# Learning to bin: differentiable and Bayesian optimization for multi-dimensional discriminants in high-energy physics

arXiv: https://arxiv.org/abs/2601.07756 · HTML: https://mlsanity.com/paper/2601.07756/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 23 references that are in the map.
- First posted on arXiv 12 Jan 2026.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Tree-Structured Parzen Estimator: Understanding Its Algorithm Components and Their Roles for Better Empirical Performance](https://mlsanity.com/paper/2304.11127/) (2023)
- [INFERNO: Inference-Aware Neural Optimisation](https://mlsanity.com/paper/1806.04743/) (2018)
- [neos: End-to-End-Optimised Summary Statistics for High Energy Physics](https://mlsanity.com/paper/2203.05570/) (2022)
- [Optimal statistical inference in the presence of systematic uncertainties using neural network optimization based on binned Poisson likelihoods with nuisance parameters](https://mlsanity.com/paper/2003.07186/) (2020)

## Abstract (arXiv)

Categorizing events using discriminant observables is central to many high-energy physics analyses. Yet, bin boundaries are often chosen manually. A simple, popular choice in multi-classification tasks is to assign events according to the largest per-class score ("argmax") and to apply equidistant binning to the resulting one-dimensional discriminants. We propose a binning optimization for signal significance directly in multi-dimensional discriminants. We use a Gaussian Mixture Model (GMM) to define flexible regions in the score space, which can be interpreted either as bins or as analysis categories. While this GMM-based strategy is applicable in both one and multiple dimensions, we also study a direct bin-boundary optimization in one dimension as a simpler alternative for binary discriminants. On this binning model, we study two optimization strategies: a differentiable and a Bayesian optimization approach. We study two toy setups: a binary classification and a three-class problem with two signals and backgrounds. In the one-dimensional case, both approaches achieve similar gains in signal sensitivity compared to equidistant binning for a given number of bins, while in the multi-dimensional case the differentiable approach performs best. We show that the GMM-based optimization can outperform argmax classification even after optimized binning is applied to the one-dimensional projections. We further study the performance of our methods on the FAIR Universe Hrightarrowττ dataset, where the GMM-based optimization gives the highest signal significance. Both methods are released as lightweight Python plugins intended for straightforward integration into existing analyses.