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A compact, interrogable Tree Tensor Network Jet Tagger on Lund declustering trees

This paper introduces a highly compact, quantum-inspired Tree Tensor Network jet tagger that leverages a shared tensor core and strong radiation priors on Lund declustering trees to achieve performance comparable to much larger models in quark/gluon discrimination and top tagging, while enabling unique interpretability through latent space analysis across tree recursions and generator transfer.

Original authors: Fabrizio Napolitano, Luca Della Penna, Tommaso Tedeschi, Livio Fanò

Published 2026-10-09

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CC BY 4.0

Original authors: Fabrizio Napolitano, Luca Della Penna, Tommaso Tedeschi, Livio Fanò

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

At the heart of the Large Hadron Collider, where protons smash together at nearly the speed of light, a chaotic spray of particles erupts from the collision. Physicists call these sprays "jets." Most of the time, these jets are just ordinary debris from the strong force that binds atomic nuclei together. But occasionally, a jet is born from something far more exotic: the decay of a heavy, short-lived particle like a top quark, which is a fundamental building block of matter. Distinguishing a jet from a heavy particle from a jet of ordinary debris is one of the most critical tasks in modern particle physics, as it allows scientists to hunt for new laws of nature hidden within the noise. To do this, researchers look at the internal structure of the jet, tracing how it was built up from smaller pieces. They use a specific map, known as the Lund plane, which charts the history of how a jet split apart, showing the energy and angle of every split. This map is clean and theoretically sound, but turning it into a reliable signal requires a computer program that can read the map without getting confused by the quirks of the simulation software used to create the training data.

A team of researchers has developed a new way to read these jet maps, creating a tool that is both incredibly small and surprisingly effective. Instead of using the massive, complex neural networks that have become standard in the field, they built a "Tree Tensor Network." Imagine the jet's history not as a cloud of data, but as a family tree, where every split in the jet is a parent node branching into two children. The researchers designed a system where a single, tiny brain is shared by every node in this tree. This brain looks at the local details of a split—the energy and angle—and passes a summary of that information up to the next level. Because the same brain is used everywhere, the system learns the universal rules of how jets break apart, rather than memorizing the specific details of every single jet. This approach is inspired by methods used in quantum physics to describe complex systems with limited resources, but here it is applied to classical data to create a model that is compact and easy to interrogate.

The researchers tested this new tool on two difficult challenges: telling the difference between jets started by quarks versus those started by gluons, and identifying jets that came from top quarks. They trained the model on data generated by one computer simulation, called Pythia, and then tested it on data from a completely different simulation, called Herwig. This is a crucial test because real-world physics does not care which simulation software was used to generate the data; a good detector should work regardless of the theoretical model used to train it. The results showed that this tiny model, with only about 4,000 adjustable settings, performed nearly as well as much larger models that have hundreds of thousands of settings. In the task of distinguishing quarks from gluons, the new tool matched the performance of the larger models almost exactly. When it came to spotting top quarks, it was slightly less effective than the giants, but it still held its own, especially when moving from one simulation to another.

What makes this work particularly valuable is not just the performance, but the transparency it offers. Because the model uses the same small brain at every step of the jet's history, the researchers can pause the process at any point and ask, "What does the model see right now?" They found that the model learns to focus on specific regions of the jet's history where the two different simulations start to disagree. By looking at where the model's internal representation changes as it climbs up the tree, they could pinpoint exactly which parts of the jet's structure are most sensitive to the details of the simulation. They discovered that for ordinary jets, the differences between the simulations appear mostly in the soft, low-energy splittings, while for the complex top quark jets, the differences are concentrated in the hard, energetic splits. This ability to locate the source of uncertainty is a powerful feature that larger, black-box models cannot easily provide.

The study also explored how the size of the model's "brain" affects its ability to learn. They found that for simple tasks like telling quarks from gluons, a very small brain was sufficient, suggesting that the rules for these jets are straightforward and universal. However, for the more complex top quark jets, a slightly larger brain was needed to capture the intricate connections between the different parts of the jet. Furthermore, they tested the model by ignoring the very softest parts of the jet, which are the most difficult to simulate accurately. Even when they cut away these uncertain regions, the model remained robust, losing very little of its ability to distinguish between signal and background. This suggests that the model is learning the fundamental physics of the jet rather than memorizing the noise of the simulation.

Ultimately, this work demonstrates that you do not need a massive, data-hungry computer to understand the structure of a particle jet. By respecting the natural tree-like structure of how jets form and using a shared, efficient processing unit, the researchers created a tool that is both powerful and interpretable. It performs competitively with the largest models available today while using a fraction of the computational resources. More importantly, it opens a window into the decision-making process of the machine, allowing scientists to see exactly where the physics is clear and where the simulations diverge. As the field moves toward the High-Luminosity LHC, where data will be scarce and precision will be paramount, having tools that are both efficient and transparent will be essential for making the most of every collision.

Technical Summary: A Compact, Interrogable Tree Tensor Network Jet Tagger on Lund Declustering Trees

Problem Statement
Jet substructure analysis at the Large Hadron Collider (LHC) relies on machine learning (ML) taggers to identify boosted heavy particles and distinguish quarks from gluons. Current state-of-the-art approaches fall into two categories: those enforcing strict kinematic symmetries (Lorentz/permutation equivariance) with reduced capacity, and those utilizing low-level constituents with highly expressive architectures (e.g., Graph Neural Networks like ParticleNet) that achieve high discrimination power but suffer from significant modeling dependence and limited interpretability. A critical challenge is the robustness of these models across different parton shower and hadronization generators (e.g., Pythia vs. Herwig); expressive models often lose discrimination power when transferred between generators. Furthermore, existing tree-based taggers (like LundNet) utilize the declustering tree as a graph for message passing but do not strictly constrain the computation to follow the physical branching structure, potentially missing opportunities to encode the radiation history directly into the architecture.

