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Local Diagnostics of Learned Event Representations for Anomaly Detection at the HL-LHC

This paper evaluates supervised and self-supervised neural embedding strategies for anomaly detection at the HL-LHC using the COLLIDE-2V dataset, demonstrating that supervised approaches outperform others and introducing a local diagnostic pipeline that profiles flagged events and ranks observables to bridge the gap between model-agnostic detection and physical interpretation.

Original authors: Donatella Genovese, Philip Ploner, Simone Scardapane, Stefano Giagu, Thea Klaeboe Aarrestad

Published 2026-10-12

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CC BY 4.0

Original authors: Donatella Genovese, Philip Ploner, Simone Scardapane, Stefano Giagu, Thea Klaeboe Aarrestad

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 edge of the known universe, inside a machine the size of a small town, protons smash together at nearly the speed of light. This is the Large Hadron Collider, a laboratory where physicists hope to find cracks in the Standard Model, the rulebook that describes how the fundamental particles of nature behave. Most of the time, these collisions produce a familiar spray of particles that physicists have seen thousands of times before. But occasionally, something strange happens: a collision produces a pattern of debris that does not fit the rulebook. Finding these rare, anomalous events is like looking for a single, unique grain of sand on a beach that stretches for miles. The challenge is that the "beach" is made of billions of collisions, and the "grain" might look like a normal pebble until you examine it very closely.

For decades, scientists have searched for these anomalies by hand-crafting specific questions to ask the data. They would decide in advance that a new particle might show up as a specific energy spike or a particular angle of flight, and then build tools to hunt for exactly those signs. This approach works well when you know what you are looking for, but it fails if the new physics looks nothing like what anyone expected. To solve this, researchers have turned to artificial intelligence, teaching computers to learn the shape of "normal" collisions directly from the data, without telling them what to expect. The computer builds a mental map of the familiar, and when a new event falls outside that map, it raises a flag. However, this creates a new problem: when the computer flags an event, it often cannot explain why. It says, "This is strange," but not "It is strange because it has too many heavy particles" or "It is strange because it is missing energy." Without that explanation, physicists cannot know if the anomaly is a sign of new physics or just a glitch in the detector.

A team of researchers has now developed a way to fix this blind spot. They tested their ideas on a massive dataset of 750 million simulated collisions, designed to mimic the conditions of the High-Luminosity LHC, the next major upgrade of the collider. Their goal was twofold: first, to see if teaching the computer with labeled examples of known physics (like specific types of particle collisions) would make it better at spotting the unknown than teaching it with no labels at all; and second, to build a diagnostic tool that could explain exactly why a flagged event was considered strange. They found that the computer learned much better when it was allowed to see the "names" of the known collision types during training. When they used these smarter representations to hunt for anomalies, the system caught more of the rare, hidden signals than older methods that relied on human-designed measurements.

But the real breakthrough was in the explanation. The researchers built a pipeline that takes a flagged event and places it into a specific neighborhood within the computer's mental map. They then asked a simple question: what physical features make this event stand out from its neighbors? They tested this on two types of hidden signals. One was a process that produces four heavy quarks, and the other was a hypothetical particle that decays into many pairs of muons. The system correctly identified that the four-quark events were strange because they contained an unusually high number of heavy-flavored jets, and that the muon events were strange because they had an unusually high number of leptons. In other words, the computer didn't just say "this is weird"; it pointed to the specific physical property that made it weird.

Interestingly, the study revealed a subtle but important distinction in how these systems work. For the muon events, the system correctly identified that the number of muons was the most defining feature separating them from normal collisions. However, the computer's internal "strangeness score" did not track the number of muons most closely; instead, it reacted more strongly to other, secondary features of the collision. This means that while the system successfully isolated the strange events, the reason it gave them a high score was slightly different from the reason they were physically unique. This is a crucial insight for future searches: knowing that an event is an outlier is not enough; scientists must also understand which physical variables are driving the detection. By combining a powerful learning method with a local diagnostic tool, the researchers have shown a path forward where artificial intelligence can not only find the needle in the haystack but also describe the needle's shape, ensuring that when a discovery is made, the physics community knows exactly what it has found.

Technical Summary: Local Diagnostics of Learned Event Representations for Anomaly Detection at the HL-LHC

Problem Statement

Anomaly detection (AD) is a primary strategy for discovering new physics at the Large Hadron Collider (LHC) by identifying collision events that deviate from Standard Model (SM) expectations. Traditional AD pipelines rely on hand-crafted high-level observables (e.g., invariant masses, transverse momentum), which are limited by the completeness and quality of the chosen features. Recent approaches utilize deep learning to learn low-dimensional event representations directly from lower-level detector data, removing the need for a priori observable selection. However, these learned representations often lack immediate physical interpretability. A critical gap exists in the "discovery pipeline": when a model flags an event as anomalous, there is no systematic method to diagnose why it was flagged, distinguish potential new physics from mismodeling or detector effects, or identify the specific physical observables driving the anomaly. This paper addresses the need for local diagnostics to interpret learned representations and the anomaly scores derived from them.

Methodology

Dataset and Event Representation

The study utilizes COLLIDE-2V, a 750-million-event dataset simulating High-Luminosity LHC (HL-LHC) conditions with realistic pileup ( $\langle\mu\rangle=200$ ). Events are processed at the "Full-Reco" level, providing analysis-quality particle-flow objects (jets, electrons, muons, photons, and missing transverse energy).

