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Intrinsic dimension of collider events and model-independent searches in 100 dimensions

Raffaele Tito D’Agnolo1,2, Alfredo Glioti3, Gabriele Rigo1, and Alessandro Valenti4

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Phys. Rev. D 114, 016022 – Published 22 July, 2026

DOI: https://doi.org/10.1103/b88w-s5kl

Abstract

The phase space of hadron collider events spans hundreds of dimensions, generating an intricate geometry that we are just starting to explore. The number of possible new physics signals is exponential in the number of dimensions and detecting all of them is currently impossible for any human or artificial intelligence. In this work we introduce a method to search for new physics model independently in this high-dimensional space. It is based on the measurement of the most basic property of the manifold of collider events, its dimensionality. Our proposed technique does not suffer from a look-elsewhere effect that grows exponentially with the number of dimensions of the dataset, and by construction is insensitive to energy scale uncertainties. We illustrate its potential by finding new physics in simulated events with hundreds of phase space dimensions, taking as input single particles rather than jets. This study sets the stage for new model-independent search strategies based on global properties of collider data manifolds.

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References (196)

  1. P. T. Komiske, E. M. Metodiev, and J. Thaler, Metric space of collider events, Phys. Rev. Lett. 123, 041801 (2019).
  2. P. T. Komiske, E. M. Metodiev, and J. Thaler, The hidden geometry of particle collisions, J. High Energy Phys. 07 (2020) 006.
  3. E. Levina and P. J. Bickel, Maximum likelihood estimation of intrinsic dimension, in Neural Information Processing Systems (MIT Press, Cambridge, MA, 2004), https://api.semanticscholar.org/CorpusID:14865278.
  4. C. Ceruti, S. Bassis, A. Rozza, G. Lombardi, E. Casiraghi, and P. Campadelli, Danco: Dimensionality from angle and norm concentration, arXiv:1206.3881.
  5. E. Facco, M. d’Errico, A. Rodriguez, and A. Laio, Estimating the intrinsic dimension of datasets by a minimal neighborhood information, Sci. Rep. 7, 12140 (2017).
  6. F. Denti, D. Doimo, A. Laio, and A. Mira, The generalized ratios intrinsic dimension estimator, Sci. Rep. 12, 20005 (2022).
  7. P. Campadelli, E. Casiraghi, C. Ceruti, and A. Rozza, Intrinsic dimension estimation: Relevant techniques and a benchmark framework, Math. Problems Eng. 2015, 759567 (2015).
  8. F. Camastra and A. Staiano, Intrinsic dimension estimation: Advances and open problems, Inf. Sci. (NY) 328, 26 (2016).
  9. C. Cesarotti and J. Thaler, A robust measure of event isotropy at colliders, J. High Energy Phys. 08 (2020) 084.
  10. D. Ba, A. S. Dogra, R. Gambhir, A. Tasissa, and J. Thaler, SHAPER: Can you hear the shape of a jet?, J. High Energy Phys. 06 (2023) 195.
  11. T. Cai, J. Cheng, N. Craig, and K. Craig, Linearized optimal transport for collider events, Phys. Rev. D 102, 116019 (2020).
  12. T. Cai, J. Cheng, K. Craig, and N. Craig, Which metric on the space of collider events?, Phys. Rev. D 105, 076003 (2022).
  13. T. Cai, J. Cheng, B. Schmitzer, and M. Thorpe, The linearized Hellinger–Kantorovich distance, SIAM J. Imaging Sci. 15, 45 (2022).
  14. P. T. Komiske, R. Mastandrea, E. M. Metodiev, P. Naik, and J. Thaler, Exploring the space of jets with CMS open data, Phys. Rev. D 101, 034009 (2020).
  15. P. T. Komiske, S. Kryhin, and J. Thaler, Disentangling quarks and gluons in CMS open data, Phys. Rev. D 106, 094021 (2022).
  16. A. Mullin, S. Nicholls, H. Pacey, M. Parker, M. White, and S. Williams, Does SUSY have friends? A new approach for LHC event analysis, J. High Energy Phys. 02 (2021) 160.
  17. M. Crispim Romão, N. F. Castro, J. G. Milhano, R. Pedro, and T. Vale, Use of a generalized energy Mover’s distance in the search for rare phenomena at colliders, Eur. Phys. J. C 81, 192 (2021).
  18. A. Davis, T. Menzo, A. Youssef, and J. Zupan, Earth mover’s distance as a measure of CP violation, J. High Energy Phys. 06 (2023) 098.
  19. S. Tsan, R. Kansal, A. Aportela, D. Diaz, J. Duarte, S. Krishna et al., Particle graph autoencoders and differentiable, learned energy mover’s distance, in Proceedings of the 35th Conference on Neural Information Processing Systems (2021), arXiv:2111.12849.
