Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift

• URL: http://arxiv.org/abs/2605.04932v1
• Date: Wed, 06 May 2026 13:57:03 GMT
• Title: Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift
• Abstract summary: A time-domain Poincaré inequality reduces temporal risk volatility to derivative energy.<n>A Jacobian-velocity theorem identifies directional tangent energy as the governing quantity under explicit along-path regularity.<n>We validate the theorem-to-method pipeline in four experiments.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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