Localized anomaly detection with a calorimeter normalizing flow

Machine-learned anomaly detection is reshaping searches for new physics, but it has outrun the statistics used to interpret it. A raw anomaly score has no calibrated meaning, a model that scans many regions inflates the look-elsewhere effect, and the asymptotic significances the field relies on are blind to the background mismodelling that anomaly detectors are especially prone to. We propose a calibration layer, built on conformal prediction, that turns any anomaly score into a defensible significance with distribution-free, finite-sample guarantees. Conformal prediction converts scores into valid local p-values, weighted and Mondrian variants repair the sideband-to-signal-region exchangeability failures that resonant searches suffer, and a Gross-Vitells step carries the result through to a look-elsewhere-aware global significance. The layer does two things at once. It exposes miscalibration that the standard pipeline cannot see, and it corrects it without retraining the detector. On public LHC Olympics data, a classifier develops a substructure-mass correlation that makes sideband-calibrated background p-values anti-conservative. Taken at face value, this manufactures a $\sim 46σ$ excess from background sculpting alone, which the label-free weighted correction removes, restoring an honest null. When run as a blind wide-mass bump hunt, the standard asymptotic and unweighted procedures fabricate $\gtrsim10σ$ excesses and $\approx5σ$ excesses even in signal-free windows, while the conformal layer raises no false alarms and its global false-positive rate is verified on background-only pseudoexperiments. The result is an auditable, detector-agnostic path from an uncalibrated score to a trials-factor-aware significance, ready to be folded into experimental anomaly searches.

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.

Deep generative models with tractable likelihoods, exemplified by normalizing flows, offer an effective basis for anomaly detection through likelihood-based scoring. We demonstrate that, unlike in the image domain where deep generative models frequently assign higher likelihoods to anomalous data, such counterintuitive behavior occurs rarely in tabular settings. We first introduce a domain-agnostic formulation that enables consistent detection and evaluation of the counterintuitive phenomenon, addressing the lack of a precise definition in prior work. Through extensive experiments on 47 tabular datasets benchmarked against 13 baseline models and on 10 CV/NLP embedding datasets from ADBench, we show that the phenomenon is consistently rare in general tabular data and that normalizing flow likelihood achieves competitive anomaly detection performance. We further provide theoretical and empirical analyses attributing this disparity to differences in dimensionality and feature correlation between tabular and image data. Therefore, our results indicate that likelihood-based detection with normalizing flows is a practical approach for tabular anomaly detection.