# Likelihood-Based Unsupervised Anomaly Detection in CMS Dijet Events

arXiv: https://arxiv.org/abs/2609.06686 · HTML: https://mlsanity.com/paper/2609.06686/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 37 references that are in the map.
- First posted on arXiv 6 Sep 2026.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Anomaly Detection with Density Estimation](https://mlsanity.com/paper/2001.04990/) (2020)
- [Mining gold from implicit models to improve likelihood-free inference](https://mlsanity.com/paper/1805.12244/) (2018)
- [Machine Learning in the Search for New Fundamental Physics](https://mlsanity.com/paper/2112.03769/) (2021)
- [Variational Autoencoders for New Physics Mining at the Large Hadron Collider](https://mlsanity.com/paper/1811.10276/) (2018)
- [JUNIPR: a Framework for Unsupervised Machine Learning in Particle Physics](https://mlsanity.com/paper/1804.09720/) (2018)
- [Mono-Z Dark Matter Search with Neural Spline Flows Using CMS Run 2015D Open Data](https://mlsanity.com/paper/2607.13771/) (2026)
- [Hadronic Mono-Z Dark Matter Sensitivity with Flow Matching on CMS Open Data](https://mlsanity.com/paper/2609.02923/) (2026)

## Abstract (arXiv)

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.