The Sequential Price of Continual Learning

arXiv:2609.29674v1 Announce Type: new Abstract: Sequential task updates are fundamental to continual learning, but their recency bias can impose a lasting performance cost. We study this cost in an overparameterized linear-regression model with i.i.d. task sampling. We prove that distribution-level forgetting and population loss converge to the same stationary limit. This common limit separates exactly into the intrinsic loss asymptotically attained by joint training and an additional sequential price, and in more homogeneous task geometries the two terms coincide, making the total loss twice that of joint training. We further analyze fixed-strength elastic weight consolidation (EWC) under general task curvatures and characterize its stationary sequential price at every regularization strength. Under strong regularization, the price decays inversely with EWC strength while convergence to stationarity slows at the same scale. On the Jester joke-rating dataset, the theory exactly quantifies both the sequential price generated by naturally conflicting user preferences and its reduction by EWC.