Likelihood-Based Unsupervised Anomaly Detection in CMS Dijet Events

Bhavishya Chebrolu; Hitesh Rasineni; Prajwal Aaryan Immadi

hep-exSep 6, 2026

Likelihood-Based Unsupervised Anomaly Detection in CMS Dijet Events

Authors: Bhavishya Chebrolu, Hitesh Rasineni, Prajwal Aaryan Immadi

Organizations: VIT-AP University, Amaravati, India · Mohan Babu University, Tirupati, 517102, India · VIT-AP University, Amaravati, 522241, India

Abstract

We present an unsupervised search for anomalous dijet events in proton--proton collision data using neural spline flow density estimation. A normalizing flow model is trained on a high-dimensional feature space comprising jet, dijet, and event-level observables to learn the dominant Standard Model background directly from data, without assuming a specific signal hypothesis. Events assigned low likelihood under the learned density are identified as potential anomalous events. Using this approach on a CMS Open Data dijet sample, we investigate extreme events in the tail of the anomaly-score distribution and perform an extensive validation and robustness study. This study includes feature-level statistical comparisons, mass decorrelation tests, permutation-based null tests, and evaluations of training stability. The selected anomalous events exhibit notable departures from the background-only expectation, primarily in jet-substructure observables, while remaining stable under several known sources of bias in unsupervised learning. The identified anomalies are distributed across the kinematic phase space and do not exhibit a narrow structure in the dijet invariant-mass spectrum. Instead, they show correlated deviations across multiple observables, consistent with a multivariate difference in jet substructure and event topology rather than a localized resonance. While no claim of new physics is made, this study demonstrates that neural spline flow-based density estimation can be sensitive to rare, structured deviations in collider data and may provide a model-independent exploratory tool for searches for physics beyond the Standard Model at the LHC.

Figures & tables

Figure 1: Schematic overview of the anomaly detection pipeline based on the neural spline flow. Reconstructed event observables are subjected first to angular encoding and feature normalization. Then, the feature vector goes through a sequence of invertible-flow blocks, where each block consists of a random permutation and masked piecewise rational-quadratic autoregressive coupling transformation. The flow transforms the events into a latent space whose prior is expressed as a standard multivariate normal distribution, allowing for the exact calculation of the event log-likelihood that serves as the anomaly score.

Figure 2: Distribution of neural spline flow anomaly scores, as given by $-\log p(x)$ , for a total of $378{,}278$ events. The bulk of the QCD multijet background is concentrated at low anomaly-score values, while the distribution develops a long tail extending over several decades in event density.

Feature	KS (Anomaly vs Background)
j1_girth	0.5749
j1_tau1	0.5485
j1_tau2	0.5409
j1_tau3	0.5182
j1_ECF_ratio	0.5084
j1_tau32	0.4980

Table 1: Top 15 Distinct Features based on KS Statistic

Figure 3: Two-dimensional subspace projection of the anomalous events (orange points) in the girth versus $\tau_{21}$ (standardized) subspace. The background density is represented by a two-dimensional color-coded density map (blue = low density, yellow = high density). The anomalous events preferentially occupy the low-background-density regions (blue), evidencing their systematic displacement relative to the learned background distribution. The concentration of events at $\tau_{21}=0$ corresponds to jets with fewer than 3 constituents, a known feature of the CMS particle-flow reconstruction.

Figure 4: Feature level distributions for anomalous (99.9-th percentile, red) and background (black) events for selected observables: (a) jet girth (D = 0.575), (b) energy correlation function ratio (D = 0.508), (c) tau32(D = 0.498), (d) tau21 (D = 0.441), (e) jet mass (D = 0.373), and (f) $H_{T}$ (D = 0.343). The distributions show clear differences between anomalous and background events, with the most significant deviations seen in observables related to jet substructure.

Figure 5: Dijet invariant mass ( $m_{jj}$ ) distribution comparing the inclusive background event sample and anomalous events retained at the $99.9$ th percentile of anomaly scores. The background shows a smooth distribution typical of a QCD multijet process, while anomalous events are dispersed across the invariant mass spectrum. No evident resonance structure is seen; consistent with a multivariate deviation across multiple correlated kinematic and event-shape variables.

Figure 6: Dijet invariant mass ( $m_{jj}$ ) distribution for anomalous events identified with the mass-decorrelated neural spline flow model. The model was trained on input variables explicitly excluding $m_{jj}$ and $j1\_mass$ to investigate mass sculpting effects. There is no significant excess in the distribution over background predictions, indicating the anomaly selection is not largely influenced by mass variables.