  20. O. Kitouni, N. Nolte, and M. Williams, Finding NEEMo: Geometric fitting using neural estimation of the energy mover’s distance, arXiv:2209.15624.
  21. S. Alipour-Fard, P. T. Komiske, E. M. Metodiev, and J. Thaler, Pileup and infrared radiation annihilation (PIRANHA): A paradigm for continuous jet grooming, J. High Energy Phys. 09 (2023) 157.
  22. A. J. Larkoski and T. Melia, Covariantizing phase space, Phys. Rev. D 102, 094014 (2020).
  23. T. Cai, J. Cheng, N. Craig, G. Koszegi, and A. J. Larkoski, The phase space distance between collider events, J. High Energy Phys. 09 (2024) 054.
  24. T. Cai, N. Craig, K. Craig, and X. Lin, Multi-scale Optimal Transport for Complete Collider Events, Phys. Rev. D 112, 036021 (2025).
  25. K. W. Pettis, T. A. Bailey, A. K. Jain, and R. C. Dubes, An intrinsic dimensionality estimator from near-neighbor information, in IEEE Transactions on Pattern Analysis and Machine Intelligence (IEEE Computer Society, Los Alamitos, CA, 1979), p. 25.
  26. L. van der Maaten, E. O. Postma, and J. van den Herik, Dimensionality reduction: A comparative review (2008), https://api.semanticscholar.org/CorpusID:12051918.
  27. A. Rozza, G. Lombardi, C. Ceruti, E. Casiraghi, and P. Campadelli, Novel high intrinsic dimensionality estimators, Mach. Learn. 89, 37 (2012).
  28. A. Ansuini, A. Laio, J. H. Macke, and D. Zoccolan, Intrinsic dimension of data representations in deep neural networks, Adv. Neural Inf. Process. Syst. 32, 6111 (2019).
  29. P. Pope, C. Zhu, A. Abdelkader, M. Goldblum, and T. Goldstein, The intrinsic dimension of images and its impact on learning, arXiv:2104.08894.
  30. L. Valeriani, D. Doimo, F. Cuturello, A. Laio, A. Ansuini, and A. Cazzaniga, The geometry of hidden representations of large transformer models, arXiv:2302.00294.
  31. J. Gliozzo, M. Soto-Gomez, V. Guarino, A. Bonometti, A. Cabri, E. Cavalleri, J. Reese, P. N. Robinson, M. Mesiti, G. Valentini, and E. Casiraghi, Intrinsic-dimension analysis for guiding dimensionality reduction and data fusion in multi-omics data processing, Artif. Intell. Med. 160, 103049 (2025).
  32. P. Grassberger and I. Procaccia, Characterization of strange attractors, Phys. Rev. Lett. 50, 346 (1983).
  33. H. G. E. Hentschel and I. Procaccia, The infinite number of generalized dimensions of fractals and strange attractors, Physica D (Amsterdam) 8, 435 (1983).
  34. E. Levina and P. Bickel, Maximum likelihood estimation of intrinsic dimension, in Advances in Neural Information Processing Systems, edited by L. Saul, Y. Weiss, and L. Bottou (MIT Press, Cambridge, MA, 2004), Vol. 17, https://proceedings.neurips.cc/paper_files/paper/2004/file/74934548253bcab8490ebd74afed7031-Paper.pdf.
  35. CMS Collaboration, MUSiC: A model-unspecific search for new physics in proton–proton collisions at s=13  TeV, Eur. Phys. J. C 81, 629 (2021).
  36. J. A. Aguilar-Saavedra, J. H. Collins, and R. K. Mishra, A generic anti-QCD jet tagger, J. High Energy Phys. 11 (2017) 163.
  37. J. H. Collins, K. Howe, and B. Nachman, Anomaly detection for resonant new physics with machine learning, Phys. Rev. Lett. 121, 241803 (2018).
  38. R. T. D’Agnolo and A. Wulzer, Learning new physics from a machine, Phys. Rev. D 99, 015014 (2019).
  39. A. De Simone and T. Jacques, Guiding new physics searches with unsupervised learning, Eur. Phys. J. C 79, 289 (2019).
  40. J. Hajer, Y.-Y. Li, T. Liu, and H. Wang, Novelty detection meets collider physics, Phys. Rev. D 101, 076015 (2020).
  41. M. Farina, Y. Nakai, and D. Shih, Searching for new physics with deep autoencoders, Phys. Rev. D 101, 075021 (2020).
  42. T. Heimel, G. Kasieczka, T. Plehn, and J. M. Thompson, QCD or what?, SciPost Phys. 6, 030 (2019).
  43. A. Casa and G. Menardi, Nonparametric semisupervised classification for signal detection in high energy physics, arXiv:1809.02977.
