Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift
For practitioners deploying frozen models under dynamic covariate shift, DTR offers a principled method to reduce risk volatility by regularizing only along drift directions, with empirical gains over isotropic approaches.
The paper introduces a Jacobian-velocity theorem to bound deployment risk under covariate drift, proposing drift-aligned tangent regularization (DTR) that penalizes sensitivity only along estimated drift directions. Experiments on synthetic and real datasets show DTR reduces risk volatility and directional gain, outperforming isotropic smoothing under low-rank drift.
We study long-horizon deployment of a frozen predictor under dynamic covariate shift. A time-domain Poincaré 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. Rather than smoothing the network isotropically, DTR penalizes sensitivity only along estimated drift directions. We validate the theorem-to-method pipeline in four experiments: a synthetic benchmark for the time-domain inequality, a controlled synthetic comparison against isotropic Jacobian regularization, and two frozen-deployment studies on the UCI Air Quality and Tetouan power-consumption datasets. DTR reduces risk volatility and directional gain in the controlled low-rank regime, beats isotropic smoothing there, and gives validation-selected deployment gains on both real datasets when the Air Quality drift subspace is estimated from target-orthogonal sensor motion. Moderate drift-subspace misspecification is tolerable while orthogonal misspecification largely removes the benefit.