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Self-supervised learning (SSL) has great potential for molecularrepresentation learning given the complexity of molecular graphs, the largeamounts of unlabelled data available, the considerable cost of obtaining labelsexperimentally, and the hence often only small training datasets. Theimportance of the topic is reflected in the variety of paradigms andarchitectures that have been investigated recently. Yet the differences inperformance seem often minor and are barely understood to date. In this paper,we study SSL based on persistent homology (PH), a mathematical tool formodeling topological features of data that persist across multiple scales. Ithas several unique features which particularly suit SSL, naturally offering:different views of the data, stability in terms of distance preservation, andthe opportunity to flexibly incorporate domain knowledge. We (1) investigate anautoencoder, which shows the general representational power of PH, and (2)propose a contrastive loss that complements existing approaches. We rigorouslyevaluate our approach for molecular property prediction and demonstrate itsparticular features in improving the embedding space: after SSL, therepresentations are better and offer considerably more predictive power thanthe baselines over different probing tasks; our loss increases baselineperformance, sometimes largely; and we often obtain substantial improvementsover very small datasets, a common scenario in practice.

Improving Self-supervised Molecular Representation Learning using Persistent Homology