TIGER: A Topology-Agnostic, Hierarchical Graph Network for Event Reconstruction

The paper introduces TIGER, a novel topology-agnostic hierarchical graph network that overcomes the limitations of single-topology models by leveraging the universal structure of sequential two-body decays to perform flexible, multi-task event reconstruction and classification for diverse physics processes at the LHC.

The Gist

Imagine the Large Hadron Collider (LHC) as a massive, high-speed car crash. When two protons smash together, they don't just break into pieces; they shatter into a chaotic cascade of smaller particles that fly off in all directions. These particles are unstable and decay (fall apart) almost instantly, creating a "family tree" of debris.

The job of Event Reconstruction is to look at the final pile of debris (the particles hitting the detector) and figure out exactly which original "parent" particle each piece came from. It's like trying to look at a pile of broken Lego bricks and correctly sorting them back into the specific Lego sets they originally belonged to, even though you can't see the original sets.

The Problem with Old Methods

Traditionally, scientists used rigid rules (like math formulas) to sort this debris. However, when the crash is complex, there are too many possible ways to sort the pieces, and the math gets stuck.

Recently, scientists started using Artificial Intelligence (AI) to help. But most of these AI models are like specialized detectives:

• One detective is hired only to solve "Car Crash A." They know exactly what the car looked like before it crashed.
• Another detective is hired only for "Car Crash B."

If you give the "Car Crash A" detective a pile of debris from "Car Crash B," they get confused because they are expecting a specific shape. In real physics experiments, you often have a mix of different types of crashes (signals) and background noise. If your AI is too specialized, it forces every event to look like the one it was trained on, leading to mistakes.

The Solution: TIGER

The authors introduce TIGER (Topology-Independent Graph-based Event Reconstruction). Think of TIGER not as a specialized detective, but as a master puzzle solver who understands the rules of how puzzles are built, rather than memorizing specific pictures.

TIGER is Topology-Agnostic. This means it doesn't need to know in advance what the final picture looks like. It doesn't need a "blueprint" of the event.

How TIGER Works (The Analogy)

TIGER uses a "hierarchical" approach, which is like solving a puzzle in two steps:

1. Step 1: Finding the Intermediate Pieces.
   Imagine the debris falls into groups. TIGER first looks for small clusters that likely came from a middle-level parent. For example, it might spot two particles that clearly came from a "W boson" (a middleman particle), even if it doesn't know what the final parent was yet. It treats these clusters as "meta-nodes" (super-pieces).

   • Metaphor: It's like seeing two Lego bricks snapped together and realizing, "Ah, this is a wheel assembly," without knowing yet if that wheel belongs to a car or a truck.

2. Step 2: Building the Final Picture.
   Once it has identified these "wheel assemblies" (intermediate particles), it looks at how they connect with other loose pieces to form the final "mother" particles (like a Top quark or a Higgs boson).

   • Metaphor: Now it takes that "wheel assembly" and snaps it onto a chassis to realize, "Oh, this is a car!"

The Secret Sauce: TIGER assumes that most particles decay in a simple chain: one parent splits into two children, and those children might split into two more. It doesn't assume what those parents are, just how they split. This allows it to handle complex, messy events where the number of particles varies, or where different types of crashes happen at the same time.

What the Paper Found

The researchers tested TIGER on two types of particle collisions:

1. Fully Hadronic $t\bar{t}$: A complex crash involving top quarks.
2. Semi-leptonic $t\bar{t}H$: An even messier crash involving top quarks and a Higgs boson.

They compared TIGER to the current "champion" AI models (HyPER and SPANet), which are like the specialized detectives mentioned earlier.

• Accuracy (Efficiency): TIGER was just as good at finding the right particles as the specialized models.
• Cleanliness (Purity): This is where TIGER shined. Because TIGER doesn't force the data to fit a pre-set shape, it made far fewer "fake" connections.
  • The Result: While specialized models often guessed "two top quarks" even when the data only supported one (leading to errors), TIGER said, "I only see one," and was right. It reduced the number of wrong guesses by a significant margin (sometimes doubling the purity).

Bonus: The Two-in-One Trick

The paper also showed that TIGER can do two jobs at once. While it is sorting the debris, it can also look at the whole pile and say, "This is a signal event" (the interesting physics we want) or "This is background noise" (boring stuff). It did this classification task better than the specialized models, too.

The Bottom Line

TIGER is a flexible, smart tool that doesn't need to be told what kind of event it's looking at. It learns the fundamental rules of how particles break apart and uses that to reconstruct the past. It's more adaptable and makes fewer mistakes when the data is messy or mixed, making it a powerful new tool for physicists trying to understand the universe.

