Energy Flow Networks: Deep Sets for Particle Jets (1810.05165v2)

Abstract: A key question for machine learning approaches in particle physics is how to best represent and learn from collider events. As an event is intrinsically a variable-length unordered set of particles, we build upon recent machine learning efforts to learn directly from sets of features or "point clouds". Adapting and specializing the "Deep Sets" framework to particle physics, we introduce Energy Flow Networks, which respect infrared and collinear safety by construction. We also develop Particle Flow Networks, which allow for general energy dependence and the inclusion of additional particle-level information such as charge and flavor. These networks feature a per-particle internal (latent) representation, and summing over all particles yields an overall event-level latent representation. We show how this latent space decomposition unifies existing event representations based on detector images and radiation moments. To demonstrate the power and simplicity of this set-based approach, we apply these networks to the collider task of discriminating quark jets from gluon jets, finding similar or improved performance compared to existing methods. We also show how the learned event representation can be directly visualized, providing insight into the inner workings of the model. These architectures lend themselves to efficiently processing and analyzing events for a wide variety of tasks at the Large Hadron Collider. Implementations and examples of our architectures are available online in our EnergyFlow package.

• The paper introduces a deep sets approach adapted for particle jet analysis, enabling permutation-invariant representations of collider events.
• It demonstrates that PFNs, utilizing additional particle-level information, outperform EFNs in distinguishing quark from gluon jets.
• The framework preserves infrared and collinear safety, offering interpretable models that align with quantum chromodynamics observables.

Overview of "Energy Flow Networks: Deep Sets for Particle Jets"

The paper "Energy Flow Networks: Deep Sets for Particle Jets" by Komiske, Metodiev, and Thaler introduces a novel machine learning framework for analyzing collider data, leveraging the intrinsic representation of events as sets of particles with variable lengths and no specific order. This paper proposes Energy Flow Networks (EFNs) and Particle Flow Networks (PFNs), extending the Deep Sets approach to particle physics, notably ensuring respect for infrared and collinear safety (IRC safety). By focusing on set-based representations, these architectures achieve competitive performance in tasks such as distinguishing quark jets from gluon jets, a critical challenge in high energy physics.

Methodology

The primary innovation in this research is adapting the Deep Sets theorem to particle physics. This theorem allows for the construction of permutation-invariant functions of sets, enabling a more natural representation of collider events. EFNs incorporate IRC safety by weighting individual particles by energy and limiting dependence on geometry, whereas PFNs allow for general energy dependence and include additional particle-level information such as charge and flavor. These network architectures process events efficiently and are designed to directly reflect the set-like nature of particle collisions.

EFNs and PFNs decompose traditional observables into a sum of per-particle mappings followed by a global function. This decomposition aligns with existing observables such as calorimeter images and radiation moments. It effectively encodes the event's latent representation, facilitating both efficient computation and interpretability.

Results

The paper demonstrates the capabilities of EFNs and PFNs in a practical application: distinguishing quark jets from gluon jets at the Large Hadron Collider (LHC). The models achieved similar or improved performance compared to traditional methods. The paper shows that PFNs, particularly when using additional particle identification inputs, outperform EFNs, indicating the usefulness of non-IRC-safe information in certain contexts. Notably, when applying EFNs, visualizing the learned representations provided insight into QCD singularity structures, as the model naturally adjusted pixel sizes in the latent space akin to the intricate radiation profiles observed in QCD jets.

Implications and Future Directions

This research has profound implications for practical and theoretical aspects of particle physics. Practically, the framework supports a wide range of collider analyses beyond the specific discrimination tasks studied here, offering a new standard for event representation at the LHC. Theoretically, the ability to inspect learned models offers a pathway to discover new physics observables. Additionally, the approach may bridge the gap between machine learning methods and traditional physics analyses, promoting better integration of data-driven techniques in high-energy experiments.

Future work includes extending these methods to more complex events at the LHC, incorporating further physics constraints, and refining the theoretical underpinnings connecting machine learning with field theories. Given the immense data from current and upcoming collider experiments, EFNs and PFNs could significantly enhance the discovery potential for new physics signatures. Moreover, exploring the equivariant case of Deep Sets could optimize learning from the granular structure of complex collider events.

In conclusion, "Energy Flow Networks: Deep Sets for Particle Jets" presents a robust, adaptable framework addressing a key challenge in high-energy physics, balancing computational efficiency, interpretability, and adherence to fundamental physics principles.