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  • Open Access

Mapping machine-learned physics into a human-readable space

Taylor Faucett1, Jesse Thaler2,3, and Daniel Whiteson1

  • 1Department of Physics and Astronomy, UC Irvine, Irvine, CA 92627
  • 2Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139
  • 3The NSF AI Institute for Artificial Intelligence and Fundamental Interactions

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Phys. Rev. D 103, 036020 – Published 26 February, 2021

DOI: https://doi.org/10.1103/PhysRevD.103.036020

Abstract

We present a technique for translating a black-box machine-learned classifier operating on a high-dimensional input space into a small set of human-interpretable observables that can be combined to make the same classification decisions. We iteratively select these observables from a large space of high-level discriminants by finding those with the highest decision similarity relative to the black box, quantified via a metric we introduce that evaluates the relative ordering of pairs of inputs. Successive iterations focus only on the subset of input pairs that are misordered by the current set of observables. This method enables simplification of the machine-learning strategy, interpretation of the results in terms of well-understood physical concepts, validation of the physical model, and the potential for new insights into the nature of the problem itself. As a demonstration, we apply our approach to the benchmark task of jet classification in collider physics, where a convolutional neural network acting on calorimeter jet images outperforms a set of six well-known jet substructure observables. Our method maps the convolutional neural network into a set of observables called energy flow polynomials, and it closes the performance gap by identifying a class of observables with an interesting physical interpretation that has been previously overlooked in the jet substructure literature.

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References (118)