Encoder: A Transformer encoder maps variable-length lists of reconstructed objects into a fixed-dimensional latent space ( $z$ ).
Training Objectives: The authors compare four configurations based on two loss functions (SimCLR and VICReg) in both self-supervised and supervised variants:
- Self-supervised: Relies solely on physics-motivated augmentations (azimuthal rotation, longitudinal boost, $p_T$ smearing, random masking) to define similarity.
- Supervised: Uses SM process labels available in simulation to group events by their underlying hard-scattering process during training (SupCon and VCReg).
Anomaly Scoring: An autoencoder is trained exclusively on the dominant SM background (QCD-inclusive) within the learned latent space. The reconstruction error serves as the anomaly score.

Local Diagnostic Pipeline

To interpret flagged events, the authors introduce a lightweight, label-free diagnostic framework:

Partitioning: A Gaussian Mixture Model (GMM) is fitted to the SM training embeddings to partition the latent space into $K$ components.
Label-free Profiling: Each GMM component is characterized by the distributions of high-level observables (e.g., $H_T$ , $n_{jets}$ , $n_{b-tag}$ ) over the SM events it contains, establishing a physical baseline without process labels.
Localization: Flagged signal events are assigned to the GMM component with the highest posterior responsibility.
Local Separation: Within the dominant components, observables are ranked by their ability to separate the flagged signal from the local SM background using the Wasserstein-1 distance.
Score Correlation: The Spearman correlation between the anomaly score and physical observables is computed to determine if the score tracks the specific observable that defines the anomaly.

Key Contributions

Comparison of Embedding Strategies: The authors demonstrate that, under a shared Transformer backbone, supervised objectives (SupCon and VCReg) that exploit SM process labels yield significantly more informative latent spaces than self-supervised counterparts (SimCLR and VICReg), as measured by linear-probe quality.
Anomaly Detection Performance: In their best configurations, supervised latent spaces improve signal efficiency over an autoencoder trained directly on raw kinematic features across all held-out processes considered. Specifically, VCReg with $d_{model}=256$ achieved a signal efficiency of 97.2% at 10% background acceptance for the $HH \to 4b$ proxy.
Local Diagnostic Framework: The paper introduces a pipeline that localizes flagged events in the latent space, profiles the surrounding SM background using high-level observables, and ranks variables by local discriminating power. This framework successfully recovers the defining physics of held-out processes (heavy-flavour content for $HH \to 4b$ and lepton multiplicity for $Z' \to n(\mu\mu)$ ).
Decoupling of Score and Physics: The study reveals a critical distinction between the observable that best separates a signal from the local background and the observable most correlated with the anomaly score. For the $Z'$ signal, lepton multiplicity was the strongest local discriminant, yet the anomaly score correlated more strongly with secondary kinematic features (e.g., $H_T$ , $M_{jj}$ ), highlighting that global performance metrics do not fully capture the behavior of the scoring model.

Results

Embedding Quality: Supervised models (VCReg, SupCon) achieved macro-averaged AUROC scores of $\approx 0.90$ on a linear probe over 12 SM classes, outperforming self-supervised models (SimCLR: $\approx 0.87$ , VICReg: $\approx 0.77$ ) and raw feature baselines ( $\approx 0.87$ ).
Detection Efficiency: On the $HH \to 4b$ signal, the best supervised configuration (VCReg, $d=256$ ) reached 97.2% signal efficiency at 10% background acceptance, compared to 77.3% for the raw feature autoencoder. For the $Z'$ signal, all supervised configurations (except VCReg at $d=32$ ) exceeded the baseline efficiency of 96.8%.
Diagnostic Insights:
- $HH \to 4b$ : Flagged events localized primarily in GMM components C4 and C5. The local ranking correctly identified $n_{b-tag}$ as the top discriminator. The anomaly score correlated most strongly with $n_{b-tag}$ ( $\rho=0.43$ ), indicating the score tracks the defining physics.
- $Z' \to n(\mu\mu)$ : Flagged events localized almost entirely in component C2. While $n_{leptons}$ was the top discriminator ( $W_1 = 8.61$ ), the anomaly score showed only a weak correlation with lepton multiplicity ( $\rho \approx 0.30$ ) but stronger correlations with $H_T$ and $M_{jj}$ . This suggests the representation routes the signal to a specific leptonic region, but the reconstruction error within that region is driven by other kinematic variations.

Significance and Claims

The paper claims that for anomaly detection to be a viable part of a discovery pipeline, flagged events must be locally diagnosed to distinguish new physics from artifacts and to guide targeted follow-up searches. The authors assert that their diagnostic framework provides a necessary bridge between the "black box" nature of learned representations and the physical observables required for interpretation.

The work highlights that while supervised learning on simulated data currently offers superior performance and interpretability, it relies on process labels unavailable in real collision data. Consequently, the authors note that developing robust self-supervised representations remains a critical future direction to reduce dependence on simulation accuracy and enable learning directly from experimental data. The paper concludes that the combined analysis of local separation and score correlation offers insights into the anomaly-scoring model's behavior that cannot be inferred from global performance metrics alone.