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Designing Observables for Measurements with Deep Learning

Owen Long, Benjamin Nachman

TL;DR

The paper addresses the challenge of extracting physics parameters from unfolding analyses where observables are manually chosen and distorted by detector effects. It introduces a neural-network observable trained with a two-term loss $L[f] = L_{\text{classic}}[f(z), \\mu] + \\lambda\\, L_{\text{new}}[f(x), f(z)]$ to maximize parameter sensitivity while suppressing detector distortions. The authors validate the approach on toy continuous-parameter estimation and a binary-discrimination task in deep inelastic scattering (H1/DIS), demonstrating improved discrimination power and reduced unfolding dependence compared with classical observables. The work offers a path toward more informative unfolded cross sections and potential applications in precise measurements and MC-tuning, with open-source code for replication.

Abstract

Many analyses in particle and nuclear physics use simulations to infer fundamental, effective, or phenomenological parameters of the underlying physics models. When the inference is performed with unfolded cross sections, the observables are designed using physics intuition and heuristics. We propose to design targeted observables with machine learning. Unfolded, differential cross sections in a neural network output contain the most information about parameters of interest and can be well-measured by construction. The networks are trained using a custom loss function that rewards outputs that are sensitive to the parameter(s) of interest while simultaneously penalizing outputs that are different between particle-level and detector-level (to minimize detector distortions). We demonstrate this idea in simulation using two physics models for inclusive measurements in deep inelastic scattering. We find that the new approach is more sensitive than classical observables at distinguishing the two models and also has a reduced unfolding uncertainty due to the reduced detector distortions.

Designing Observables for Measurements with Deep Learning

TL;DR

The paper addresses the challenge of extracting physics parameters from unfolding analyses where observables are manually chosen and distorted by detector effects. It introduces a neural-network observable trained with a two-term loss to maximize parameter sensitivity while suppressing detector distortions. The authors validate the approach on toy continuous-parameter estimation and a binary-discrimination task in deep inelastic scattering (H1/DIS), demonstrating improved discrimination power and reduced unfolding dependence compared with classical observables. The work offers a path toward more informative unfolded cross sections and potential applications in precise measurements and MC-tuning, with open-source code for replication.

Abstract

Many analyses in particle and nuclear physics use simulations to infer fundamental, effective, or phenomenological parameters of the underlying physics models. When the inference is performed with unfolded cross sections, the observables are designed using physics intuition and heuristics. We propose to design targeted observables with machine learning. Unfolded, differential cross sections in a neural network output contain the most information about parameters of interest and can be well-measured by construction. The networks are trained using a custom loss function that rewards outputs that are sensitive to the parameter(s) of interest while simultaneously penalizing outputs that are different between particle-level and detector-level (to minimize detector distortions). We demonstrate this idea in simulation using two physics models for inclusive measurements in deep inelastic scattering. We find that the new approach is more sensitive than classical observables at distinguishing the two models and also has a reduced unfolding uncertainty due to the reduced detector distortions.
Paper Structure (9 sections, 4 equations, 9 figures)

This paper contains 9 sections, 4 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Methodology
  3. Toy example for continuous parameter estimation
  4. Full example for binary classification
  5. Datasets
  6. Results
  7. Conclusions and Outlook
  8. Alternative loss function for the regression example
  9. Additional distributions for the model dependence and discrimination tests

Figures (9)

  • Figure 1: Input features and resolution model for toy regression example. Two different experimental resolution functions, A and B, are shown.
  • Figure 2: Results of toy regression example as a function of the $\lambda$ hyperparameter.
  • Figure 3: Particle level distributions of the nine NN input features for the Djangoh and Rapgap generators.
  • Figure 4: Neural Network output distributions for four values of the $\lambda$ hyperparameter, which sets the scale for the Detector - Particle disagreement penalty in the loss function. The top row shows the results for $\lambda = 0$, where there is no penalty if the NN predictions for Detector-level input features and Particle-level input features disagree. The bottom three rows show increasing values of $\lambda$ : 1, 20, and 100.
  • Figure 5: Results of unfolding the NN output. The top (bottom) row shows the unfolding for the Rapgap (Djangoh) generator. The left column shows the response matrix for the unfolding, where the distribution of the NN output given the Detector-based input features (horizontal axis) is normalized to unit area for each bin of the NN output given the Particle-based input features (vertical axis). The center column shows the unfolded distribution compared to the true distribution. The right column shows the matrix of correlation coefficients from the unfolding.
  • ...and 4 more figures