# Data-Driven, Geometry-Aware Optimal-Transport Calibration of Flavor Tagger

arXiv: https://arxiv.org/abs/2605.01363 · HTML: https://mlsanity.com/paper/2605.01363/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 17 references that are in the map.
- First posted on arXiv 2 May 2026.

## Builds on (most cited first, 5 of 5)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)

## Abstract (arXiv)

Flavor-tagging calibrations are often provided either as scale factors measured at a finite set of working points or as binned corrections to a chosen one-dimensional discriminant. However, this approach falls short of providing continuous, event-level calibration across the full multicomponent outputs of modern taggers. This limitation leads to information loss in analyses that demand high-performance flavor tagging, restricting analyses to a limited set of predefined variables. In this work, we propose a geometry-aware framework that formulates flavor-tagger calibration as an optimal transport problem on the probability simplex. The transport maps are parameterized and trained in the isometric log-ratio coordinate system. Because the quadratic Euclidean cost of Brenier transport in this coordinate system is equivalent to the Aitchison distance on the simplex, the learned map induces a minimal deformation under the Aitchison geometry. Furthermore, we extract flavor-conditional target distributions directly from control-region data using an expectation-maximization (EM) technique that simultaneously fits multiple control regions, models each flavor component with a normalizing flow, and estimates the regional mixture fractions. The extracted targets are subsequently used to learn flavor-factorized transport maps. Because the joint estimation of mixture fractions and flexible component densities admits weakly constrained directions, we further introduce a linearized feedback-operator analysis that propagates the fitted composition covariance into the extracted component densities, separating data-constrained modes from those dominated by the composition prior. The simulation-based closure study demonstrates improved closure in dedicated control regions and in independent validation mixtures.