Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift

ArXi:2605.04932v1 Announce Type: cross We study long-horizon deployment of a frozen predictor under dynamic covariate shift. A time-domain Poincar\'e inequality reduces temporal risk volatility to derivative energy, and a Jacobian-velocity theorem identifies directional tangent energy along the deployment path as the governing quantity under explicit along-path regularity and domination assumptions. Under low-rank drift, that quantity reduces to directional Jacobian energy in the drift subspace, motivating drift-aligned tangent regularization (DTR) and a matched monitoring proxy.