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

Donatella Genovese; Philip Ploner; Simone Scardapane; Stefano Giagu; Thea Klaeboe Aarrestad

cs.AIOct 9, 2026

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

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

Organizations: 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 · Department of Physics, Sapienza University of Rome

Abstract

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.

Figures & tables

Figure 1: End-to-end pipeline. Left: a Transformer encoder maps each event to a low-dimensional embedding

z

, trained on SM background processes; held-out events are passed at inference only. Center: a GMM partitions the latent space into

K

components. Top right: an autoencoder flags anomalous events (

\star

) based on reconstruction error. Bottom right: the diagnostic pipeline locates flagged events, ranks observables by local discriminating power, and tests their correlation with the anomaly score.

Object	Max.	# features	Variables
AK4 jets (PUPPI)	12	7	$p_{T}$ , $\eta$ , $\phi$ , mass, b-tag, $n_{\text{charged}}$ , $n_{\text{neutral}}$
Electrons	8	8	$p_{T}$ , $\eta$ , $\phi$ , charge, isolation, $d_{0}$ , $d_{z}$ , $E_{\text{had}}/E_{\text{em}}$
Muons	8	7	$p_{T}$ , $\eta$ , $\phi$ , charge, isolation, $d_{0}$ , $d_{z}$
Photons	8	5	$p_{T}$ , $\eta$ , $\phi$ , $E_{\text{had}}/E_{\text{em}}$ , isolation
MET	–	2	magnitude, $\phi$

Table 1: Reconstructed objects in the Full-Reco view. Variable-length lists are zero-padded to the maximum multiplicity.

Type	# processes	Process
SM background	12	QCD inclusive ( $H_{\mathrm{T}}>50$ GeV)
		QCD $\to b\bar{b}$
		$W\to\ell\nu$
		$W\to q\bar{q}$
		$Z\to\nu\nu$ + jets
		$Z\to qq$ (uds)

Table 2: SM processes used to train the encoder, and the two held-out processes used to evaluate anomaly-detection performance.

Observable	Physical meaning
$H_{T}$	Hadronic activity
MET	Missing transverse energy
$n_{\rm jets}$	Jet multiplicity
$n_{b\text{-tag}}$	Heavy-flavour content
$n_{\rm leptons}$	Lepton multiplicity
$M_{jj}$	Leading dijet invariant mass

Table 3: High-level physical observables used to profile the GMM components and to rank the variables that separate flagged signal events from the local SM background. Exact definitions are given in Section A.5 .

Model	$d_{\text{model}}$	AUROC
SupCon	128	$0.9051\pm 0.0020$
SimCLR	256	$0.8684\pm 0.0014$
VCReg	128	$\mathbf{0.9075\pm 0.0002}$
VICReg	256	$0.7682\pm 0.0314$
CE (standard)	256	$0.9022\pm 0.0004$
Raw features	—	$0.8653\pm 0.0007$

Table 4: Macro-averaged AUROC (mean

\pm

std over 5 seeds) of a linear probe on the 12 SM classes, for each model in its best configuration ( Section A.3 ). For CE the AUROC is obtained from the classifier’s own test predictions.

		$HH\!\to\!4b$		$Z^{\prime}\to n(\mu\mu)$
Model	$d_{\text{model}}$	AUROC	TPR @ 10% [%]	AUROC	TPR @ 10% [%]
Raw AE	—	$0.931\pm 0.001$	$77.3\pm 0.7$	$0.984\pm 0.001$	$96.8\pm 0.1$
SupCon	32	$0.892\pm 0.031$	$65.2\pm 9.6$	$\mathbf{0.996\pm 0.001}$	$\mathbf{99.0\pm 0.2}$
	64	$0.937\pm 0.017$	$79.9\pm 6.8$	$0.995\pm 0.001$	$99.0\pm 0.1$
	128	$0.943\pm 0.005$	$82.4\pm 1.9$	$0.995\pm 0.001$	$98.9\pm 0.1$
	256	$0.954\pm 0.009$	$86.4\pm 4.2$	$0.995\pm 0.001$	$98.9\pm 0.1$

Table 5: Anomaly-detection performance on the two held-out processes for each model and embedding dimension: AUROC and signal efficiency at 10% background acceptance (TPR @ FPR = 10%), mean

\pm

std over 5 seeds. Raw AE is trained directly on preprocessed kinematic features.

