arXiv:2610.19013v2 Announce Type: replace Abstract: Current scaling law formulations suggest that increasing the number of unique samples in a dataset consistently improves model performance, while repeated exposure to the same samples provides diminishing value. In this work, we challenge this assumption for image self-distillation models. We train iBOT models on random subsets of seven datasets spanning satellite imagery, driving scenes, egocentric video, and natural images, and evaluate their frozen representations on downstream tasks. We propose a density-interaction scaling law that combines unique-image count $U$ and repetition $R$, fitting it on runs with at most 50 million image presentations and testing it at larger budgets $C$. On Maxar dataset, a random subset containing approximately 1.5% of the training pool improves average nearest-neighbor classification accuracy by 3.11 percentage points over training on the full pool at the same budget of 200 million image presentations. Smaller subsets also outperform the full pool on SATLAS and Ego4D, whereas ImageNet favors larger pools at higher budgets. At a fixed subset size, further training can improve performance, lead to a plateau, or reduce performance. Our law captures smaller-subset advantages that the compared baselines cannot represent and improves prediction at higher budgets on Maxar, SATLAS, and Ego4D under nearest-neighbor evaluation. These findings show that both the number of unique images and how often they are repeated matter when allocating a training budget.