Technical Summary

Technical Summary: TIGER – A Topology-Agnostic, Hierarchical Graph Network for Event Reconstruction

Problem Statement
Event reconstruction at the Large Hadron Collider (LHC) involves assigning observed detector objects (jets, leptons) to their true parent particles. This is a combinatorial challenge that becomes intractable for traditional statistical methods (e.g., $\chi^2$, likelihood) in events with multiple unstable particles. While recent machine learning approaches like Topograph, HyPER, and SPANet have improved performance by embedding physical knowledge into network architectures, they suffer from a critical limitation: they rely on a single, predefined event topology. In realistic analyses where signal and background processes with different structures coexist, these specialized models either require architectural modifications for new topologies or force background events into the signal topology, limiting their generalizability and purity.

Methodology: The TIGER Architecture
The authors introduce TIGER (Topology-Independent Graph-based Event Reconstruction), a hierarchical graph network designed to be fundamentally topology-agnostic. The model operates on the observation that most LHC processes involve sequential two-body decays (e.g., $t \to Wb \to qq'b$), though it does not hard-code specific decay chains.

The architecture consists of three primary components:

1. Encoding: Input features (transverse momentum $p_T$, pseudorapidity $\eta$, azimuthal angle $\phi$, mass $m$, and Missing Transverse Energy MET) are concatenated with one-hot encoded tags (b-tag, lepton-tag). These are embedded via Multi-Layer Perceptrons (MLPs) and processed by a Diffusion Transformer (DiT) to update hidden representations, incorporating global context (mean node features and total object count).
2. Hierarchical Graph Learning: This is the core innovation, proceeding in two stages:
   • Stage 1: A fully connected graph is constructed from input objects. An MLP classifies edges to determine if two objects originate from the same parent particle (e.g., forming a $W$ boson or Higgs). Identified intermediate particles are promoted to "meta-nodes."
   • Stage 2: A new graph is formed containing original nodes and the selected meta-nodes. Edge classification is performed again to combine intermediate particles with remaining objects to form final-state particles (e.g., combining a $W$ meta-node and a $b$-jet to form a top quark).
   • Design Choice: To prevent error propagation, nodes incorporated into meta-nodes are not discarded; they remain available for the second stage. Ambiguous assignments (e.g., shared jets) are permitted during training but resolved via a dedicated post-processing algorithm during evaluation to ensure physical consistency (no double-counting).
3. Event Classification (Optional): A pooling layer aggregates features from nodes and meta-nodes, passing them through an MLP for binary signal-vs-background classification.

The total loss function is a weighted sum of the cross-entropy losses from both graph learning stages, an auxiliary classification task (predicting particle origins), and the event-level classification.

Key Contributions

• Topology Agnosticism: Unlike HyPER or SPANet, TIGER requires no prior knowledge of the event topology or the number of reconstructable particles. It learns the decay structure directly from data.
• Multi-Task Learning: The framework supports simultaneous event reconstruction and classification, leveraging shared representations to improve performance.
• Generalizability: By relying only on the common underlying structure of sequential two-body decays, the model can theoretically handle diverse signal and background processes without architectural changes.

Results
The model was evaluated on two datasets: fully hadronic $t\bar{t}$ events and semileptonic $t\bar{t}H$ events.

• Fully Hadronic $t\bar{t}$: Compared to the specialized HyPER baseline, TIGER achieved comparable reconstruction efficiencies but demonstrated significantly higher purity. For single top quarks, purity improved by nearly 10% on average. At the event level, TIGER's purity was more than double that of the baseline in low jet multiplicity scenarios. This is attributed to the baseline's tendency to force a two-top reconstruction even when the event topology does not support it, whereas TIGER adapts to the actual event structure.
• Semileptonic $t\bar{t}H$: Compared to SPANet, TIGER showed comparable efficiencies for reconstructing the Higgs boson and leptonic top. While it slightly underperformed in reconstructing the hadronic top and the full event, it achieved a substantial purity improvement (approx. 10% average) across hadronic tops, Higgs bosons, and full-event reconstructions.
• Signal vs. Background: In a classification task distinguishing $t\bar{t}H$ from the dominant background $t\bar{t} + bb$, TIGER outperformed a fine-tuned SPANet baseline, validating its effectiveness as a multi-task learning framework.

Significance and Claims
The paper claims that TIGER provides a powerful and generalizable tool for LHC physics analysis. Its primary significance lies in bridging the gap between the high performance of specialized models and the flexibility required for realistic experimental conditions where event topologies are not known in advance. By removing the need for predefined topological assumptions, TIGER offers a more robust framework for analyses involving mixed signal and background processes. The authors note that while the current work focuses on two-body decay chains, the architecture is naturally extensible to more complex topologies (e.g., three-prong decays) via additional hierarchical levels, though such generalizations are beyond the scope of this specific study.