Methodology
The authors propose a novel Tree Tensor Network (TTN) architecture that is "quantum-inspired" and constructed directly along the Cambridge/Aachen (C/A) jet declustering tree. Key methodological features include:

Architecture: The network employs a single, shared tensor core ( $C \in \mathbb{R}^{d \times \chi \times \chi \times \chi}$ ) applied recursively to every internal node of the declustering tree. Unlike standard graph networks where edges are processed individually, this TTN enforces a shared splitting map across all scales of the QCD radiation history.
Inputs: The model uses IRC-safe Lund plane coordinates ( $\ln k_t, \ln(R_0/\Delta), \ln z, \ln m, \psi$ ) derived from resolved splittings. It operates without particle identification or detector-level information.
Encoding: Local features are encoded via a projective sphere mapping for the first three coordinates and bounded tanh functions for the remaining two, producing a 6-dimensional vector.
State Propagation: At each node, the hidden state is a sum of a "tree message" (obtained by contracting the shared core with the encoded local feature and the bond vectors of the left and right children) and a "local residual" (a small MLP). Missing children are handled by a learned vacuum state.
Physics Gates: The architecture includes optional multiplicative gates (QCD and Sudakov gates) that modulate the tree message based on perturbative QCD information (splitting kernels and coupling constants), though these are treated as ablation targets.
Interrogability: Because the same map acts identically at every node, the model can be evaluated on truncated trees. This allows for the comparison of latent spaces across recursion depths and the localization of where generator representations diverge on the Lund jet plane.

Key Contributions

Compactness: The TTN achieves competitive performance with an extremely low parameter count. The default model ( $\chi=8$ ) has 4,014 trainable parameters, compared to approximately 391,000 for LundNet and 365,578 for ParticleNet.
Structural Constraint: The architecture strictly follows the physical branching structure of the jet, contrasting with unconstrained constituent-level taggers.
Generator Robustness: The model demonstrates transferability between Pythia and Herwig comparable to much larger baselines, despite the two-order-of-magnitude difference in capacity.
Latent Space Analysis: The shared-core structure enables a unique analysis of where in the declustering history (tree depth) and on the Lund plane the latent representations of different generators diverge.

Results
The model was evaluated on boosted top tagging and quark/gluon discrimination using particle-level samples from Pythia8 and Herwig7.

Native Performance (Pythia $\to$ Pythia):
- Quark/Gluon: The TTN achieves an AUC of 0.8917, closely matching LundNet (0.8941) and slightly underperforming ParticleNet (0.9014).
- Top Tagging: The TTN achieves an AUC of 0.9531, slightly below LundNet (0.9574) and ParticleNet (0.9592).
Transfer Performance (Pythia $\to$ Herwig):
- The TTN shows transfer behavior similar to the baselines. In quark/gluon discrimination, the AUC drops to 0.8114 (vs. 0.8098 for LundNet and 0.8107 for ParticleNet). In top tagging, the TTN AUC is 0.9472 (vs. 0.9474 for LundNet and 0.9479 for ParticleNet).
- The relative AUC loss from Pythia to Herwig is comparable across all models, suggesting the TTN's lower capacity does not inherently improve or degrade transfer robustness in this specific regime.
Capacity and Threshold Scans:
- Increasing the bond dimension $\chi$ yields marginal gains for quark/gluon discrimination but more significant improvements for top tagging, where complex topologies require higher information flow between subtrees.
- Applying an IRC-safe cut ( $\ln(k_t/\text{GeV}) = -2$ ) results in a negligible performance decrease (at most ~0.003 AUC).
Latent Space Localization:
- Analysis of truncated trees reveals that for quark/gluon discrimination, differences between Pythia and Herwig accumulate constantly from depth 3, with significant divergence in the soft-emitting regime (depth 10–15).
- For top tagging, the latent representation changes most significantly in the region of hard, large-angle emissions (top of the Lund plane), corresponding to the electroweak decay of the top quark, while differences between generators concentrate in the soft, collinear region ( $\ln(k_t/\text{GeV}) < 0$ ).

Significance and Claims
The paper claims that the TTN offers a highly parameter-efficient alternative to large graph networks, achieving near-state-of-the-art performance with a fraction of the parameters. Its primary significance lies in its interrogability: the recursive, shared-core design allows researchers to pinpoint exactly where in the jet's radiation history and on the Lund plane the model's latent representation changes or where generator-dependent differences arise.

The authors suggest that this capability could allow future models to be trained and evaluated specifically on regions of phase space where theoretical uncertainties (showering and hadronization) are minimized. By focusing on regions where experimental uncertainties (such as the measured primary Lund plane density) are also small, the TTN approach could help reduce the overall uncertainty budget in High-Luminosity LHC (HL-LHC) measurements. The paper concludes that while full generator robustness requires further study (e.g., fixed-threshold efficiencies and multiple seeds), the TTN provides a promising, compact, and physically grounded framework for jet tagging.

Technical Summary: A Compact, Interrogable Tree Tensor Network Jet Tagger on Lund Declustering Trees

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