R²-WAM: Functional Reuse and Refinement of Historical Adaptations for World-Action Models

World-Action Models (WAMs) offer a promising foundation for robot manipulation, yet existing adaptation methods typically learn each new task independently from the same base policy. We study a history-aware adaptation setting where task-specific adaptations accumulated during deployment are reused to accelerate future learning. We propose R²-WAM, which organizes historical adaptations into Video, Context, and Action functional routes, selects compact historical support using target-loss signals, and jointly refines reused residuals with new task-specific capacity. Experiments on LIBERO and RoboCasa365 show that the proposed function-structured adapter is data-efficient under limited demonstrations. In our history-aware LIBERO evaluation, historical reuse improves overall success from 57.9% with fresh structured adaptation to 70.4%, surpassing Full Fine-Tuning at 61.9%. Further analysis shows that effective reuse depends on task-group structure, support organization, and controlled refinement.