Source-linked AI summary
Deep-learned Top Tagging with a Lorentz Layer
Anja Butter, Gregor Kasieczka, Tilman Plehn, Michael Russell
TL;DR
The paper addresses the challenge of tagging boosted hadronic top quarks when tracking information has much finer resolution than calorimeter-based jet images. It introduces DeepTopLoLa, a Lorentz-vector deep neural network with Combination and Lorentz layers, and finds negligible tracker gains for moderately boosted tops but a large gain for strongly boosted tops.
Problem
Image-based top taggers face too many sparsely distributed pixels when tracking information is included, making particle-flow extensions and tracking gains difficult to assess reliably.
Method
DeepTopLoLa processes jet constituents as Lorentz vectors using a Combination layer, a Lorentz layer, and fully connected layers, with particle-flow inputs extending beyond calorimeter information.
Results
DeepTopLoLa is competitive with QCD-inspired and image-based taggers for moderately boosted tops, while tracker information gives negligible gains there but makes a big difference for strongly boosted tops.
Takeaways & Limitations
The flexible 4-vector input allows calorimeter and tracker information to be combined at their respective experimental resolutions and supports studying tracking benefits across boost regimes.
Takeaways & Limitations
The performance study ignores multi-parton interactions and pile-up, leaving this aspect to a dedicated study.
Abstract
from arXiv · showhide
We introduce a new and highly efficient tagger for hadronically decaying top quarks, based on a deep neural network working with Lorentz vectors and the Minkowski metric. With its novel machine learning setup and architecture it allows us to identify boosted top quarks not only from calorimeter towers, but also including tracking information. We show how the performance of our tagger compares with QCD-inspired and image-recognition approaches and find that it significantly increases the performance for strongly boosted top quarks.
1 Introduction
Hadronic top tagging requires analyzing complex fat-jet substructure, but image-based CNNs face a major resolution problem when tracking information is added. DeepTopLoLa addresses this by processing jet constituents as Lorentz vectors and extending naturally to tracking inputs.
- Motivation: CNN top taggers can outperform multivariate QCD-based taggers, but tracking creates too many sparsely distributed active pixels.The problem arises because tracking has much finer experimental resolution than calorimeter images.
- Proposed approach: DeepTopLoLa analyzes fat-jet constituents directly using the Lorentz group and Minkowski metric rather than image or language-recognition analogies.Its architecture combines a Combination layer, a Lorentz layer, and two fully connected layers.
- Proposed approach: The tagger extends from calorimeter towers to tracking information with finer resolution, avoiding the mismatched-resolution problem of image-based networks.This setup also permits studying the performance gain from tracking and combining the tagger with b-tagging in ATLAS and CMS analyses.
- Evaluation: The study compares DeepTopLoLa with multivariate QCD-inspired and image-based convolutional taggers, then evaluates calorimeter versus particle-flow information for different boost regimes.The comparisons use standard fat jets from hadronic top decays and include mildly and strongly boosted top quarks.
2 Tagger
The tagger first forms trainable combinations of ordered jet 4-vectors, then transforms them into measurement-motivated observables using a Lorentz layer before neural-network classification.
- Input representation: The inputs are N measured 4-vectors sorted by transverse momentum and organized as a matrix of constituent components.The constituent representation supplies the basic objects for the subsequent subjet analysis.
- Combination layer: The Combination layer multiplies the input 4-vectors by a matrix to produce M combined 4-vectors.The output retains every original momentum and adds M − N trainable linear combinations.
- Combination layer: The combined 4-vectors are analyzed for structures such as the mass drops associated with top-quark and W-boson decays.The framework illustrates these structures through the corresponding on-shell conditions.
- Implementation: For numerical studies, the authors vary the maximum number of retained constituents and use 15 trainable combinations, giving M = 15 + N.They report that changing M has no effect in their tests.
- Lorentz layer: The Lorentz layer transforms the M combined 4-vectors into measurement-motivated objects using invariant masses, transverse momenta, weighted energies, and Minkowski distances.The Minkowski metric supplies the relevant distance measure between substructure objects, while trainable weights are included in the transformations.
- Lorentz layer: The Lorentz-layer objects serve as the DNN inputs, and the authors report that combining invariant mass with energy or transverse momentum and including trainable weights is important.They found that the exact composition and number of entries do not affect performance, while the resulting transformation can make relevant information more accessible.
3 Performance
DeepTopLoLa is competitive with QCD-inspired and image-based calorimeter taggers for moderately boosted tops, while particle-flow information yields its largest gain for strongly boosted tops.
- 3.1 Calorimeter: DeepTopLoLa is competitive with both QCD-inspired and image-based taggers using calorimeter information for moderately boosted top quarks.The comparison uses soft fat jets with pT,fat = 350 ... 450 GeV.
- 3.2 Learning the Minkowski metric: The tagger’s Minkowski-metric discrimination is associated with the same mass-drop feature used by QCD-based and image-based top taggers.The authors report this as important for understanding what the network exploits.
- 3.3 Calorimeter and tracking: Particle-flow extension is straightforward because the LoLa-based approach directly accepts all particle-flow objects as constituents.This avoids the fine-resolution tracking difficulty faced by jet-image approaches.
- 3.3 Calorimeter and tracking: 5% better top-transverse-momentum resolution from particle-flow objects is unlikely to significantly improve the analysis by itself.The authors distinguish improved kinematic measurement from tagging performance.
- 3.3 Calorimeter and tracking: For pT,fat = 350 ... 450 GeV, particle flow gives hardly any improvement over calorimeter inputs, whereas at pT,fat = 1300 ... 1400 GeV background rejection increases by a factor of two to three at fixed signal efficiency.At higher transverse momenta, calorimeter resolution is no longer sufficient to separate the substructures.
4 Conclusions
DeepTopLoLa is a flexible Lorentz-vector tagger that matches established approaches for moderately boosted tops, while tracker information yields a substantial benefit for strongly boosted tops. Its detector-flexible inputs and tracking compatibility support applications in ATLAS and CMS analyses.
- Architecture: DeepTopLoLa combines a constituent 4-vector input with a Combination layer, Lorentz layer, and fully connected layers.The architecture supports detector information beyond a single output and allows additional subjet information to be added straightforwardly.
- Performance: For moderately boosted top quarks, DeepTopLoLa is competitive with QCD-inspired and image-based convolutional taggers using calorimeter information.The comparison also found that the Minkowski metric related to a mass-drop condition drives signal-background distinction.
- Performance: Tracker information provides negligible performance gain for moderately boosted tops but makes a big difference for strongly boosted tops.The result uses particle-flow objects combining calorimeter and tracker information at their respective full experimental resolutions.
- Applications: Coverage of the full transverse-momentum range and compatibility with tracking-based b-tagging make DeepTopLoLa a starting point for machine learning in ATLAS and CMS subjet analyses.The same 4-vector framework also supports applications involving structures such as matrix elements or phase space.