Energy-Energy Flow Networks

TL;DR

The paper addresses how neural network jet taggers can be misled by non-perturbative QCD effects and proposes EnFN and PnFN architectures to directly exploit higher-point jet correlations while enforcing infrared and collinear safety. It introduces perturbative regularization via jet re-clustering and develops RMS-based robustness metrics plus Pareto visualizations to quantify resilience to hadronization. Through a Z-boson tagging study, EnFN/E2FN demonstrate competitive performance with strong robustness, while ParticleNet remains high-performing but more sensitive to non-perturbative systematics. The work provides a framework for balancing performance and theoretical reliability in ML-driven jet searches, with implications for improved theory-experiment synergy in high energy physics.

Abstract

Jet substructure provides one of the most exciting new approaches for searching for physics in and beyond the Standard Model at the Large Hadron Collider. Modern jet substructure searches are often performed with Neural Network (NN) taggers which study the jets' radiation distributions in great detail, far beyond what is theoretically described by parton shower generators. While this represents a great opportunity, as NNs look deeper into the structure of jets they become increasingly sensitive both to perturbative and non-perturbative theoretical uncertainties. It is therefore important to be able to control which aspects of both regimes the networks focus on, and to develop techniques for quantifying these uncertainties. In this paper we take two steps in this direction: First, we introduce EnFNs, a generalization of the Energy Flow Networks (EFNs) which directly probes higher point correlations in jets, as motivated by recent advances in the study of energy correlators. Second, we introduce a number of techniques to quantify and visualize their robustness to non-perturbative corrections. We highlight the importance of such considerations in a toy study incorporating systematics into a search, and maximizing for the network's discovery significance, as opposed to absolute tagging performance. We hope this study continues the interest in understanding the role QCD systematics play in Machine Learning applications and opens the door to a better interplay between theory and experiment in HEP.

Figures (10)

• Figure 1: A graphical representation of the inputs fed to the $\Phi$ network, and their pairwise structure. The features can include any IRC safe information, such as a jet constituent's angular information, as well as jet-level data. These features live in a space $\mathbb{R}^{n\times f}$ which is then combined in a pairwise manner with features from other particles within the same jet; thus creating a $\mathbb{R}^{n\times n \times f}$ input structure.
• Figure 2: A graphical representation of the data flow logic for an E2FN and P2FN network. The input for both networks is given by a set of features defined for any pair of particles. This input is then passed through a $\Phi$ network which maps them into latent space, $\Phi:\mathbb{R}^{n \times n \times f} \rightarrow \mathbb{R}^{n \times n \times L}$. In the case of the E2FN, the outputs of the $\Phi$ network are then multiplied by the corresponding pairwise energy and damping factor, in order to ensure IRC safety. On the other hand, the P2FN requires no such modifications and its $\Phi$ outputs can be directly summed over all particle pairs. Finally, the sum is given as input to the $F$ network which maps the data from the latent space back to the desired output. For illustration purposes, this is chosen as $F:\mathbb{R}^L \rightarrow \mathbb{R}^2$.
• Figure 3: The performance of the E2FN and P2FN networks given eight $\Phi$ input variations. The signal efficiency versus background rejection curves illustrate how the performance of the particle-correlating architectures vary with different $\Phi$ inputs. As is to be expected, both architectures exhibit improved performance when $p_{T_{jet}}$ is included as an additional input, likely due to the useful kinematic context such a variable provides.
• Figure 4: An illustration of 32 of the E2FN's $\Phi$ network filters, when trained with the scalar distance $R$ on boosted Z boson events. The vertical dashed line denotes the angular scale of the boosted Z boson decay. Multiple filters are active in this region, highlighting that the network correctly identifies this characteristic angular scale.
• Figure 5: Scan of the E2FN's $\Phi$ Network, when trained with the vector distance as input. The network is damped according to Eq. (\ref{['eq:damping']}) with $\tau$ and $\omega$ set to 0.03 and 0.25, respectively. For simplicity, only the non-zero $\Phi$ layers are shown in the figure.