example, MI is notoriously hard to estimate, and using it as an objective for representation learning may lead to highly entangled representations due to its invariance under arbitrary invertible transformations. Nevertheless, these methods have been repeatedly shown to excel in practice. In this paper we argue, and provide empirical evidence, that the success of these methods cannot be attributed to the properties of MI alone, and that they strongly depend on the inductive bias in both the choice of feature extractor architectures and the parametrization of the employed MI estimators. Finally, we establish a connection to deep metric learning and argue that this interpretation may be a plausible explanation for the success of the recently introduced methods.

Review:
The paper addresses a question on whether mutual information (MI) based models for representation learning succeed primarily thanks to the MI maximization. The motivation of the work comes from the fact that although MI is known to be problematic in treatment, it has been successfully applied in a number of recent works in computer vision and natural language processing. The paper conducts a series of experiments that constitute a convincing evidence for a weak connection between the InfoMax principle and these practical successes by showing that maximizing established lower bounds on MI are not predictive of the downstream performance and that contrary to the theory higher capacity instantiations of the critics of MI may result in worse downstream performance of learned representations. The paper concludes that there is a considerable inductive bias in the architectural choices inside MI models that are beneficial for downstream tasks and note that at least one of the lower bounds on MI can be interpreted as a triplet loss connecting it with a metric learning approach.
I consider this paper to be a considerable contribution to the understanding of what underlies the performance of unsupervised representation learning with MI maximization and provides a good discussion and analogous insights from parallel works and a number of possible directions to explore. Although I still have a couple of questions addressing which will help to understand the paper.
-  In experiment 3.1, when using RealNVP and maximizing the lower bound of MI may it be the case that the representations are learned to benefit the downstream task because of the form of the lower bounds? In other words, the lower bound is possibly not very tight and its maximization has a side effect of weights adjusting to yield simple representations useful for a linear classifier?
-  It would be interesting to see which factor contributes more to the performance: I_NCE being a triplet loss or an inductive bias in the design choice?