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Machine-learning techniques for model-independent searches in dijet final states

This paper presents and evaluates machine-learning-based anomaly detection methods for model-independent searches for new physics in dijet final states using 13 TeV proton-proton collision data from the CMS experiment, demonstrating their effectiveness in identifying anomalous jets and boosted top quarks without relying on specific theoretical models.

Original authors: CMS Collaboration

Published 2026-07-08

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: CMS Collaboration

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

Imagine you are a detective trying to find a single, unique counterfeit coin hidden inside a massive warehouse filled with billions of genuine coins. In the world of particle physics, this warehouse is the Large Hadron Collider (LHC), and the "coins" are the particles created when protons smash into each other.

Usually, scientists know exactly what the counterfeit coin looks like before they start searching. They build a specific mold (a theory) and look for anything that fits that shape. But what if the counterfeit coin is something completely new, something no one has ever imagined? If you only look for a specific shape, you'll miss it.

This paper from the CMS Collaboration at CERN is about a new way to hunt for these "unknown unknowns." Instead of looking for a specific shape, they use Machine Learning (AI) to act like a super-sensitive metal detector that screams, "This doesn't look like the millions of normal coins I've seen before!"

Here is a breakdown of how they did it, using simple analogies:

1. The Problem: The "Needle in a Haystack"

When protons collide, they mostly produce standard particles (the "hay"). Occasionally, a new, heavy particle might be created that decays into two sprays of particles called jets (the "needle").

The Old Way: Scientists would guess what the new particle looks like, build a filter for it, and look. If they guessed wrong, they missed the discovery.
The New Way: The team decided to stop guessing. Instead, they asked their AI to learn what "normal" looks like perfectly, so it could instantly spot anything that is "weird" or "anomalous."

2. The Five Detectives (The Methods)

The paper tests five different AI "detectives," each with a different strategy to find the weird jets. Think of them as five different ways to spot a fake coin:

The Copycat (VAE-QR): Imagine an AI that tries to redraw every coin it sees. If it sees a normal coin, it can redraw it perfectly. If it sees a weird, counterfeit coin, its drawing comes out blurry and wrong. The "blurry-ness" is the score that says, "This is an anomaly!"
The "Label-Free" Learners (CWoLa, TNT, CATHODE): These are clever because they don't need to know what the fake coin looks like. They are given a mixed bag of coins and told, "Find the ones that are different from the ones in the next room." They learn by comparing the "Signal Room" (where the weird stuff might be) with the "Side Rooms" (where we know only normal stuff exists). If the AI notices a pattern in the Signal Room that isn't in the Side Rooms, it flags it.
- CATHODE is particularly smart; it builds a 3D map of what "normal" looks like in the side rooms and then projects that map into the signal room to see what's missing or different.
The "Semi-Know-it-all" (QUAK): This detective is given a few examples of what might be a fake coin (based on past theories) to help it focus, but it still keeps an open mind for other weird things.

3. The "Sculpting" Trap

There was a big risk: If the AI got too good at spotting "weirdness," it might accidentally start sorting coins by their weight or size just because the weird ones happened to be heavy. This would ruin the search because it would create fake "peaks" in the data that look like discoveries but aren't.

The Fix: The team used a mathematical trick (called Quantile Regression) to ensure that the AI's "weirdness score" didn't accidentally depend on the size of the collision. It's like making sure your metal detector doesn't just beep louder because the coin is bigger, but only because it's made of a different metal.

4. The Real-World Test: Finding the Top Quark

To prove their system actually works, they didn't just look for imaginary new particles. They tried to find something they already knew existed but was hard to spot in this specific setup: the Top Quark.

The Analogy: Imagine you are trying to find a specific type of rare bird in a forest full of sparrows. You tell your AI, "Find me anything that looks different from the sparrows."
The Result: The AI successfully filtered out the millions of ordinary "sparrow" jets and highlighted the "Top Quark" jets. It recovered the key features of the Top Quark (like its mass and how it breaks apart) almost as well as if the scientists had told the AI exactly what a Top Quark looked like from the start. This proved the system is powerful enough to find real physics without needing a specific theory first.

5. The Conclusion

The paper concludes that:

No single detective is perfect: Different AI methods found different types of "weird" events. Some were better at finding one type of anomaly, others at a different type.
They work together: Because the methods look for anomalies in different ways, using all of them together gives the best chance of finding something new.
It works on real data: The system successfully identified known particles (Top Quarks) in real collision data, proving it can handle the messy reality of the LHC.

In short: This paper is a manual for a new kind of "universal search engine" for particle physics. Instead of searching for a specific key, it looks for any key that doesn't fit the lock, opening the door to discoveries we haven't even thought of yet.

Technical Summary: Machine-learning techniques for model-independent searches in dijet final states

Problem Statement
The search for physics beyond the Standard Model (SM) at the Large Hadron Collider (LHC) is increasingly challenged by the overwhelming background of SM processes, particularly those mediated by the strong interaction (QCD multijets). Traditional searches rely on supervised machine learning (ML) classifiers trained to distinguish specific SM backgrounds from hypothesized Beyond-the-Standard-Model (BSM) signals. This approach requires explicit theoretical formulations for every alternative model, limiting the scope of discovery to known hypotheses. Furthermore, traditional "bump hunt" techniques, which look for resonant peaks in the invariant mass of dijet systems ( $m_{jj}$ ), may fail if the signal fraction is too small to produce a visible peak against the smoothly falling SM background. The paper addresses the need for model-agnostic (anomaly detection) methods that can identify anomalous jets without prior knowledge of the signal's specific properties, while avoiding the "sculpting" of the $m_{jj}$ distribution, which would invalidate statistical interpretations.

