Knowledge distillation trains a student language model to match a teacher's predictions on the training text. We ask whether learning the teacher's behavior beyond the training text can further improve the student. We investigate this using three input perturbations: additive token noise, blending two documents, and blending neighboring tokens. Specifically, for an early part of pretraining we perturb the inputs and train the student to match the teacher on them, and we spend the rest of the same token budget on ordinary distillation.
When pretraining from scratch, the best method improves on standard distillation at both scales we tried, by 0.025 nats at 135M parameters and by 0.020 nats at 0.5B (mean of three seeds). At 135M this is 1.45 times the gain that distillation itself provides over next-token training. We also observe promising downstream transfer: at 0.5B, the best variant improves average zero-shot accuracy by about one percentage point across seven tasks. It also retains its validation-loss advantage after low-bit weight quantization. We also test a data-limited setting in which training data must be reused, and find that the gains persist. Finally, ablations suggest that, for additive noise, perturbing the teacher's inputs contributes most of the gain, while perturbing only the student's inputs yields much less.