  1. D. Guest, K. Cranmer, and D. Whiteson, Deep learning and its application to LHC physics, Annu. Rev. Nucl. Part. Sci. 68, 161 (2018).
  2. A. Radovic, M. Williams, D. Rousseau, M. Kagan, D. Bonacorsi, A. Himmel, A. Aurisano, K. Terao, and T. Wongjirad, Machine learning at the energy and intensity frontiers of particle physics, Nature (London) 560, 41 (2018).
  3. J. K. Kohne et al., Realization of a second level neural network trigger for the H1 experiment at HERA, Nucl. Instrum. Methods Phys. Res., Sect. A 389, 128 (1997).
  4. G. Aad et al. (ATLAS Collaboration), A neural network clustering algorithm for the ATLAS silicon pixel detector, J. Instrum. 9, P09009 (2014).
  5. C. Peterson, Track finding with neural networks, Nucl. Instrum. Methods Phys. Res., Sect. A 279, 537 (1989).
  6. H. Abramowicz, A. Caldwell, and R. Sinkus, Neural network based electron identification in the ZEUS calorimeter, Nucl. Instrum. Methods Phys. Res., Sect. A 365, 508 (1995).
  7. V. Khachatryan et al. (CMS Collaboration), Observation of the diphoton decay of the Higgs boson and measurement of its properties, Eur. Phys. J. C 74, 3076 (2014).
  8. V. M. Abazov et al. (D0 Collaboration), First measurement of σ(pp¯→Z)·Br(Z→ττ) at s=1.96  TeV, Phys. Rev. D 71, 072004 (2005); Erratum, 77, 039901 (2008).
  9. DELPHI Collaboration, Classification of the hadronic decays of the Z0 into b and c quark pairs using a neural network, Phys. Lett. B 295, 383 (1992).
  10. DZero Collaboration, Search for single top quark production at dø using neural networks, Phys. Lett. B 517, 282 (2001).
  11. CDF Collaboration, Search for the Higgs Boson Using Neural Networks in Events with Missing Energy and b-Quark Jets in pp¯ Collisions at s=1.96 TeV, Phys. Rev. Lett. 104, 141801 (2010).
  12. P. Baldi, P. Sadowski, and D. Whiteson, Searching for exotic particles in high-energy physics with deep learning, Nat. Commun. 5, 4308 (2014).
  13. P. Baldi, P. Sadowski, and D. Whiteson, Enhanced Higgs Boson to τ+τ− Search with Deep Learning, Phys. Rev. Lett. 114, 111801 (2015).
  14. R. Santos, M. Nguyen, J. Webster, S. Ryu, J. Adelman, S. Chekanov, and J. Zhou, Machine learning techniques in searches for tt¯h in the h→bb¯ decay channel, J. Instrum. 12, P04014 (2017).
  15. A. Aurisano, A. Radovic, D. Rocco, A. Himmel, M. D. Messier, E. Niner, G. Pawloski, F. Psihas, A. Sousa, and P. Vahle, A convolutional neural network neutrino event classifier, J. Instrum. 11, P09001 (2016).
  16. T. Cohen, M. Freytsis, and B. Ostdiek, (Machine) learning to do more with less, J. High Energy Phys. 02 (2018) 034.
  17. M. Andrews, M. Paulini, S. Gleyzer, and B. Poczos, End-to-end event classification of high-energy physics data, J. Phys. Conf. Ser. 1085, 042022 (2018).
  18. L. G. Almeida, M. Backović, M. Cliche, S. J. Lee, and M. Perelstein, Playing tag with ANN: Boosted top identification with pattern recognition, J. High Energy Phys. 07 (2015) 086.
  19. L. de Oliveira, M. Kagan, L. Mackey, B. Nachman, and A. Schwartzman, Jet-images—Deep learning edition, J. High Energy Phys. 07 (2016) 069.
  20. P. Baldi, K. Bauer, C. Eng, P. Sadowski, and D. Whiteson, Jet substructure classification in high-energy physics with deep neural networks, Phys. Rev. D 93, 094034 (2016).
  21. A. J. Larkoski, I. Moult, and B. Nachman, Jet substructure at the large hadron collider: A review of recent advances in theory and machine learning, Phys. Rep. 841, 1 (2020).
  22. G. Kasieczka, T. Plehn, M. Russell, and T. Schell, Deep-learning top taggers or the end of QCD?, J. High Energy Phys. 05 (2017) 006.
  23. D. Guest, J. Collado, P. Baldi, S.-C. Hsu, G. Urban, and D. Whiteson, Jet flavor classification in high-energy physics with deep neural networks, Phys. Rev. D 94, 112002 (2016).
  24. Identification of jets containing b-hadrons with recurrent neural networks at the ATLAS experiment, CERN Tech. Report No. ATL-PHYS-PUB-2017-003, 2017.
  25. CMS Collaboration, Heavy flavor identification at CMS with deep neural networks, CERN Tech. Report No. CMS-DP-2017-005, 2017.
  26. A. M. Sirunyan et al. (CMS Collaboration), Identification of heavy-flavour jets with the CMS detector in pp collisions at 13 TeV, J. Instrum. 13, P05011 (2018).
