Development of systematic uncertainty-aware neural network trainings for binned-likelihood analyses at the LHC

CMS Collaboration (2025) — SANNT

Why it matters here

$(F^{-1})_{r_sr_s}$ is the inverse Schur complement, so the SANNT objective is the profiled criterion of DS-SCHUR with $s=1$ — the production-scale realisation of the $D_s$ theme, arrived at independently.

Method

replaces cross-entropy with $\Delta r_s=\sqrt{(F^{-1})_{r_s r_s}}$, where $F$ is the Fisher information of the binned likelihood over $\{r_s\}\cup\{\theta_j\}$ and the $\theta_j$ are up to 224 nuisance parameters. Applied to $H\to\tau\tau$; 12–16% improvement in the signal-strength uncertainty over a cross-entropy training.

Motivation datum

the paper names our problem as its own open issue — the Fisher loss "introduces an ambiguous choice of binning" and the binned likelihood "is not differentiable at its bin edges". Its cited workarounds are INFERNO's softmax histogram and a KDE surrogate; neither is an exact hard-partition result.

Not prior art for any registry theorem

no claim cites it, deliberately. It uses the profiled Fisher as a training loss and never studies the geometry of the optimal partition.