  44. O. Cerri, T. Q. Nguyen, M. Pierini, M. Spiropulu, and J.-R. Vlimant, Variational autoencoders for new physics mining at the Large Hadron Collider, J. High Energy Phys. 05 (2019) 036.
  45. J. H. Collins, K. Howe, and B. Nachman, Extending the search for new resonances with machine learning, Phys. Rev. D 99, 014038 (2019).
  46. T. S. Roy and A. H. Vijay, A robust anomaly finder based on autoencoders, arXiv:1903.02032.
  47. B. M. Dillon, D. A. Faroughy, and J. F. Kamenik, Uncovering latent jet substructure, Phys. Rev. D 100, 056002 (2019).
  48. A. Blance, M. Spannowsky, and P. Waite, Adversarially-trained autoencoders for robust unsupervised new physics searches, J. High Energy Phys. 10 (2019) 047.
  49. M. Romão Crispim, N. F. Castro, R. Pedro, and T. Vale, Transferability of deep learning models in searches for new physics at colliders, Phys. Rev. D 101, 035042 (2020).
  50. R. T. D’Agnolo, G. Grosso, M. Pierini, A. Wulzer, and M. Zanetti, Learning multivariate new physics, Eur. Phys. J. C 81, 89 (2021).
  51. B. Nachman and D. Shih, Anomaly detection with density estimation, Phys. Rev. D 101, 075042 (2020).
  52. A. Andreassen, B. Nachman, and D. Shih, Simulation assisted likelihood-free anomaly detection, Phys. Rev. D 101, 095004 (2020).
  53. O. Amram and C. M. Suarez, Tag N’ train: A technique to train improved classifiers on unlabeled data, J. High Energy Phys. 01 (2021) 153.
  54. M. Crispim Romão, N. F. Castro, J. G. Milhano, R. Pedro, and T. Vale, Use of a generalized energy Mover’s distance in the search for rare phenomena at colliders, Eur. Phys. J. C 81, 192 (2021).
  55. O. Knapp, O. Cerri, G. Dissertori, T. Q. Nguyen, M. Pierini, and J.-R. Vlimant, Adversarially learned anomaly detection on CMS open data: Re-discovering the top quark, Eur. Phys. J. Plus 136, 236 (2021).
  56. ATLAS Collaboration, Dijet resonance search with weak supervision using s=13  TeV pp collisions in the ATLAS detector, Phys. Rev. Lett. 125, 131801 (2020).
  57. B. M. Dillon, D. A. Faroughy, J. F. Kamenik, and M. Szewc, Learning the latent structure of collider events, J. High Energy Phys. 10 (2020) 206.
  58. M. Crispim Romão, N. F. Castro, and R. Pedro, Finding new physics without learning about it: Anomaly detection as a tool for searches at colliders, Eur. Phys. J. C 81, 27 (2021).
  59. T. Cheng, J.-F. Arguin, J. Leissner-Martin, J. Pilette, and T. Golling, Variational autoencoders for anomalous jet tagging, Phys. Rev. D 107, 016002 (2023).
  60. C. K. Khosa and V. Sanz, Anomaly awareness, SciPost Phys. 15, 053 (2023).
  61. P. Thaprasop, K. Zhou, J. Steinheimer, and C. Herold, Unsupervised outlier detection in heavy-ion collisions, Phys. Scr. 96, 064003 (2021).
  62. J. A. Aguilar-Saavedra, F. R. Joaquim, and J. F. Seabra, Mass unspecific supervised tagging (MUST) for boosted jets, J. High Energy Phys. 03 (2021) 012.
  63. S. Alexander, S. Gleyzer, H. Parul, P. Reddy, M. W. Toomey, E. Usai et al., Decoding dark matter substructure without supervision, arXiv:2008.12731.
  64. K. Benkendorfer, L. L. Pottier, and B. Nachman, Simulation-assisted decorrelation for resonant anomaly detection, Phys. Rev. D 104, 035003 (2021).
  65. A. A. Pol, V. Berger, G. Cerminara, C. Germain, and M. Pierini, Anomaly detection with conditional variational autoencoders, in Eighteenth International Conference on Machine Learning and Applications (2020), arXiv:2010.05531.
  66. V. Mikuni and F. Canelli, Unsupervised clustering for collider physics, Phys. Rev. D 103, 092007 (2021).
  67. M. van Beekveld, S. Caron, L. Hendriks, P. Jackson, A. Leinweber, S. Otten, Riley Patrick, R. R. de Austri, M. Santoni, and M. White, Combining outlier analysis algorithms to identify new physics at the LHC, J. High Energy Phys. 09 (2021) 024.
  68. S. E. Park, D. Rankin, S.-M. Udrescu, M. Yunus, and P. Harris, Quasi Anomalous Knowledge: Searching for new physics with embedded knowledge, J. High Energy Phys. 21 (2020) 030.