  27. P. T. Komiske, E. M. Metodiev, and M. D. Schwartz, Deep learning in color: Towards automated quark/gluon jet discrimination, J. High Energy Phys. 01 (2017) 110.
  28. 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).
  29. K. Datta, D. Kar, and D. Roy, Unfolding with generative adversarial networks, arXiv:1806.00433 [J. High Energy Phys. (to be published)].
  30. M. Bellagente, A. Butter, G. Kasieczka, T. Plehn, A. Rousselot, R. Winterhalder, L. Ardizzone, and U. Kthe, Invertible networks or partons to detector and back again, SciPost Phys. 9, 074 (2020).
  31. C. Englert, P. Galler, P. Harris, and M. Spannowsky, Machine learning uncertainties with adversarial neural networks, Eur. Phys. J. C 79, 4 (2019).
  32. J. Barnard, E. N. Dawe, M. J. Dolan, and N. Rajcic, Parton shower uncertainties in jet substructure analyses with deep neural networks, Phys. Rev. D 95, 014018 (2017).
  33. S. Bollweg, M. Haußmann, G. Kasieczka, M. Luchmann, T. Plehn, and J. Thompson, Deep-learning jets with uncertainties and more, SciPost Phys. 8, 006 (2020).
  34. B. Nachman, A guide for deploying deep learning in LHC searches: How to achieve optimality and account for uncertainty, SciPost Phys. 8, 090 (2020).
  35. G. Kasieczka, M. Luchmann, F. Otterpohl, and T. Plehn, Per-object systematics using deep-learned calibration, SciPost Phys. 9, 089 (2020).
  36. 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.
  37. E. M. Metodiev, B. Nachman, and J. Thaler, Classification without labels: Learning from mixed samples in high energy physics, J. High Energy Phys. 10 (2017) 174.
  38. A. Andreassen, I. Feige, C. Frye, and M. D. Schwartz, JUNIPR: A framework for unsupervised machine learning in particle physics, Eur. Phys. J. C 79, 102 (2019).
  39. J. H. Collins, K. Howe, and B. Nachman, Anomaly Detection for Resonant New Physics with Machine Learning, Phys. Rev. Lett. 121, 241803 (2018).
  40. C. Buciluundefined, R. Caruana, and A. Niculescu-Mizil, Model compression, in Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 06 (Association for Computing Machinery, New York, 2006), p. 535–541.
  41. J. Duarte et al., Fast inference of deep neural networks in FPGAs for particle physics, J. Instrum. 13, P07027 (2018).
  42. S. Chang, T. Cohen, and B. Ostdiek, What is the machine learning?, Phys. Rev. D 97, 056009 (2018).
  43. A. A. Alemi, I. Fischer, J. V. Dillon, and K. Murphy, Deep variational information bottleneck, arXiv:1612.00410.
  44. S. Wunsch, R. Friese, R. Wolf, and G. Quast, Identifying the relevant dependencies of the neural network response on characteristics of the input space, Comput. Softw. Big Sci. 2, 5 (2018).
  45. T. Roxlo and M. Reece, Opening the black box of neural nets: case studies in stop/top discrimination, arXiv:1804.09278.
  46. M. G. Kendall, A new measure of rank correlation, Biometrika 30, 81 (1938).
  47. M. H. Seymour, Tagging a heavy Higgs boson, in ECFA Large Hadron Collider (LHC) Workshop: Physics and Instrumentation (1991), pp. 557–569, https://inspirehep.net/literature/29197.
  48. M. H. Seymour, Searches for new particles using cone and cluster jet algorithms: A comparative study, Z. Phys. C 62, 127 (1994).
  49. J. M. Butterworth, B. E. Cox, and J. R. Forshaw, WW scattering at the CERN LHC, Phys. Rev. D 65, 096014 (2002).
  50. J. M. Butterworth, J. R. Ellis, and A. R. Raklev, Reconstructing sparticle mass spectra using hadronic decays, J. High Energy Phys. 05 (2007) 033.
  51. J. M. Butterworth, A. R. Davison, M. Rubin, and G. P. Salam, Jet Substructure as a New Higgs Search Channel at the LHC, Phys. Rev. Lett. 100, 242001 (2008).
  52. A. Abdesselam et al., Boosted objects: A probe of beyond the standard model physics, Eur. Phys. J. C 71, 1661 (2011).
  53. A. Altheimer et al., Jet substructure at the tevatron and LHC: New results, new tools, new benchmarks, J. Phys. G 39, 063001 (2012).
  54. J. Shelton, Jet substructure, in Theoretical Advanced Study Institute in Elementary Particle Physics: Searching for New Physics at Small and Large Scales (2013), pp. 303–340, https://doi.org/10.1142/9789814525220_0007.
