Journal ArticleInfrared-safe energy weighting does not guarantee small nonperturbative effectsBright-Thonney, Samuel; Nachman, Benjamin; Thaler, Jesse<p>Infrared and collinear (IRC) safety has long been used a proxy for robustness when developing new jet substructure observables. This guiding philosophy has been carried into the deep learning era, where IRC-safe neural networks have been used for many jet studies. For graph-based neural networks, the most straightforward way to achieve IRC safety is to weight particle inputs by their energies. However, energy-weighting by itself does not guarantee that perturbative calculations of machine-learned observables will enjoy small nonperturbative corrections. In this paper, we demonstrate the sensitivity of IRC-safe networks to nonperturbative effects, by training an energy flow network (EFN) to maximize its sensitivity to hadronization. We then show how to construct Lipschitz energy flow networks (<math display='inline'><mrow><mi>L</mi></mrow></math>-EFNs), which are both IRC safe and relatively insensitive to nonperturbative corrections. We demonstrate the performance of<math display='inline'><mi>L</mi></math>-EFNs on generated samples of quark and gluon jets, and showcase fascinating differences between the learned latent representations of EFNs and<math display='inline'><mi>L</mi></math>-EFNs.</p> <sec><supplementary-material><permissions><copyright-statement>Published by the American Physical Society</copyright-statement><copyright-year>2024</copyright-year></permissions></supplementary-material></sec>American Physical Society2024-07-0110532075Physical Review D11012470-0010https://doi.org/10.1103/PhysRevD.110.0140292209443; 2019786National Science Foundation