  69. D. A. Faroughy, Uncovering hidden new physics patterns in collider events using Bayesian probabilistic models, Proc. Sci. ICHEP2020 (2021) 238 [arXiv:2012.08579].
  70. G. Stein, U. Seljak, and B. Dai, Unsupervised in-distribution anomaly detection of new physics through conditional density estimation, in Proceedings of the 34th Conference on Neural Information Processing Systems (2020), arXiv:2012.11638.
  71. G. Kasieczka et al., The LHC Olympics 2020 a community challenge for anomaly detection in high energy physics, Rep. Prog. Phys. 84, 124201 (2021).
  72. P. Chakravarti, M. Kuusela, J. Lei, and L. Wasserman, Model-independent detection of new physics signals using interpretable semi-supervised classifier tests, arXiv:2102.07679.
  73. J. Batson, C. G. Haaf, Y. Kahn, and D. A. Roberts, Topological obstructions to autoencoding, J. High Energy Phys. 04 (2021) 280.
  74. A. Blance and M. Spannowsky, Unsupervised event classification with graphs on classical and photonic quantum computers, J. High Energy Phys. 21 (2020) 170.
  75. B. Bortolato, A. Smolkovič, B. M. Dillon, and J. F. Kamenik, Bump hunting in latent space, Phys. Rev. D 105, 115009 (2022).
  76. J. H. Collins, P. Martín-Ramiro, B. Nachman, and D. Shih, Comparing weak- and unsupervised methods for resonant anomaly detection, Eur. Phys. J. C 81, 617 (2021).
  77. B. M. Dillon, T. Plehn, C. Sauer, and P. Sorrenson, Better latent spaces for better autoencoders, SciPost Phys. 11, 061 (2021).
  78. T. Finke, M. Krämer, A. Morandini, A. Mück, and I. Oleksiyuk, Autoencoders for unsupervised anomaly detection in high energy physics, J. High Energy Phys. 06 (2021) 161.
  79. D. Shih, M. R. Buckley, L. Necib, and J. Tamanas, Via machinae: Searching for stellar streams using unsupervised machine learning, Mon. Not. R. Astron. Soc. 509, 5992 (2021).
  80. O. Atkinson, A. Bhardwaj, C. Englert, V. S. Ngairangbam, and M. Spannowsky, Anomaly detection with convolutional graph neural networks, J. High Energy Phys. 08 (2021) 080.
  81. A. Kahn, J. Gonski, I. Ochoa, D. Williams, and G. Brooijmans, Anomalous jet identification via sequence modeling, J. Instrum. 16, P08012 (2021).
  82. T. Aarrestad et al., The dark machines anomaly score challenge: Benchmark data and model independent event classification for the Large Hadron Collider, SciPost Phys. 12, 043 (2022).
  83. T. Dorigo, M. Fumanelli, C. Maccani, M. Mojsovska, G. C. Strong, and B. Scarpa, RanBox: Anomaly detection in the copula space, J. High Energy Phys. 01 (2023) 008.
  84. S. Caron, L. Hendriks, and R. Verheyen, Rare and different: Anomaly scores from a combination of likelihood and out-of-distribution models to detect new physics at the LHC, SciPost Phys. 12, 077 (2022).
  85. E. Govorkova, E. Puljak, T. Aarrestad, M. Pierini, K. A. Woźniak, and J. Ngadiuba, LHC physics dataset for unsupervised new physics detection at 40 MHz, Sci. Data 9, 118 (2022).
  86. G. Kasieczka, B. Nachman, and D. Shih, New methods and datasets for group anomaly detection from fundamental physics, in Conference on Knowledge Discovery and Data Mining (2021), arXiv:2107.02821.
  87. S. Volkovich, F. De Vito Halevy, and S. Bressler, A data-directed paradigm for BSM searches: The bump-hunting example, Eur. Phys. J. C 82, 265 (2022).
  88. E. Govorkova et al., Autoencoders on field-programmable gate arrays for real-time, unsupervised new physics detection at 40 MHz at the Large Hadron Collider, Nat. Mach. Intell. 4, 154 (2022).
  89. A. Hallin, J. Isaacson, G. Kasieczka, C. Krause, B. Nachman, T. Quadfasel, M. Schlaffer, D. Shih, and M. Sommerhalder, Classifying anomalies through outer density estimation, Phys. Rev. D 106, 055006 (2022).
  90. B. Ostdiek, Deep set auto encoders for anomaly detection in particle physics, SciPost Phys. 12, 045 (2022).
  91. K. Fraser, S. Homiller, R. K. Mishra, B. Ostdiek, and M. D. Schwartz, Challenges for unsupervised anomaly detection in particle physics, J. High Energy Phys. 03 (2022) 066.
  92. P. Jawahar, T. Aarrestad, N. Chernyavskaya, M. Pierini, K. A. Wozniak, J. Ngadiuba et al., Improving variational autoencoders for new physics detection at the LHC with normalizing flows, Front. Big Data 5, 803685 (2022).
