Residual-Guided Adaptive Function-Space Projection for Replay-Free Continual Learning

Replay-free continual learning projects new-task gradients away from stored old-function directions, but a fixed-memory sketch must allocate protection without suppressing the signal needed for the new task. We develop residual-guided adaptive function-space projection: a first-order bound motivates selecting protected rank from the streaming Jacobian residual, while a plasticity gate relaxes protection when too much new-task gradient would be removed. On Split CIFAR-100, NULLAUDIT reaches 71.8% average accuracy, 8.9 points of forgetting, and 75.2% new-task accuracy using 9.6 MB; the nearest sketched-Jacobian baseline reaches 71.0%, 9.8, and 74.1% using 12.4 MB. Fixed-rank and no-gate ablations distinguish adaptive rank selection and plasticity control from raw memory allocation alone. The reported evidence establishes an improved memory–stability–plasticity trade-off for the evaluated task sequence without treating the local residual bound as an empirically calibrated drift predictor or a lifelong preservation guarantee.