# Finite-Probe Total-Variation Certificates for Finite-Basis Drifting Models

arXiv: https://arxiv.org/abs/2608.01547 · HTML: https://mlsanity.com/paper/2608.01547/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 37 references that are in the map.
- First posted on arXiv 3 Aug 2026.

## Builds on (most cited first, 16 of 16)

- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Generative Modeling via Drifting](https://mlsanity.com/paper/2602.04770/) (2026)
- [Interpretable Distribution Features with Maximum Testing Power](https://mlsanity.com/paper/1605.06796/) (2016)
- [Fast Two-Sample Testing with Analytic Representations of Probability Measures](https://mlsanity.com/paper/1506.04725/) (2015)
- [A Linear-Time Kernel Goodness-of-Fit Test](https://mlsanity.com/paper/1705.07673/) (2017)
- [Sinkhorn-Drifting Generative Models](https://mlsanity.com/paper/2603.12366/) (2026)
- [Generative Drifting is Secretly Score Matching: a Spectral and Variational Perspective](https://mlsanity.com/paper/2603.09936/) (2026)
- [Gradient Flow Drifting: Generative Modeling via Wasserstein Gradient Flows of KDE-Approximated Divergences](https://mlsanity.com/paper/2603.10592/) (2026)
- [Drifting Fields are not Conservative](https://mlsanity.com/paper/2604.06333/) (2026)
- [A Unified View of Score-Based and Drifting Models](https://mlsanity.com/paper/2603.07514/) (2026)
- [On the Wasserstein Gradient Flow Interpretation of Drifting Models](https://mlsanity.com/paper/2605.05118/) (2026)
- [Kernel-Gradient Drifting Models](https://mlsanity.com/paper/2605.10727/) (2026)
- [Finite-Particle Convergence Rates for Conservative and Non-Conservative Drifting Models](https://mlsanity.com/paper/2605.22795/) (2026)
- [DriftXpress: Faster Drifting Models via Projected RKHS Fields](https://mlsanity.com/paper/2605.12183/) (2026)
- [Kernel Tests of Equivalence](https://mlsanity.com/paper/2603.10886/) (2026)

## Abstract (arXiv)

Drifting objectives compare a target and model distribution through a vector field observed noisily at finitely many locations. We ask what distributional conclusion such a frozen measurement system warrants. For integrable antisymmetric interactions and absolutely continuous laws in a declared finite density basis, the unnormalized sampled numerator satisfies operatornamevec(VX)=Mc, where c is an antisymmetric mismatch and M is probe-dependent. This identity yields an a posteriori total-variation (TV) upper confidence bound accounting for held-out field noise, estimated-operator error, and externally validated L1 residual radii around normalized density approximants in the span; a nonpositive observability margin returns the trivial TV bound and abstains. The audit recomputes this numerator from held-out samples; a normalized drift statistic requires a separate joint numerator--denominator analysis. For Gaussian-RBF interactions, a global envelope supports distribution-free and empirical-Bernstein radii without truncation, with companion bounds for the Laplace similarity in the original drifting objective. We characterize random-probe observability by a population Gram matrix, identify rank and symmetry degeneracies, and prove large-bandwidth collapse toward mean matching. Synthetic studies exercise Gaussian and Laplace numerators, separately prespecified bounded-vector and variance-adaptive radii, Monte Carlo-calibrated operators, nonzero residual radii around normalized finite-basis approximants, outward-rounded observability bounds, and designed abstention. A joint basis-size/dimension stress path extends evaluation through m=8. The result is a conditional diagnostic for a finite density class, or for normalized finite-basis density approximants with external residual radii, not a universal guarantee from small training drift.