Figure 2: Physical profile of each latent region, computed on the SM events assigned to it. The labels C0–C6 index the mixture components. Each cell displays the standardized median deviation: the median of the observable within the component minus the global SM median, divided by the observable’s standard deviation over the SM population. Deviations are computed relative to the full SM population. For

n_{b\text{-tag}}

and

n_{\text{leptons}}

the global SM median is zero, so those rows cannot deviate downwards. Medians are used to ensure robustness against long distribution tails. Cells with absolute deviations smaller than 0.35 are left unlabeled to avoid visual clutter. Hatched cells are those where fewer than

15\%

of the component’s events yield a value.

Figure 3: Assignment of the AE-flagged signal to the mixture components, for

HH\to 4b

(left) and

Z^{\prime}\to n(\mu\mu)

(right), with the SM population shown for reference. Fractions are normalized independently for each population; the plotted occupancies therefore indicate localization in latent space rather than signal purity.

	Observable	$W_{1}^{\mathrm{SM}}$	$W_{1}^{\mathrm{QCD}}$
C5	$n_{b\text{-tag}}$	2.06	2.36
	$n_{\mathrm{jets}}$	0.65	0.34
	$H_{T}$	0.52	0.26
	$n_{\mathrm{leptons}}$	0.49	0.54
	$M_{jj}$	0.23	0.14
	$\|\Delta\eta_{jj}\|$	0.23	0.38

Table 6: Local discriminating power of the high-level observables within the mixture components that hold the AE-flagged signal, for

HH\rightarrow 4b

(left) and

Z^{\prime}\to n(\mu\mu)

(right). Only components holding at least

10\%

of the flagged signal are reported.

W_{1}^{\text{SM}}

is the Wasserstein-1 distance between the flagged signal and all SM events assigned to the same component, irrespective of their anomaly score, standardized by the standard deviation of each observable over the SM population.

W_{1}^{\text{QCD}}

, computed against the local QCD background (the autoencoder’s trained normality), is reported as a control baseline. Observables are ranked by

W_{1}^{\text{SM}}

, with the top-ranked observable set in bold. C2 is essentially free of QCD, so the control cannot be computed there.

Figure 4: Density distributions of the top-ranked observable in the dominant component for each flagged signal:

n_{b\text{-tag}}

in C5 for

HH\rightarrow 4b

(left) and

n_{\text{leptons}}

in C2 for

Z^{\prime}\to n(\mu\mu)

(right). The distributions compare the AE-flagged signal against the local SM background in the same latent region.

Panel of Figure 5 — Figure 5: Spearman correlation between the autoencoder reconstruction error (anomaly score) and the physical observables for the flagged signal events, computed within their dominant GMM components. In each panel the observable ranked first by Wasserstein distance is marked in vermilion ( $\bigstar$ ), and the one most strongly correlated with the score in green ( $\blacklozenge$ ).

Appendix figures & tables16 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 6: Preprocessing and event representation. Each event contains a variable number of reconstructed jets, electrons, muons, photons and MET. Features are transformed and normalized, then each group is truncated to its top-

k

objects and zero padded to a fixed length, with the true per-group multiplicity appended as a trailing scalar. The resulting flat vector is tokenized by projecting every object slot to

d_{\text{model}}

, giving the token sequence shown below, color-coded by object group and preceded by an event token (EVT) built from the multiplicity counts, which the Transformer encoder then consumes. The dashed path denotes the baseline experiments, where the flat vector bypasses tokenization and is fed directly to the autoencoder or the linear probe.