  55. A. Altheimer et al., Boosted objects and jet substructure at the LHC. Report of BOOST2012, held at IFIC Valencia, 23rd-27th of July 2012, Eur. Phys. J. C 74, 2792 (2014).
  56. D. Adams et al., Towards an understanding of the correlations in jet substructure, Eur. Phys. J. C 75, 409 (2015).
  57. R. Kogler et al., Jet substructure at the large hadron collider: Experimental review, Rev. Mod. Phys. 91, 045003 (2019).
  58. S. Marzani, G. Soyez, and M. Spannowsky, Looking Inside Jets: An Introduction to Jet Substructure and Boosted-Object Phenomenology (Springer, New York, 2019), Vol. 958.
  59. Y. Cui, Z. Han, and M. D. Schwartz, W-jet tagging: Optimizing the identification of boosted hadronically-decaying W bosons, Phys. Rev. D 83, 074023 (2011).
  60. J. Thaler and K. Van Tilburg, Identifying boosted objects with N-subjettiness, J. High Energy Phys. 03 (2011) 015.
  61. J. Thaler and K. Van Tilburg, Maximizing boosted top identification by minimizing N-subjettiness, J. High Energy Phys. 02 (2012) 093.
  62. A. J. Larkoski, G. P. Salam, and Jesse Thaler, Energy correlation functions for jet substructure, J. High Energy Phys. 06 (2013) 108.
  63. G. Aad et al. (ATLAS Collaboration), Measurement of the cross-section of high transverse momentum vector bosons reconstructed as single jets and studies of jet substructure in pp collisions at s=7  TeV with the ATLAS detector, New J. Phys. 16, 113013 (2014).
  64. A. J. Larkoski, I. Moult, and D. Neill, Power counting to better jet observables, J. High Energy Phys. 12 (2014) 009.
  65. F. Pandolfi, Search for the standard model Higgs boson in the H→ZZ→l+l−qq¯ decay channel at CMS, Ph.D. thesis, Zurich, ETH, New York, 2012.
  66. S. Chatrchyan et al. (CMS Collaboration), Search for a Higgs boson in the decay channel H→ZZ(*)→qq¯ℓ−ℓ+ in pp collisions at s=7  TeV, J. High Energy Phys. 04 (2012) 036.
  67. A. J. Larkoski, J. Thaler, and W. J. Waalewijn, Gaining (Mutual) information about quark/gluon discrimination, J. High Energy Phys. 11 (2014) 129.
  68. P. Gras, S. Hche, D. Kar, A. Larkoski, L. Lnnblad, S. Pltzer, A. Sidmok, P. Skands, G. Soyez, and J. Thaler, Systematics of quark/gluon tagging, J. High Energy Phys. 07 (2017) 091.
  69. R. E. Schapire, The strength of weak learnability, Mach. Learn. 5, 197 (1990).
  70. Y. Freund, Boosting a weak learning algorithm by majority, Inf. Comput. 121, 256 (1995).
  71. P. T. Komiske, E. M. Metodiev, and J. Thaler, Energy flow networks: Deep sets for particle jets, J. High Energy Phys. 01 (2019) 121.
  72. H. Qu and L. Gouskos, ParticleNet: Jet tagging via particle clouds, Phys. Rev. D 101, 056019 (2020).
  73. E. A. Moreno, O. Cerri, J. M. Duarte, H. B. Newman, T. Q. Nguyen, A. Periwal, M. Pierini, A. Serikova, M. Spiropulu, and J.-R. Vlimant, JEDI-net: A jet identification algorithm based on interaction networks, Eur. Phys. J. C 80, 58 (2020).
  74. V. Mikuni and F. Canelli, ABCNet: An attention-based method for particle tagging, Eur. Phys. J. Plus 135, 463 (2020).
  75. A. Bogatskiy, B. Anderson, J. T. Offermann, M. Roussi, D. W. Miller, and R. Kondor, Lorentz Group Equivariant neural network for particle physics, arXiv:2006.04780.
  76. J. Shlomi, S. Ganguly, E. Gross, K. Cranmer, Y. Lipman, H. Serviansky, H. Maron, and N. Segol, Secondary vertex finding in jets with neural networks, arXiv:2008.02831.
  77. J. Cogan, M. Kagan, E. Strauss, and A. Schwarztman, Jet-images: Computer vision inspired techniques for jet tagging, J. High Energy Phys. 02 (2015) 118.
  78. D. E. Kaplan, K. Rehermann, M. D. Schwartz, and B. Tweedie, Top Tagging: A Method for Identifying Boosted Hadronically Decaying Top Quarks, Phys. Rev. Lett. 101, 142001 (2008).
  79. L. G. Almeida, S. J. Lee, G. Perez, G. F. Sterman, I. Sung, and J. Virzi, Substructure of high-p_T jets at the LHC, Phys. Rev. D 79, 074017 (2009).
  80. S. D. Ellis, C. K. Vermilion, and J. R. Walsh, Recombination algorithms and jet substructure: Pruning as a tool for heavy particle searches, Phys. Rev. D 81, 094023 (2010).
  81. T. Plehn, M. Spannowsky, M. Takeuchi, and D. Zerwas, Stop reconstruction with tagged tops, J. High Energy Phys. 10 (2010) 078.
