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This research introduces differentiable and Bayesian optimization techniques to improve signal significance in high-energy physics by defining flexible bin boundaries directly within multi-dimensional discriminant spaces. By leveraging Gaussian Mixture Models, the method outperforms traditional manual or equidistant binning strategies, offering lightweight Python plugins for immediate integration into existing analysis pipelines. The study demonstrates that these advanced machine learning approaches can enhance classification sensitivity beyond standard argmax methods, particularly in complex multi-dimensional scenarios.
Learning to bin: differentiable and Bayesian optimization for multi-dimensional discriminants in high-energy physics
arXiv:2601.07756v2 Announce Type: replace-cross Abstract: 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 $H\rightarrow\tau\tau$ 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.
Abstract: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 $H\rightarrow\tau\tau$ 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.
Data Analysis, Statistics and Probability (physics.data-an); Machine Learning (cs.LG); High Energy Physics - Experiment (hep-ex)
arXiv:2601.07756 [physics.data-an]
(or arXiv:2601.07756v2 [physics.data-an] for this version)
https://doi.org/10.48550/arXiv.2601.07756 Focus to learn more arXiv-issued DOI via DataCite
Eur. Phys. J. C 86 (2026) 1014
https://doi.org/10.1140/epjc/s10052-026-16255-1 Focus to learn more DOI(s) linking to related resources
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