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One-Step Curvature Probes Miss the Fitting Operator: Retained Capacity and Terminal Null-Space Correction for Continual Learning
A one-step curvature probe evaluates an initial direction, whereas continual learners are judged after reaching comparable new-task fit. In an overparameterized linearization, projected gradient descent converges to $Δ_P=PJ^\top(JPJ^\top)^{-1}r$, and its squared-displacement inflation is exactly the
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