Shape is (almost) all!: Persistent homology features (PHFs) are an information rich input for efficient molecular machine learning

3-D shape is important to chemistry, but how important? Machine learning works best when the inputs are simple and match the problem well. Chemistry datasets tend to be very small compared to those generally used in machine learning so we need to get the most from each datapoint. Persistent homology measures the topological shape properties of point clouds at different scales and is used in topological data analysis. Here we investigate what persistent homology captures about molecular structure and create persistent homology features (PHFs) that encode a molecule's shape whilst losing most of the symbolic detail like atom labels, valence, charge, bonds etc. We demonstrate the usefulness of PHFs on a series of chemical datasets: QM7, lipophilicity, Delaney and Tox21. PHFs work as well as the best benchmarks. PHFs are very information dense and much smaller than other encoding methods yet found, meaning ML algorithms are much more energy efficient. PHFs success despite losing a large amount of chemical detail highlights how much of chemistry can be simplified to topological shape.