Age of Learning: Temporal Persistence of Prediction Errors as a Learning Signal

Current machine learning algorithms primarily rely on instantaneous signals such as loss, margin, and prediction confidence to characterize model behavior. These signals indicate how difficult a prediction is at the current optimization step, but they do not capture how long the model has remained incorrect. We study this temporal dimension of learning and introduce Age of Learning (AoL), a learning-state variable that measures the persistence of prediction errors over time. AoL increases while an error remains unresolved and resets when a correct prediction is achieved, thereby distinguishing persistent under-learning from transient mistakes. We develop AoL-based training strategies for both offline and streaming settings. In offline learning, sample-level AoL is accumulated over training and aggregated into class-level states that guide adaptive reweighting and resampling. In streaming learning, where full historical access is unavailable, we maintain lightweight class-level AoL states using current and buffered observations. Across long-tailed classification settings, AoL improves or matches standard training baselines, with larger benefits when learning difficulty persists over time. Multi-seed streaming experiments further show reproducible gains under temporally stable imbalance. Analysis of class frequency, loss, and margin shows that AoL is related to conventional difficulty measures but captures additional information about error duration. These results suggest that temporal persistence provides a useful complementary signal for characterizing and controlling learning dynamics in imbalanced and non-stationary environments.