  93. J. Herrero-Garcia, R. Patrick, and A. Scaffidi, A semi-supervised approach to dark matter searches in direct detection data with machine learning, J. Cosmol. Astropart. Phys. 02 (2022) 039.
  94. C. G. Lester and R. Tombs, Using unsupervised learning to detect broken symmetries, with relevance to searches for parity violation in nature. (Previously: “Stressed GANs snag desserts”), arXiv:2111.00616.
  95. J. A. Aguilar-Saavedra, Anomaly detection from mass unspecific jet tagging, Eur. Phys. J. C 82, 130 (2022).
  96. R. Tombs and C. G. Lester, A method to challenge symmetries in data with self-supervised learning, J. Instrum. 17, P08024 (2022).
  97. V. Mikuni, B. Nachman, and D. Shih, Online-compatible unsupervised nonresonant anomaly detection, Phys. Rev. D 105, 055006 (2022).
  98. S. Chekanov and W. Hopkins, Event-based anomaly detection for searches for new physics, Universe 8, 494 (2022).
  99. R. T. d’Agnolo, G. Grosso, M. Pierini, A. Wulzer, and M. Zanetti, Learning new physics from an imperfect machine, Eur. Phys. J. C 82, 275 (2022).
  100. F. Canelli, A. de Cosa, L. L. Pottier, J. Niedziela, K. Pedro, and M. Pierini, Autoencoders for semivisible jet detection, J. High Energy Phys. 02 (2022) 074.
  101. V. S. Ngairangbam, M. Spannowsky, and M. Takeuchi, Anomaly detection in high-energy physics using a quantum autoencoder, Phys. Rev. D 105, 095004 (2022).
  102. J. A. Aguilar-Saavedra, Taming modeling uncertainties with mass unspecific supervised tagging, Eur. Phys. J. C 82, 270 (2022).
  103. T. Buss, B. M. Dillon, T. Finke, M. Krämer, A. Morandini, A. Mück, I. Oleksiyuk, and T. Plehn, What’s anomalous in LHC jets?, SciPost Phys. 15, 168 (2023).
  104. L. Bradshaw, S. Chang, and B. Ostdiek, Creating simple, interpretable anomaly detectors for new physics in jet substructure, Phys. Rev. D 106, 035014 (2022).
  105. M. Birman, B. Nachman, R. Sebbah, G. Sela, O. Turetz, and S. Bressler, Data-directed search for new physics based on symmetries of the SM, Eur. Phys. J. C 82, 508 (2022).
  106. J. A. Raine, S. Klein, D. Sengupta, and T. Golling, CURTAINs for your sliding window: Constructing unobserved regions by transforming adjacent intervals, Front. Big Data 6, 899345 (2023).
  107. M. Letizia, G. Losapio, M. Rando, G. Grosso, A. Wulzer, M. Pierini, M. Zanetti, and L. Rosasco, Learning new physics efficiently with nonparametric methods, Eur. Phys. J. C 82, 879 (2022).
  108. C. Fanelli, J. Giroux, and Z. Papandreou, “Flux + Mutability”: A conditional generative approach to one-class classification and anomaly detection, Mach. Learn. Sci. Tech. 3, 045012 (2022).
  109. T. Finke, M. Krämer, M. Lipp, and A. Mück, Boosting mono-jet searches with model-agnostic machine learning, J. High Energy Phys. 08 (2022) 015.
  110. R. Verheyen, Event generation and density estimation with surjective normalizing flows, SciPost Phys. 13, 047 (2022).
  111. B. M. Dillon, R. Mastandrea, and B. Nachman, Self-supervised anomaly detection for new physics, Phys. Rev. D 106, 056005 (2022).
  112. S. Alvi, C. W. Bauer, and B. Nachman, Quantum anomaly detection for collider physics, J. High Energy Phys. 02 (2023) 220.
  113. B. M. Dillon, L. Favaro, T. Plehn, P. Sorrenson, and M. Krämer, A normalized autoencoder for LHC triggers, SciPost Phys. Core 6, 074 (2023).
  114. S. Caron, R. R. de Austri, and Z. Zhang, Mixture-of-theories training: Can we find new physics and anomalies better by mixing physical theories?, J. High Energy Phys. 03 (2023) 004.
  115. S. E. Park, P. Harris, and B. Ostdiek, Neural embedding: Learning the embedding of the manifold of physics data, J. High Energy Phys. 07 (2023) 108.
  116. G. Kasieczka, R. Mastandrea, V. Mikuni, B. Nachman, M. Pettee, and D. Shih, Anomaly detection under coordinate transformations, Phys. Rev. D 107, 015009 (2023).