Augmentation	SupCon	SimCLR	VICReg
Random feature	$0.8952\pm 0.0009$	$\mathbf{0.8514\pm 0.0020}$	$\mathbf{0.7258\pm 0.0300}$
Random particle	$0.8988\pm 0.0009$	$0.7712\pm 0.0003$	$0.7209\pm 0.0235$
Physics	$\mathbf{0.8991\pm 0.0006}$	$0.8491\pm 0.0017$	$0.7203\pm 0.0097$

Appendix

Table 7: Linear probe macro-averaged AUROC (mean

\pm

std over 5 seeds) for the three augmentation strategies. Bold denotes the best result per model.

\alpha

AUROC 5

0.8998\pm 0.0010

0.9017\pm 0.0003

\mathbf{0.9030\pm 0.0007}

0.9020\pm 0.0017

\beta

AUROC 1

\mathbf{0.9030\pm 0.0007}

0.9019\pm 0.0012

0.9007\pm 0.0002

\lambda

AUROC 0

0.7192\pm 0.0144

0.7191\pm 0.0318

0.7239\pm 0.0072

\mathbf{0.7269\pm 0.0090}

0.7170\pm 0.0251

Appendix

Table 8: VCReg and VICReg loss ablation. Linear probe macro-averaged AUROC (mean

\pm

std over 5 seeds). Left: VCReg variance weight scan with

\beta=1

fixed. Center: VCReg covariance weight scan with

\alpha=25

fixed. Right: VICReg invariance weight scan with

\mu=25

\nu=1

fixed. Bold denotes the best result per column.

$\tau$	SupCon	SimCLR
0.05	$0.9005\pm 0.0006$	$0.8670\pm 0.0010$
0.07	$0.9005\pm 0.0004$	$0.8643\pm 0.0023$
0.10	$\mathbf{0.9007\pm 0.0005}$	$\mathbf{0.8680\pm 0.0015}$
0.15	$0.9007\pm 0.0004$	$0.8405\pm 0.0022$
0.20	$0.9007\pm 0.0002$	$0.8343\pm 0.0053$

Appendix

Table 9: Temperature ablation for SupCon and SimCLR. Linear probe macro-averaged AUROC (mean

\pm

std over 5 seeds). Bold denotes the best result per model.

$\lambda_{\text{cls}}$	SupCon
0.00	$0.8991\pm 0.0006$
0.05	$0.9000\pm 0.0007$
0.10	$0.9007\pm 0.0005$
0.20	$0.9010\pm 0.0005$
0.50	$\mathbf{0.9019\pm 0.0001}$

Appendix

Table 10: Classification head weight ablation for SupCon (

\tau=0.10

fixed). Linear probe macro-averaged AUROC (mean

\pm

std over 5 seeds). Bold denotes the best result.

Model	$d_{\text{model}}{=}32$	$d_{\text{model}}{=}64$	$d_{\text{model}}{=}128$	$d_{\text{model}}{=}256$
VCReg	$0.898\pm 0.001$	$0.902\pm 0.001$	$\mathbf{0.903\pm 0.001}$	$0.901\pm 0.007$
SupCon	$0.890\pm 0.000$	$0.896\pm 0.001$	$\mathbf{0.902\pm 0.001}$	$0.902\pm 0.001$
SimCLR	$0.853\pm 0.036$	$0.858\pm 0.006$	$0.867\pm 0.001$	$\mathbf{0.869\pm 0.001}$
VICReg	$0.686\pm 0.030$	$0.717\pm 0.004$	$0.721\pm 0.024$	$\mathbf{0.739\pm 0.015}$

Appendix

Table 11: Linear probe macro-averaged AUROC for the

d_{\text{model}}

ablation on the reduced ablation subset ( Section A.3 ). Values are mean

\pm

standard deviation across 5 random seeds.

Figure 7: Occupancy of the least-populated mixture component as a function of

K

, as a fraction of the share it would hold under a uniform partition; the dashed line is the occupancy floor.

