  Synthetic-to-real transfer learning is a framework in which a synthetically
generated dataset is used to pre-train a model to improve its performance on
real vision tasks. The most significant advantage of using synthetic images is
that the ground-truth labels are automatically available, enabling unlimited
expansion of the data size without human cost. However, synthetic data may have
a huge domain gap, in which case increasing the data size does not improve the
performance. How can we know that? In this study, we derive a simple scaling
law that predicts the performance from the amount of pre-training data. By
estimating the parameters of the law, we can judge whether we should increase
the data or change the setting of image synthesis. Further, we analyze the
theory of transfer learning by considering learning dynamics and confirm that
the derived generalization bound is consistent with our empirical findings. We
empirically validated our scaling law on various experimental settings of
benchmark tasks, model sizes, and complexities of synthetic images.
