  We investigate trends in the data-error scaling behavior 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
computationally generated training data. Our synthetic datasets comprise 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. In contrast to typical data-error scaling, 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 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.
