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.

通过研究在蛋白质或有机小分子等易突变的离散组合空间中训练的机器学习（ML）模型的数据误差缩放行为的趋势，我们发现了学习过程中出现的不连续的单调阶跃现象，其表现为特定训练数据阈值时测试误差的快速下降。我们发现了饱和和渐近衰减两种学习模式，并发现它们取决于训练集中含有的突变复杂性水平（即突变数量）。本研究对于在可突变离散空间中的机器学习，如化学性质或蛋白质表型预测，并改善基本统计学习理论的理解具有重要意义。