Branches of a Tree: Taking Derivatives of Programs with Discrete and Branching Randomness in High Energy Physics

TL;DR

This paper introduces methods for differentiating programs with discrete randomness in High Energy Physics, enabling gradient-based optimization for detector design, simulation, and data analysis.

Contribution

It presents the first fully differentiable branching program and compares various gradient estimation techniques in simplified detector experiments.

Findings

Successful application of gradient estimation techniques to branching programs

Development of the first fully differentiable branching program

Potential for improved optimization in High Energy Physics workflows

Abstract

We propose to apply several gradient estimation techniques to enable the differentiation of programs with discrete randomness in High Energy Physics. Such programs are common in High Energy Physics due to the presence of branching processes and clustering-based analysis. Thus differentiating such programs can open the way for gradient based optimization in the context of detector design optimization, simulator tuning, or data analysis and reconstruction optimization. We discuss several possible gradient estimation strategies, including the recent Stochastic AD method, and compare them in simplified detector design experiments. In doing so we develop, to the best of our knowledge, the first fully differentiable branching program.