Methodology
The paper presents a detailed comparison of five distinct machine-learning techniques applied to proton-proton collision data collected by the CMS experiment at $\sqrt{s} = 13$ TeV (2016–2018, 138 fb $^{-1}$ ). The analysis targets dijet final states where a heavy resonance ( $A$ ) decays into two lighter particles ( $B$ and $C$ ), which subsequently decay into SM particles forming two large-radius jets. The methods are categorized by their training paradigms:

Unsupervised (VAE-QR): A Variational Autoencoder (VAE) is trained on low-level jet constituent momenta from a sideband region (where signal is suppressed) to learn the SM background distribution. The reconstruction loss serves as an anomaly score. To prevent the selection from distorting the $m_{jj}$ spectrum (sculpting), a Quantile Regression (QR) step is employed to normalize the anomaly threshold as a function of $m_{jj}$ , ensuring a constant fraction of events is selected regardless of mass.
Weakly Supervised (CWoLa Hunting, TNT, CATHODE, CATHODE-b): These methods utilize "Classification Without Labels" (CWoLa) to learn the likelihood ratio between background and data directly from data samples, without explicit signal labels.
- CWoLa Hunting: Trains classifiers on individual jets using high-level substructure features (e.g., soft-drop mass, N-subjettiness ratios, b-tagging scores) to distinguish jets in a signal region (SR) from those in adjacent sidebands. Reweighting techniques are applied to decorrelate the anomaly score from jet kinematics to mitigate mass sculpting.
- TNT (Tag N' Train): Combines weak supervision with an initial unsupervised autoencoder preselection. One jet is used to "tag" the other as signal-like or background-like based on autoencoder loss, creating enriched samples for weakly supervised training.
- CATHODE / CATHODE-b: Uses a conditional generative model (Normalizing Flows) trained on sideband data to estimate the background density in the signal region. A weakly supervised classifier then distinguishes between the observed data and the generated background. CATHODE-b extends this by including b-tagging scores to enhance sensitivity to third-generation quark couplings.
Semi-supervised (QUAK): Incorporates a set of simulated signal priors to guide the search. It uses Normalizing Flows trained on both background and specific signal benchmarks to define a "QUAK space," selecting events that are dissimilar to background but similar to the signal priors.

Key Contributions

Comprehensive Comparison: This work provides the first detailed comparison of these five diverse anomaly detection methods using actual collider data, moving beyond previous studies limited to simulated events.
Sculpting Mitigation: The paper details specific technical countermeasures (quantile regression, reweighting, generative modeling) implemented to ensure that the anomaly selection does not artificially create or distort peaks in the $m_{jj}$ distribution, a critical requirement for valid statistical inference.
Feature Impact Analysis: The study investigates how different input feature sets (low-level constituents vs. high-level substructure variables) impact performance, revealing that feature choice can explain sensitivity differences between methods but does not fully account for performance gaps between algorithms.
Data Validation: A novel application of weakly supervised anomaly detection is demonstrated to identify Lorentz-boosted top quark pairs ( $t\bar{t}$ ) in the fully hadronic decay channel, validating the methods' ability to recover known physics in a model-agnostic framework.

Results

Sensitivity: All five methods demonstrate increased sensitivity to simulated BSM signals compared to an inclusive search (no substructure selection) and simple model-specific substructure cuts. However, no single method is optimal for all signal topologies.
Complementarity: Correlation analysis of anomaly scores reveals low correlations (typically < 60%) between the methods, indicating they identify anomalous events based on different criteria. This suggests that combining these approaches could yield more powerful search strategies.
Performance Gaps: While supervised classifiers trained on the same features achieve high significance improvement characteristics (SIC), the model-agnostic methods achieve lower SIC values (roughly 50% of the supervised performance for some methods). This gap is attributed to the lack of signal labels during training and the need to account for systematic uncertainties in the limit-setting procedure.
Top Quark Recovery: In the validation study, the weakly supervised method successfully isolated $t\bar{t}$ events from the QCD background, achieving a significance improvement comparable to a fully supervised classifier trained with the same inputs. Interpretability techniques (permutation feature importance) successfully identified the physical properties of the excess (jet mass near 175 GeV, high b-tagging scores, and three-prong substructure), demonstrating the feasibility of interpreting positive anomaly search results.

Significance
The paper claims that these anomaly detection techniques successfully enhance the sensitivity to new particle signatures in a model-agnostic fashion, offering a robust alternative to traditional hypothesis-driven searches. By demonstrating that these methods can recover the properties of known particles (top quarks) without prior knowledge of their existence, the work validates the potential of ML-driven anomaly detection to discover unexpected new physics. The study emphasizes that the complementarity of the different methods underscores the value of employing a diverse toolkit of anomaly detection strategies in future LHC analyses.

1. The Problem: The "Needle in a Haystack"

2. The Five Detectives (The Methods)

3. The "Sculpting" Trap

4. The Real-World Test: Finding the Top Quark

5. The Conclusion

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