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Autoencoders for unsupervised anomaly detection in high energy physics
Thorben Finke, Michael Krämer, Alessandro Morandini, Alexander Mück, Ivan Oleksiyuk
TL;DR
Model-independent new-physics searches need anomaly taggers that can find signals without relying on labels or a specific signal model. This paper studies reconstruction-loss autoencoders on top and QCD jet images, including a test that swaps background and signal roles. The standard setup tags top jets but fails on the inverse task, while proposed changes are promising first steps toward improving model-independence.
Problem
New-physics searches seek anomalous events in Standard Model collider data, motivating unsupervised taggers that can detect a wide variety of signals without labels or a specific model.
Source: §1 · pp. 2–4Method
Results
The standard autoencoder tags top jets but fails to tag QCD jets when trained on top jets, performing worse than random selection; proposed modifications are promising first steps toward more model-independent tagging.
Source: §1 · p. 4, §4 · p. 21Takeaways & Limitations
Inverting a tagging task can expose bias toward a particular anomaly, and the authors propose comparing the two AUCs or the area between their ROC curves.
Source: §1 · p. 4, §4 · p. 21A good result on one anomaly does not establish model-independence, and the top-tagging setup can fail to tag dark-matter jets from a strongly interacting sector.
Source: §4 · pp. 20–21
Abstract
from arXiv · showhide
Autoencoders are widely used in machine learning applications, in particular for anomaly detection. Hence, they have been introduced in high energy physics as a promising tool for model-independent new physics searches. We scrutinize the usage of autoencoders for unsupervised anomaly detection based on reconstruction loss to show their capabilities, but also their limitations. As a particle physics benchmark scenario, we study the tagging of top jet images in a background of QCD jet images. Although we reproduce the positive results from the literature, we show that the standard autoencoder setup cannot be considered as a model-independent anomaly tagger by inverting the task: due to the sparsity and the specific structure of the jet images, the autoencoder fails to tag QCD jets if it is trained on top jets even in a semi-supervised setup. Since the same autoencoder architecture can be a good tagger for a specific example of an anomaly and a bad tagger for a different example, we suggest improved performance measures for the task of model-independent anomaly detection. We also improve the capability of the autoencoder to learn non-trivial features of the jet images, such that it is able to achieve both top jet tagging and the inverse task of QCD jet tagging with the same setup. However, we want to stress that a truly model-independent and powerful autoencoder-based unsupervised jet tagger still needs to be developed.
1 Introduction
The introduction frames new-physics searches as finding anomalous, out-of-distribution events amid Standard Model collider data and motivates unsupervised methods that can be applied without labels. It proposes reversing the background and signal roles as a test of model-independence and studies an autoencoder on top and QCD jets.
1 Introduction
- Unsupervised learning uses data without labels, while semi-supervised anomaly detection trains on background-only data and tests on a mixed sample.The latter may suit particle-physics applications when signal-free control-region data are available.Source: §1 · p. 3
- An autoencoder compresses input into latent variables and reconstructs it; reconstruction loss can serve as an anomaly score when anomalies are reconstructed less effectively.The intended setup trains on background data so the bottleneck captures prominent background features.Source: §1 · pp. 3–4
- A model-independent tagger should remain effective when background and anomalous signal roles are interchanged; unequal performance indicates bias toward a particular anomaly.The introduction proposes this inversion as a simple test of model-independence.Source: §1 · p. 4
- The same autoencoder confirms top-jet tagging but fails to tag QCD jets as anomalies when trained on top jets, performing worse than random selection.The study uses this contrast to investigate how the autoencoder's learned features affect anomaly tagging.Source: §1 · p. 4
2 Autoencoder limitations
The section tests whether reconstruction-loss autoencoders can tag anomalies in either direction, tracing their benchmark performance to limited reconstruction and differences in jet-image complexity.
