Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift
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| Format: | Preprint |
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2026
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| _version_ | 1866911719369998336 |
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| author | Landers, Jonathan R. |
| author_facet | Landers, Jonathan R. |
| contents | We study long-horizon deployment of a frozen predictor under dynamic covariate shift. A time-domain Poincare inequality first reduces temporal risk volatility to derivative energy. A Jacobian-velocity theorem then supplies the corresponding pathwise control. Given explicit regularity and domination assumptions, the theorem identifies directional tangent energy along the deployment path as the governing quantity. 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 and beats isotropic smoothing there. It also gives validation-selected deployment gains on both real datasets, with the Air Quality subspace estimated from target-orthogonal sensor motion. Moderate drift-subspace misspecification is tolerable while orthogonal misspecification largely removes the benefit. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_04932 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Landers, Jonathan R. Machine Learning 68T05, 68T07, 62R07, 62M10 I.2.6; G.3 We study long-horizon deployment of a frozen predictor under dynamic covariate shift. A time-domain Poincare inequality first reduces temporal risk volatility to derivative energy. A Jacobian-velocity theorem then supplies the corresponding pathwise control. Given explicit regularity and domination assumptions, the theorem identifies directional tangent energy along the deployment path as the governing quantity. 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 and beats isotropic smoothing there. It also gives validation-selected deployment gains on both real datasets, with the Air Quality subspace estimated from target-orthogonal sensor motion. Moderate drift-subspace misspecification is tolerable while orthogonal misspecification largely removes the benefit. |
| title | Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift |
| topic | Machine Learning 68T05, 68T07, 62R07, 62M10 I.2.6; G.3 |
| url | https://arxiv.org/abs/2605.04932 |