  117. J. F. Kamenik and M. Szewc, Null hypothesis test for anomaly detection, Phys. Lett. B 840, 137836 (2023).
  118. A. Hallin, G. Kasieczka, T. Quadfasel, D. Shih, and M. Sommerhalder, Resonant anomaly detection without background sculpting, Phys. Rev. D 107, 114012 (2023).
  119. J. Y. Araz and M. Spannowsky, Quantum-probabilistic Hamiltonian learning for generative modeling and anomaly detection, Phys. Rev. A 108, 062422 (2023).
  120. R. Mastandrea and B. Nachman, Efficiently moving instead of reweighting collider events with machine learning, in Proceedings of the 36th Conference on Neural Information Processing Systems: Workshop on Machine Learning and the Physical Sciences (2022), arXiv:2212.06155.
  121. J. Schuhmacher, L. Boggia, V. Belis, E. Puljak, M. Grossi, M. Pierini et al., Unravelling physics beyond the standard model with classical and quantum anomaly detection, Mach. Learn. Sci. Tech. 4, 045031 (2023).
  122. T. Golling et al., The mass-ive issue: Anomaly detection in jet physics, in Proceedings of the 34th Conference on Neural Information Processing Systems (2023), arXiv:2303.14134.
  123. S. Roche, Q. Bayer, B. Carlson, W. Ouligian, P. Serhiayenka, J. Stelzer, and T. M. Hong, Nanosecond anomaly detection with decision trees and real-time application to exotic Higgs decays, Nat. Commun. 15, 3527 (2024).
  124. D. Sengupta, S. Klein, J. A. Raine, and T. Golling, CURTAINs flows for flows: Constructing unobserved regions with maximum likelihood estimation, SciPost Phys. 17, 046 (2024).
  125. J. A. Aguilar-Saavedra, E. Arganda, F. R. Joaquim, R. M. Sandá Seoane, and J. F. Seabra, Gradient boosting MUST taggers for highly-boosted jets, Eur. Phys. J. Plus 139, 1019 (2024).
  126. L. Vaslin, V. Barra, and J. Donini, GAN-AE: An anomaly detection algorithm for new physics search in LHC data, Eur. Phys. J. C 83, 1008 (2023).
  127. ATLAS Collaboration, Anomaly detection search for new resonances decaying into a Higgs boson and a generic new particle X in hadronic final states using s=13  TeV pp collisions with the ATLAS detector, Phys. Rev. D 108, 052009 (2023).
  128. V. Mikuni and B. Nachman, High-dimensional and permutation invariant anomaly detection, SciPost Phys. 16, 062 (2024).
  129. T. Golling, G. Kasieczka, C. Krause, R. Mastandrea, B. Nachman, J. A. Raine, D. Sengupta, D. Shih, and M. Sommerhalder, The interplay of machine learning-based resonant anomaly detection methods, Eur. Phys. J. C 84, 241 (2024).
  130. S. V. Chekanov and R. Zhang, Enhancing the hunt for new phenomena in dijet final states using anomaly detection filters at the high-luminosity Large Hadron Collider, Eur. Phys. J. Plus 139, 237 (2024).
  131. CMS ECAL Collaboration, Autoencoder-based anomaly detection system for online data quality monitoring of the CMS electromagnetic calorimeter, Comput. Softw. Big Sci. 8, 11 (2024).
  132. G. Bickendorf, M. Drees, G. Kasieczka, C. Krause, and D. Shih, Combining resonant and tail-based anomaly detection, Phys. Rev. D 109, 096031 (2024).
  133. T. Finke, M. Hein, G. Kasieczka, M. Krämer, A. Mück, P. Prangchaikul, T. Quadfasel, D. Shih, and M. Sommerhalder, Tree-based algorithms for weakly supervised anomaly detection, Phys. Rev. D 109, 034033 (2024).
  134. E. Buhmann, C. Ewen, G. Kasieczka, V. Mikuni, B. Nachman, and D. Shih, Full phase space resonant anomaly detection, Phys. Rev. D 109, 055015 (2024).
  135. M. Freytsis, M. Perelstein, and Y. C. San, Anomaly detection in the presence of irrelevant features, J. High Energy Phys. 02 (2024) 220.
  136. E. M. Metodiev, J. Thaler, and R. Wynne, Anomaly detection in collider physics via factorized observables, Phys. Rev. D 110, 055012 (2024).
  137. A. Banda, C. K. Khosa, and V. Sanz, Strengthening anomaly awareness, arXiv:2504.11520.
  138. E. Puljak, M. Pierini, and A. Garcia-Saez, Tensor network for anomaly detection in the latent space of proton collision events at the LHC, Mach. Learn. Sci. Tech. 6, 045001 (2025).
  139. CMS Collaboration, Wasserstein normalized autoencoder for anomaly detection, Mach. Learn. Sci. Tech. 7, 035030 (2026).
