# Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift

arXiv: https://arxiv.org/abs/2605.04932 · HTML: https://mlsanity.com/paper/2605.04932/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 23 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 12 of 12)

- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Failing Loudly: An Empirical Study of Methods for Detecting Dataset Shift](https://mlsanity.com/paper/1810.11953/) (2018)
- [Sensitivity and Generalization in Neural Networks: an Empirical Study](https://mlsanity.com/paper/1802.08760/) (2018)
- [Robust Large Margin Deep Neural Networks](https://mlsanity.com/paper/1605.08254/) (2016)
- [Wild-Time: A Benchmark of in-the-Wild Distribution Shift over Time](https://mlsanity.com/paper/2211.14238/) (2022)
- [Active Test-Time Adaptation: Theoretical Analyses and An Algorithm](https://mlsanity.com/paper/2404.05094/) (2024)
- [Model Assessment and Selection under Temporal Distribution Shift](https://mlsanity.com/paper/2402.08672/) (2024)
- [An Infinite-Width Analysis on the Jacobian-Regularised Training of a Neural Network](https://mlsanity.com/paper/2312.03386/) (2023)
- [Statistical Learning under Heterogeneous Distribution Shift](https://mlsanity.com/paper/2302.13934/) (2023)
- [Sequential Low-Rank Change Detection](https://mlsanity.com/paper/1610.00732/) (2016)
- [Robust Quickest Change Detection for Unnormalized Models](https://mlsanity.com/paper/2306.05091/) (2023)

## Built on by (most cited first, 1 of 1)

- [When Can We Trust the Matching Principle? Robust Deployment Geometry Under Finite-Sample and Model Uncertainty](https://mlsanity.com/paper/2610.02894/) (2026)

## Abstract (arXiv)

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.