PTPP-Aware Adaptation Scaling Laws: Predicting Domain-Adaptation Performance at Unseen Pre-Training Budgets

Continual pre-training (CPT) for domain adaptation must balance target-domain gains with stability on the base domain. Existing CPT scaling laws typically assume a fixed pre-training budget, which limits their ability to forecast adaptation outcomes for models trained at different tokens-per-parameter (PTPP). We present PTPP-aware adaptation scaling laws that make the pre-training budget an explicit variable, enabling accurate prediction of adaptation loss at unseen P TPP. On a multilingual setup (English/Arabic → French), PTPP-aware formulations trained on early stages (P TPP={15,31}) predict target loss at P TPP=279 and outperform a PTPP-agnostic D-CPT transfer baseline on compact metrics (Huber-on-log, MAErel, calibration slope); full diagnostics (RMSE, MAPE) are in the appendix. Beyond forecasting, we show a practical use case: planning replay ratios and adaptation token budgets that satisfy target and forgetting constraints under compute limits.