  140. CMS Collaboration, Model-agnostic search for dijet resonances with anomalous jet substructure in proton–proton collisions at s=13  TeV, Rep. Prog. Phys. 88, 067802 (2025).
  141. S. Bright-Thonney, C. Reissel, G. Grosso, N. Woodward, K. Govorkova, A. Novak et al., Autoscidact: Automated scientific discovery through contrastive embedding and hypothesis testing, arXiv:2510.21935.
  142. G. Grosso, S. S. R. Hindupur, T. Fel, S. Bright-Thonney, P. Harris, and D. Ba, Sparse, self-organizing ensembles of local kernels detect rare statistical anomalies, arXiv:2511.03095.
  143. A. van den Oord, Y. Li, and O. Vinyals, Representation learning with contrastive predictive coding, arXiv:1807.03748.
  144. Y. Wang and M. I. Jordan, Desiderata for representation learning: A causal perspective, arXiv:2109.03795.
  145. M. M. Bronstein, J. Bruna, T. Cohen, and P. Veličković, Geometric deep learning: Grids, groups, graphs, geodesics, and gauges, arXiv:2104.13478.
  146. L. Condren and D. Whiteson, Finding unexpected non-helical tracks, Phys. Rev. D 113, 092020 (2026).
  147. J. Forsyth, M. Low, C. Tenney, and C. B. Verhaaren, Visible collider signals of natural quirks, Phys. Rev. D 111, 115021 (2025).
  148. M. Farina and M. Low, Constraining quirky tracks with conventional searches, Phys. Rev. Lett. 119, 111801 (2017).
  149. Q. Sha, D. Murnane, M. Fieg, S. Tong, M. Zakharyan, Y. Fang et al., Learning to reconstruct quirky tracks, arXiv:2410.00269.
  150. S. Knapen, H. K. Lou, M. Papucci, and J. Setford, Tracking down quirks at the Large Hadron Collider, Phys. Rev. D 96, 115015 (2017).
  151. J. Li, T. Li, J. Pei, and W. Zhang, Uncovering quirk signal via energy loss inside tracker, Phys. Rev. D 102, 056006 (2020).
  152. J. Li, T. Li, J. Pei, and W. Zhang, The quirk trajectory, Eur. Phys. J. C 80, 651 (2020).
  153. S. Knapen, S. Pagan Griso, M. Papucci, and D. J. Robinson, Triggering soft bombs at the LHC, J. High Energy Phys. 08 (2017) 076.
  154. J. Kingman, Poisson Processes (Oxford Science Publications, Clarendon Press, Oxford, 1993).
  155. F. Denti, D. Doimo, A. Laio, and A. Mira, Distributional results for model-based intrinsic dimension estimators, arXiv:2104.13832.
  156. A. J. Larkoski and J. Thaler, A spectral metric for collider geometry, J. High Energy Phys. 08 (2023) 107.
  157. R. Gambhir, A. J. Larkoski, and J. Thaler, SPECTER: Efficient evaluation of the spectral EMD, J. High Energy Phys. 12 (2025) 219.
  158. G. Casella and R. Berger, Statistical Inference (Duxbury Press, Belmont, CA, 1990).
  159. P. J. Huber, Robust estimation of a location parameter, The Annals of Mathematical Statistics (Institute of Mathematical Statistics, San Francisco, CA, 1964), p. 73.
  160. P. J. Huber, Robust regression: Asymptotics, conjectures and Monte Carlo, The Annals of Statistics (Institute of Mathematical Statistics, San Francisco, CA, 1973), p. 799.
  161. I. Jolliffe, Principal Component Analysis (Springer, New York, 2002), 10.1007/b98835.
  162. M. A. A. Cox and T. F. Cox, Multidimensional scaling, in Handbook of Data Visualization (Springer, Berlin, Heidelberg, 2008), pp. 315–347.
  163. S. T. Roweis and L. K. Saul, Nonlinear dimensionality reduction by locally linear embedding, Science 290, 2323 (2000).
  164. R. R. Coifman and S. Lafon, Diffusion maps, Appl. Comput. Harmon. Anal. 21, 5 (2006).
  165. J. B. Tenenbaum, V. de Silva, and J. C. Langford, A global geometric framework for nonlinear dimensionality reduction, Science 290, 2319 (2000).
  166. M. Belkin and P. Niyogi, Laplacian eigenmaps for dimensionality reduction and data representation, Neural Comput. 15, 1373 (2003).
  167. E. Facco, M. d’Errico, A. Rodriguez, and A. Laio, Estimating the intrinsic dimension of datasets by a minimal neighborhood information, Sci. Rep. 7 (2017).
  168. D. Granata and V. Carnevale, Accurate estimation of the intrinsic dimension using graph distances: Unraveling the geometric complexity of datasets, Sci. Rep. 6, 31377 (2016).
