Benefit and Cost of Random-Token Replacement under Repeated Data: A Known-Entropy Decomposition and Evidence from Ten Real Corpora

Abstract

When unique pretraining data is scarce, models see the same tokens many times and are thought to memorize. Random-token replacement, an input-corruption augmentation, is one remedy reported to lower validation loss, but a lower loss alone does not reveal which source of error it reduces. On a controlled source whose entropy rate is known in closed form, we show that replacement shrinks predictions toward the corpus average. We also introduce a decomposition that separates validation loss into approximation, estimation, and memorization terms. This shrinkage view predicts that replacement's bias cost needs no memorization but its benefit does. Memorization raises validation loss after its minimum, so we report the effect at two points, the minimum validation loss and the end of a fixed budget. Where replacement helps, it reduces this rise by about 60%. At the end of the budget, it turns from harmful to helpful as the controlled source becomes less predictable; at the minimum, it helps at no predictability level under the fixed recipe. On Korean and Japanese web text, replacement removes about a third of the loss rise after the minimum by the end of the budget, but its effect at the minimum is much smaller. Across ten real corpora, replacement lowers the final loss on nine. It harms only the census corpus, program-generated JSON that is the most redundant of the ten and much more redundant than any of 64 further prose and code corpora we measure.