Parameter	SupCon	SimCLR	VCReg	CE	VICReg
$d_{\text{model}}$	128	256	128	256	256
$n_{\text{heads}}$	8	8	8	8	4
$n_{\text{layers}}$	6	8	4	4	4
$d_{\text{ff}}$	1024	2048	1024	2048	512
Dropout	0.10	0.226	0.10	0.10	0.10
Projection dim.	32	32	—	—	128

Appendix

Table 12: Final hyperparameter configuration per model, as used for the results of Section 4 .

Parameter	Value
Compression	4
Depth	4
Dropout	0.035
Learning rate	$1.97\times 10^{-4}$
Weight decay	$3.02\times 10^{-5}$
Train events	200,000

Appendix

Table 13: Autoencoder hyperparameters, identical for the embedding-based and raw-feature experiments

	Learned representation				Sup.	Base
Class	SupCon	SimCLR	VCReg	VICReg	CE	Raw features
	$d{=}128$	$d{=}256$	$d{=}128$	$d{=}256$	$d{=}256$
QCD incl. ( $H_{\mathrm{T}}{>}50$ GeV)	$0.8478\pm 0.0056$	$0.8143\pm 0.0028$	$\mathbf{0.8517\pm 0.0005}$	$0.6765\pm 0.0521$	$0.8443\pm 0.0003$	$0.8067\pm 0.0018$
QCD $\to b\bar{b}$	$0.8779\pm 0.0016$	$0.8107\pm 0.0019$	$\mathbf{0.8786\pm 0.0008}$	$0.6710\pm 0.0420$	$0.8684\pm 0.0007$	$0.8091\pm 0.0020$
$W\to\ell\nu$	$0.9483\pm 0.0012$	$0.9219\pm 0.0016$	$\mathbf{0.9486\pm 0.0001}$	$0.8187\pm 0.0361$	$0.9372\pm 0.0002$	$0.9219\pm 0.0019$
$W\to q\bar{q}$	$0.8291\pm 0.0044$	$0.7957\pm 0.0019$	$\mathbf{0.8333\pm 0.0005}$	$0.7056\pm 0.0264$	$0.8243\pm 0.0006$	$0.7909\pm 0.0015$

Appendix

Table 14: Per-class linear probe AUROC (mean

\pm

std over 5 seeds) for each model in its final configuration. For CE the AUROC is obtained from the classifier’s own test predictions.

		$HH\to 4b$		VBF $H\to b\bar{b}$		$ggH\to\tau\tau$		$HH\to b\bar{b}\tau\tau$
Model	$d_{\text{model}}$	AUROC	TPR [%]	AUROC	TPR [%]	AUROC	TPR [%]	AUROC	TPR [%]
Raw AE	—	$0.931\pm 0.001$	$77.3\pm 0.7$	$0.863\pm 0.002$	$51.0\pm 1.1$	$0.815\pm 0.003$	$46.5\pm 0.7$	$0.939\pm 0.001$	$79.8\pm 0.6$
SupCon	32	$0.892\pm 0.031$	$65.2\pm 9.6$	$0.753\pm 0.014$	$38.8\pm 2.3$	$0.889\pm 0.021$	$74.5\pm 3.7$	$0.967\pm 0.003$	$91.5\pm 0.4$
	64	$0.937\pm 0.017$	$79.9\pm 6.8$	$0.851\pm 0.029$	$54.4\pm 7.8$	$0.899\pm 0.006$	$\mathbf{76.0\pm 1.5}$	$0.977\pm 0.005$	$93.7\pm 1.8$
	128	$0.943\pm 0.005$	$82.4\pm 1.9$	$0.878\pm 0.026$	$61.5\pm 5.8$	$0.886\pm 0.008$	$71.6\pm 1.5$	$0.979\pm 0.003$	$94.2\pm 1.0$
	256	$0.954\pm 0.009$	$86.4\pm 4.2$	$0.906\pm 0.011$	$68.6\pm 4.4$	$\mathbf{0.901\pm 0.004}$	$74.3\pm 0.9$	$\mathbf{0.985\pm 0.002}$	$95.8\pm 0.7$

Appendix

Table 15: Held-out performance on four processes absent from training: AUROC and signal efficiency at 10% background acceptance (TPR @ FPR = 10%), mean

\pm

std over 5 seeds. Raw AE is trained directly on preprocessed kinematic features. Bold marks the best entry in each column; differences smaller than the quoted uncertainties are not significant.

