Data-Error Scaling Laws in Machine Learning on Combinatorial Mutation-prone Sets: Proteins and Small Molecules

We investigate trends in the data-error scaling laws of machine learning (ML) models trained on discrete combinatorial spaces that are prone-to-mutation, such as proteins or organic small molecules. We trained and evaluated kernel ridge regression machines using variable amounts of computational and experimental training data. Our synthetic datasets comprised i) two na"ive functions based on many-body theory; ii) binding energy estimates between a protein and a mutagenised peptide; and iii) solvation energies of two 6-heavy atom structural graphs, while the experimental dataset consisted of a full deep mutational scan of the binding protein GB1. In contrast to typical data-error scaling laws, our results showed discontinuous monotonic phase transitions during learning, observed as rapid drops in the test error at particular thresholds of training data. We observed two learning regimes, which we call saturated and asymptotic decay, and found that they are conditioned by the level of complexity (i.e. number of mutations) enclosed in the training set. We show that during training on this class of problems, the predictions were clustered by the ML models employed in the calibration plots. Furthermore, we present an alternative strategy to normalize learning curves (LCs) and introduce the concept of mutant-based shuffling. This work has implications for machine learning on mutagenisable discrete spaces such as chemical properties or protein phenotype prediction, and improves basic understanding of concepts in statistical learning theory.