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

What the math gives to ML

The paper provides a concrete observability perspective for finite-dimensional distribution matching: a sampled interaction field is a linear measurement \(\operatorname{vec}(V_X)=Mc\) of the antisymmetric coefficient mismatch, so small drift is meaningful only when the probe operator \(M\) is well-conditioned. This can be transferred into neural distribution matching by designing or reweighting probes to maximize the smallest singular value of \(M\), rather than optimizing an arbitrary fixed drift statistic. The same operator can produce an uncertainty-aware auxiliary loss and an abstention diagnostic when the estimated field noise dominates the observable subspace. The guarantee remains conditional on a finite density basis and explicit approximation residuals, but that limitation yields a falsifiable and auditable training signal.