  169. S. Bressler, I. Savoray, and Y. Zurgil, Learning new physics from data: A symmetrized approach, Phys. Rev. D 110, 095004 (2024).
  170. CMS Collaboration, High-precision measurement of the W boson mass with the CMS experiment at the LHC, Nature (London) 652, 321 (2026).
  171. ATLAS Collaboration, Measurement of the W-boson mass and width with the ATLAS detector using proton–proton collisions at s=7  TeV, Eur. Phys. J. C 84, 1309 (2024).
  172. T. Anderson, An Introduction to Multivariate Statistical Analysis, Wiley Series in Probability and Statistics (Wiley, New York, 2003).
  173. H. Hotelling, The generalization of student’s ratio, Ann. Math. Stat. 2, 54 (1931).
  174. J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, H.-S. Shao, T. Stelzer, P. Torrielli, and M. Zaro, The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations, J. High Energy Phys. 07 (2014) 079.
  175. B. C. Allanach et al., SUSY Les Houches Accord 2, Comput. Phys. Commun. 180, 8 (2009).
  176. T. Sjöstrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai, P. Ilten, S. Mrenna, S. Prestel, C. O. Rasmussen, and P. Z. Skands, An introduction to pythia 8.2, Comput. Phys. Commun. 191, 159 (2015).
  177. DELPHES 3 Collaboration, delphes 3, A modular framework for fast simulation of a generic collider experiment, J. High Energy Phys. 02 (2014) 057.
  178. P. T. Komiske, E. M. Metodiev, and J. Thaler, Energy flow polynomials: A complete linear basis for jet substructure, J. High Energy Phys. 04 (2018) 013.
  179. P. T. Komiske, E. M. Metodiev, and J. Thaler, Energy flow networks: Deep sets for particle jets, J. High Energy Phys. 01 (2019) 121.
  180. P. T. Komiske, E. M. Metodiev, and J. Thaler, Cutting multiparticle correlators down to size, Phys. Rev. D 101, 036019 (2020).
  181. A. Andreassen, P. T. Komiske, E. M. Metodiev, B. Nachman, and J. Thaler, OmniFold: A method to simultaneously unfold all observables, Phys. Rev. Lett. 124, 182001 (2020).
  182. CMS Collaboration, Measurement of the inclusive and differential WZ production cross sections, polarization angles, and triple gauge couplings in pp collisions at s=13  TeV, J. High Energy Phys. 07 (2022) 032.
  183. CMS Collaboration, Measurement of the inclusive WZ production cross section in pp collisions at s=13.6  TeV, J. High Energy Phys. 04 (2025) 115.
  184. Particle Data Group Collaboration, Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  185. delphes default CMS card, https://github.com/delphes/delphes/blob/master/cards/delphes_card_CMS.tcl.
  186. CMS Collaboration, Precision luminosity measurement in proton-proton collisions at s=13  TeV in 2015 and 2016 at CMS, Eur. Phys. J. C 81, 800 (2021).
  187. ATLAS Collaboration, Search for a new Z′ gauge boson in 4μ events with the ATLAS experiment, J. High Energy Phys. 07 (2023) 090.
  188. F. del Aguila, M. Chala, J. Santiago, and Y. Yamamoto, Collider limits on leptophilic interactions, J. High Energy Phys. 03 (2015) 059.
  189. CMS Collaboration, Measurements of pp→ZZ production cross sections and constraints on anomalous triple gauge couplings at s=13  TeV, Eur. Phys. J. C 81, 200 (2021).
  190. ATLAS Collaboration, Searches for new phenomena in events with two leptons, jets, and missing transverse momentum in 139  fb−1 of s=13  TeV pp collisions with the ATLAS detector, Eur. Phys. J. C 83, 515 (2023).
  191. CMS Collaboration, Measurement of differential cross sections for Z boson production in association with jets in proton-proton collisions at s=13  TeV, Eur. Phys. J. C 78, 965 (2018).
  192. G. Kasieczka, B. Nachman, D. Shih, O. Amram, A. Andreassen, K. Benkendorfer et al., The LHC Olympics 2020 a community challenge for anomaly detection in high energy physics, Rep. Prog. Phys. 84, 124201 (2021).
  193. S. Yoon, Y.-K. Noh, and F. Park, Autoencoding under normalization constraints, arXiv:2105.05735.
  194. http://scicore.unibas.ch/
  195. K. An, Sulla determinazione empirica di una legge didistribuzione, Giorn Dell’inst Ital Degli Att 4, 89 (1933).
  196. T. W. Anderson, On the distribution of the two-sample cramer-von mises criterion, in The Annals of Mathematical Statistics (Institute of Mathematical Statistics, San Francisco, CA, 1962), p. 1148.

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Phys. Rev. D 114, 016022– Published 22 July, 2026
  • Received 7 January 2026
  • Accepted 18 June 2026
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