Figure 7: Dijet invariant mass ( $m_{jj}$ ) distribution comparing real anomalies (selected at the $99.9$ th percentile) with anomalies selected using HT-conditionally permuted scores. The permuted selection shows no systematic deviation from the background distribution, confirming that the observed feature-level deviations are not statistical artifacts.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Comparison	Overlap (%)	Spearman $\rho$	KS
Default vs. seed 42	88.1	0.963	0.043
Default vs. seed 123	90.5	0.964	0.069
Seed 42 vs. seed 123	92.9	0.955	0.028

Appendix

Table 11: Stability of anomaly rankings and score distributions with different random initializations of NSF model. The overlap fraction of the top 0.1% anomalous events, the Spearman rank correlation coefficient (

\rho

), and Kolmogorov–Smirnov distance of anomaly scores are reported.

Figure 8: Mean Kolmogorov-Smirnov distance between anomalous and background events as a function of anomaly-score percentile threshold. The smooth and monotonic nature suggests that the observed differences in features are robust to reasonable variation of the anomaly-selection threshold.

Explore similar work

Local Diagnostics of Learned Event Representations for Anomaly Detection at the HL-LHC
Oct 9, 2026Donatella Genovese, Philip Ploner, Simone Scardapane +2Anomaly Detection Interpretable Anomaly Detection
Department of Computer, Control and Management Engineering, Sapienza University of Rome · Department of Physics, ETH Zurich · Department of Information Engineering, Electronics and Telecommunications, Sapienza University of Rome +1
Mono-Z Dark Matter Search with Neural Spline Flows Using CMS Run 2015D Open Data
Jul 15, 2026Hitesh Rasineni, Bhavishya ChebroluHigh-Energy Physics
VIT-AP University, Amaravati, India · 1VIT-AP University, Amaravati, 522241, India · Mohan Babu University, Tirupati, India +1
Conformal calibration and look-elsewhere effect in anomaly detection for new-physics searches
Jun 11, 2026Jack Y. Araz, Michael SpannowskyPost-Hoc Calibration Conformal Prediction
Department of Physics and Astronomy, University College London, London, WC1E 6B, UK · Department of Engineering, City St. George’s, University of London, London, EC1V 0HB, UK · Institute for Theoretical Physics, Campus Süd, Karlsruhe Institute of Technology (KIT), D-76128 Karlsruhe, Germany +1

Oct 9, 2026J/K move · Enter open · S save

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

Donatella Genovese, Philip Ploner, Simone Scardapane, Stefano Giagu+1

Department of Computer, Control and Management Engineering, Sapienza University of Rome · Department of Physics, ETH Zurich · Department of Information Engineering, Electronics and Telecommunications, Sapienza University of Rome+1

Anomaly Detection Interpretable Anomaly Detection Reconstruction-Based Anomaly Detection High-Energy Physics Representation Learning

Open paper AskPDF arXiv

Anomaly detection, the identification of collision events that deviate from Standard Model expectations, is one of the most promising model-agnostic strategies for new-physics searches at the Large Hadron Collider. Searching for rare events in learned low-dimensional representations removes the need to commit to hand-crafted observables a priori, but sacrifices the immediate physical interpretation those observables provide. For anomaly detection to enter a discovery pipeline, flagged events must therefore be diagnosed locally, both to distinguish potential new physics from mismodeling or detector effects and to identify observables for targeted follow-up searches. We evaluate supervised and self-supervised neural embedding strategies on COLLIDE-2V, a 750-million-event dataset simulated under realistic High-Luminosity LHC conditions, using the reconstruction error of an autoencoder trained in the learned latent space as the anomaly score. Across the configurations and benchmark signals considered, supervised objectives, which exploit simulation process labels during training, generally outperform their self-supervised counterparts and, in their best configurations, improve on an autoencoder trained directly on kinematic features, raising the signal efficiency at 10% background acceptance on all held-out processes. We further introduce a local diagnostic pipeline that fits a Gaussian Mixture Model to the SM latent space, profiles each component through high-level observables without process labels, localizes the flagged events, and ranks observables by their local discriminating power. The ranking recovers the defining kinematics of the held-out processes, while correlating the anomaly score with the same observables quantifies how closely the score tracks them, revealing cases where the most discriminating observable is not the one the score follows most closely.

Abstract

Explore similar work

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

Mono-Z Dark Matter Search with Neural Spline Flows Using CMS Run 2015D Open Data

Conformal calibration and look-elsewhere effect in anomaly detection for new-physics searches