		$H\to aa\to 4b$		$H\to aa\to 4\tau$		$Z^{\prime}\to n(\mu\mu)$
Model	$d_{\text{model}}$	AUROC	TPR@10%	AUROC	TPR@10%	AUROC	TPR@10%
Raw AE	—	$0.640\pm 0.001$	$18.5\pm 0.3$	$0.681\pm 0.004$	$25.1\pm 0.3$	$0.984\pm 0.001$	$96.8\pm 0.1$
SupCon	32	$0.739\pm 0.041$	$38.6\pm 5.7$	$\mathbf{0.876\pm 0.014}$	$\mathbf{70.8\pm 2.9}$	$\mathbf{0.996\pm 0.001}$	$\mathbf{99.0\pm 0.2}$
	64	$0.758\pm 0.018$	$39.8\pm 3.3$	$0.872\pm 0.009$	$70.5\pm 2.1$	$0.995\pm 0.001$	$99.0\pm 0.1$
	128	$0.777\pm 0.024$	$44.0\pm 4.9$	$0.842\pm 0.011$	$62.8\pm 1.9$	$0.995\pm 0.001$	$98.9\pm 0.1$
	256	$0.829\pm 0.014$	$52.8\pm 3.7$	$0.854\pm 0.009$	$65.3\pm 1.6$	$0.995\pm 0.001$	$98.9\pm 0.1$

Appendix

Table 16: AUROC and signal efficiency at 10% background acceptance (mean

\pm

std over 5 seeds). For each process, 20,000 events are drawn at random from a dedicated production of 50,000, matching the test statistics of the proxy signals of Table 15 ; the QCD reference is the same as for

HH\to 4b

SM process	AUROC	Acceptance [%]
QCD incl. ( $H_{\mathrm{T}}{>}50$ GeV)	—	$9.6\pm 0.3$
	$0.436\pm 0.015$	$10.0\pm 0.6$
$Z\to qq$ ( $uds$ )	$0.543\pm 0.015$	$11.1\pm 0.8$
$W\to q\bar{q}$	$0.558\pm 0.017$	$13.1\pm 1.3$
$Z\to cc$	$0.686\pm 0.014$	$28.2\pm 3.0$
$Z\to\nu\nu$ + jets	$0.676\pm 0.023$	$36.2\pm 2.4$

Appendix

Table 17: AUROC against QCD and acceptance of each Standard Model process at the autoencoder threshold that accepts 10% of QCD events, for VCReg with

d_{\text{model}}=256

. The threshold is calibrated on QCD validation events for each encoder seed and applied unchanged to 20,000 test events per process; mean

\pm

std over 5 seeds.

Panel of Figure 8 — Figure 8: Distributions of the eight high-level observables for the AE-flagged $HH\to 4b$ signal (dashed) and the local Standard Model background (solid), shown separately for each mixture component that holds at least $5\%$ of the flagged signal. Every histogram is normalized to unit area.

Panel of Figure 9 — Figure 9: Distributions of the eight high-level observables for the AE-flagged $Z^{\prime}\to n(\mu\mu)$ signal (dashed) and the local Standard Model background (solid), shown separately for each mixture component that holds at least $5\%$ of the flagged signal. Every histogram is normalized to unit area.

Figure 10: Distributions of the eight observables over the Standard Model events of each mixture component, with the seven components overlaid. This is the material behind the median-based summary of Fig. 2 in the main text, which reports one number per cell where this reports the full shape. No process labels enter the construction: the mixture is fitted on the embeddings alone and each region is described only by the physics of the events assigned to it.

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