  Self-supervised learning (SSL) has great potential for molecular
representation learning given the complexity of molecular graphs, the large
amounts of unlabelled data available, the considerable cost of obtaining labels
experimentally, and the hence often only small training datasets. The
importance of the topic is reflected in the variety of paradigms and
architectures that have been investigated recently. Yet the differences in
performance seem often minor and are barely understood to date. In this paper,
we study SSL based on persistent homology (PH), a mathematical tool for
modeling topological features of data that persist across multiple scales. It
has several unique features which particularly suit SSL, naturally offering:
different views of the data, stability in terms of distance preservation, and
the opportunity to flexibly incorporate domain knowledge. We (1) investigate an
autoencoder, which shows the general representational power of PH, and (2)
propose a contrastive loss that complements existing approaches. We rigorously
evaluate our approach for molecular property prediction and demonstrate its
particular features in improving the embedding space: after SSL, the
representations are better and offer considerably more predictive power than
the baselines over different probing tasks; our loss increases baseline
performance, sometimes largely; and we often obtain substantial improvements
over very small datasets, a common scenario in practice.