2 Autoencoder limitations
- The study compares semi-supervised tagging of top jets after QCD-only training with the inverse task of tagging QCD jets after top-only training.It examines how reconstruction capability and image complexity affect the two taggers.Source: §2 · p. 5
2.1 Jet data and autoencoder architecture
- For top tagging, simulated QCD jets are distinguished from hadronically decaying boosted top-quark jets; a convolutional autoencoder maps inputs to a 32-node bottleneck and uses mean squared error as the signal/background discriminator.During testing, an event is tagged as signal/anomaly when its loss exceeds a given threshold.Source: §2.1 · pp. 5–6
2.2 Limited reconstruction
- Across training, the autoencoder recovers the brightest pixels while leaving most dimmer pixels poorly reconstructed, and longer training does not substantially change this pattern.The dimmer pixels still dominate the total reconstruction error.Source: §2.2 · pp. 6, 8, Figure 3 · p. 7
2.3 Complexity bias
- Reconstruction loss rises with non-zero-pixel count, and QCD jets remain easier to reconstruct than top jets at matched counts, contributing to the inverse tagger’s difficulty.The authors describe this complexity bias as dangerous for model-independent tagging because anomaly images need not be more complex than background images.Source: §2.3 · pp. 9–10, Figure 6 · p. 10
2.4 Tagging performance
- The direct tagger performs better than random, but the inverse tagger performs worse than random, showing that this setup’s success does not transfer across anomaly directions.The authors conclude that an autoencoder can tag anomalies when it reconstructs the background better, but may fail when its bias works against detection.Source: Figure 7 · p. 11, §2.4 · p. 11
3 Improving the autoencoder performance
The paper improves autoencoder feature learning through intensity remapping and kernel MSE, then evaluates reconstruction and tagging. Remapping can improve inverse tagging, but its performance remains strongly tied to image pixel counts.
3 Improving the autoencoder performance
- The proposed remappings and KMSE are generic improvements to complexity bias and limited learning, evaluated through reconstruction and tagging performance.The authors frame them as improvements that may help any AE architecture.Source: §3 · pp. 11–12
3.1 Intensity remapping
- Intensity remapping enhances dim pixels to encourage learning more image features and may reduce complexity bias, while R4 loses information by mapping every non-zero pixel to one.After remapping, images are normalized to have pixel sum one.Source: §3.1 · p. 12
3.2 Kernel MSE
- KMSE smears images before calculating reconstruction loss, giving neighboring pixels overlapping distributions so that small shifts are less heavily penalized than under MSE.The authors propose this simpler alternative because Wasserstein-distance approaches require costly optimization or computation.Source: §3.2 · pp. 12–13
3.3 Autoencoder performance
- With R2 remapping, the AE reconstructs more leading pixels on average, but top-jet reconstruction gains come at reduced precision for the brightest pixels.For top-jet training, the remapping’s change beyond the 20th pixel concerns very soft particles.Source: §3.3 · pp. 13–14
- KMSE shifts reconstruction attention from exact leading-pixel intensities toward dimmer pixels and continuous jet structure, including regions far from the center.The authors expect this to expose more useful overall jet features than standard AE training focused almost exclusively on the brightest pixels.Source: §3.3 · pp. 14–15
- R2 reduces and reverses the QCD-trained AE’s complexity bias, but for top-trained AEs the inverse-tagging gain relies substantially on low-pixel-count QCD images.For top-trained AEs, top images are reconstructed better on average only below 40 active pixels, and the difference is small relative to distribution width and bias slope.Source: §3.3 · pp. 16–17
3.4 Tagging performance
- R2 gives ABC = 0.43 and ∆AUC = 0.06, while R3 gives the best ABC = 0.50 with ∆AUC = 0.18; R4 performs poorly with ABC = 0.11.For R2, direct and inverse tagging both have modest AUC close to 0.7; inverse tagging with remappings mostly relies on loss correlation with non-zero pixel count.Source: §3.4 · pp. 18–19
- With KMSE, R1 reaches ABC = 0.52 and ∆AUC = 0.27, while R2 has ABC = 0.27 and ∆AUC = −0.09 and R3 has ABC = 0.32 and ∆AUC = 0.02.KMSE improves overall performance for R1, but inverse taggers for R1–R4 remain close to the pixel-number tagger.Source: §3.4 · p. 19
4 Conclusion
The standard autoencoder’s success on top jets does not establish model-independent anomaly tagging: its complexity bias can favor reconstructing simpler QCD images. The authors propose task inversion and performance measures to assess this bias, and report promising but incomplete improvements.
4 Conclusion
- The autoencoder tags top jets well but reconstructs QCD images more successfully under pixel-wise MSE, whether trained on QCD or top jets.The authors attribute this mismatch to jet-image sparsity and the complexity bias of the tagger.Source: §4 · p. 20
- A strong tagger for one anomaly need not be model-independent: an autoencoder can favor background reconstruction for a particular signal, or interpolate to unseen anomalies.The authors caution that these observations arise from a specific benchmark, though they may generalize.Source: §4 · pp. 20–21
- Comparing direct and inverse tagging performance, such as their AUC difference or ROC-curve area, offers a proposed test of model-independence.The test interchanges the roles of background and signal.Source: §4 · p. 21
- Intensity remapping and kernel MSE are promising first steps, but the inverse QCD-tagging gain partly reflects reversed reconstruction bias, not a model-independent advantage.The authors say the progress is difficult to quantify and that better performance measures are needed.Source: §4 · p. 21
- A powerful, truly model-independent autoencoder for unsupervised jet-image tagging remains undeveloped.The authors also leave improved architectures and latent-space anomaly detection for future study.Source: §4 · p. 21
A Jet simulation and neural network architecture
This appendix specifies the simulated jet sample, image preprocessing, and neural-network setup used for the study. It also describes training and a supervised classifier used to check the framework.
A Jet simulation and neural network architecture
- Jets are simulated at 14 TeV with Pythia8 and fast Delphes detector simulation, clustered with anti-kT at R = 0.8, and selected within specified pT and η ranges.The sample ignores multiple interactions and pile-up, and stores the 200 highest-pT constituents, padding shorter jets with zeros.Source: A Jet simulation and neural network… · p. 22
- Preprocessing centers and rotates each jet, mirrors its hardest component into the first quadrant, and converts constituents into normalized 40×40 jet images.Pixel intensities sum to one after normalization.Source: A Jet simulation and neural network… · p. 22
- The convolutional autoencoder compresses image features through fully connected layers into a 32-node bottleneck, then decodes them to a 40×40 reconstruction.Its encoder uses convolutions and average pooling; the decoder uses fully connected layers, convolutions, and upsampling.Source: A Jet simulation and neural network… · p. 22
- Training uses 100k images with Adam and early stopping; the supervised CNN benchmark is trained on 100k images per class and has performance comparable to literature.KMSE training instead uses a 10−4 learning rate and batch size 64; the supervised CNN is validated on 40k images per class.Source: A Jet simulation and neural network… · p. 23
B Intensity distributions after remapping
The appendix describes intensity remappings that enhance dim jet-image pixels and examines their effect on pixel intensities. These transformations alter intensity distributions while preserving the number of non-zero pixels and the mean non-zero intensity after normalization.
B Intensity distributions after remapping
- The remappings R1–R4 apply root, logarithmic, or threshold functions to intensities, with different strengths of dim-pixel highlighting relative to identity mapping R0.The logarithmic remapping’s derivative remains finite at the origin, unlike the root functions.Source: B Intensity distributions after… · p. 23
- Highlighting dim pixels can make faint structure, such as a possible third top-jet sub-jet, easier for the autoencoder to learn.The original image leaves this dim region barely visible, so the authors expect remapping to expose its features.Source: B Intensity distributions after… · p. 23
- In the 100k top-jet training images, remapping compresses the non-zero pixel intensity distribution; R1 and R3 span about 1.5 orders of magnitude, while R2 lies nearly within one.The original distribution is broad, with its median more than an order of magnitude below its average.Source: B Intensity distributions after… · pp. 23–24
- After final normalization, remapping leaves the number of non-zero pixels and the average non-zero pixel intensity unchanged.R4’s intensity distribution reflects the distribution of the overall number of non-zero pixels.Source: B Intensity distributions after… · p. 24
C Further results
The appendix collects performance measures for direct and inverse taggers and adds visualizations of reconstruction behavior. The supplied passages identify the tables’ scope and the figures’ encodings, but do not provide table values or result comparisons.
C Further results
- E10 and E100 denote signal efficiencies at background rejection factors of 10 and 100, respectively.The measures are defined as ϵS(1/ϵB = 10) and ϵS(1/ϵB = 100).Source: C Further results · p. 24
- Figures 19 and 20 show reconstruction loss versus non-zero pixel count and reconstructed-to-input intensity ratios, across remappings and MSE or KMSE training.Figure 19 compares AEs trained on QCD and top jets; Figure 20 orders pixels by intensity for each test jet.Source: C Further results · p. 24, Figure 19 · p. 26, Figure 20 · p. 28
- Tables 1 and 2 collect direct- and inverse-tagger performance measures for remapped images trained with MSE and KMSE, respectively.Each table value averages four autoencoders with different initializations, and uncertainties give the envelope.Source: C Further results · p. 24, Table 1 · p. 27, Table 2 · p. 27