  82. S. D. Ellis, A. Hornig, T. S. Roy, D. Krohn, and M. D. Schwartz, Qjets: A Non-Deterministic Approach to Tree-Based Jet Substructure, Phys. Rev. Lett. 108, 182003 (2012).
  83. M. Dasgupta, A. Fregoso, S. Marzani, and G. P. Salam, Towards an understanding of jet substructure, J. High Energy Phys. 09 (2013) 029.
  84. A. J. Larkoski, S. Marzani, G. Soyez, and J. Thaler, Soft drop, J. High Energy Phys. 05 (2014) 146.
  85. A. Buckley, G. Callea, A. J. Larkoski, and S. Marzani, An optimal observable for color singlet identification, SciPost Phys. 9, 026 (2020).
  86. G. Kasieczka, T. Plehn, A. Butter et al., The machine learning landscape of top taggers, SciPost Phys. 7, 014 (2019).
  87. K. Datta and A. Larkoski, How much information is in a jet?, J. High Energy Phys. 06 (2017) 073.
  88. L. Moore, K. Nordstrm, S. Varma, and M. Fairbairn, Reports of my demise are greatly exaggerated: N-subjettiness taggers take on jet images, SciPost Phys. 7, 036 (2019).
  89. J. A. Aguilar-Saavedra and B. Zaldvar, Jet tagging made easy, Eur. Phys. J. C 80, 530 (2020).
  90. J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, and T. Stelzer, MadGraph 5: Going beyond, J. High Energy Phys. 06 (2011) 128.
  91. T. Sjostrand, S. Mrenna, and P. Z. Skands, Pythia 6.4 physics and manual, J. High Energy Phys. 05 (2006) 026.
  92. J. de Favereau, C. Delaere, P. Demin, A. Giammanco, V. Lemaître, A. Mertens, and M. Selvaggi (DELPHES 3 Collaboration), Delphes 3, A modular framework for fast simulation of a generic collider experiment, J. High Energy Phys. 02 (2014) 057.
  93. M. Cacciari, G. P. Salam, and G. Soyez, The Anti-k(t) jet clustering algorithm, J. High Energy Phys. 04 (2008) 063.
  94. M. Cacciari, G. P. Salam, and G. Soyez, FastJet user manual, Eur. Phys. J. C 72, 1896 (2012).
  95. D. Krohn, J. Thaler, and L.-T. Wang, Jet trimming, J. High Energy Phys. 02 (2010) 084.
  96. G. Aad et al. (ATLAS Collaboration), Identification of boosted, hadronically decaying W bosons and comparisons with ATLAS data taken at s=8  TeV, Eur. Phys. J. C 76, 154 (2016).
  97. M. Aaboud et al. (ATLAS Collaboration), Performance of top-quark and W-boson tagging with ATLAS in Run 2 of the LHC, Eur. Phys. J. C 79, 375 (2019).
  98. V. Khachatryan et al. (CMS Collaboration), Identification techniques for highly boosted W bosons that decay into hadrons, J. High Energy Phys. 12 (2014) 017.
  99. Quark versus Gluon Jet Tagging Using jet images with the ATLAS detector, CERN Tech. Rep. No. ATL-PHYS-PUB- 2017-017 (2017).
  100. S. Macaluso and D. Shih, Pulling out all the tops with computer vision and deep learning, J. High Energy Phys. 10 (2018) 121.
  101. A. Banfi, G. P. Salam, and G. Zanderighi, Principles of general final-state resummation and automated implementation, J. High Energy Phys. 03 (2005) 073.
  102. G. Gur-Ari, M. Papucci, and G. Perez, Classification of energy flow observables in narrow jets, arXiv:1101.2905.
  103. M. Jankowiak and A. J. Larkoski, Jet substructure without trees, J. High Energy Phys. 06 (2011) 057.
  104. I. Moult, L. Necib, and J. Thaler, New angles on energy correlation functions, J. High Energy Phys. 12 (2016) 153.
  105. P. T. Komiske, https://pypi.org/project/EnergyFlow/.
  106. S.-M. Udrescu and M. Tegmark, AI Feynman: A physics-inspired method for symbolic regression, Sci. Adv. 6, eaay2631 (2020).
  107. P. T. Komiske, E. M. Metodiev, and J. Thaler, Cutting multiparticle correlators down to size, Phys. Rev. D 101, 036019 (2020).
  108. S. Choi, S. J. Lee, and M. Perelstein, Infrared safety of a neural-net top tagging algorithm, J. High Energy Phys. 02 (2019) 132.
  109. G. Kasieczka, N. Kiefer, T. Plehn, and J. M. Thompson, Quark-gluon tagging: Machine learning vs detector, SciPost Phys. 6, 069 (2019).
  110. K. Datta and A. J. Larkoski, Novel jet observables from machine learning, J. High Energy Phys. 03 (2018) 086.
  111. K. Datta, A. Larkoski, and B. Nachman, Automating the construction of jet observables with machine learning, Phys. Rev. D 100, 095016 (2019).
  112. A. M. Sirunyan et al. (CMS Collaboration), Identification of heavy, energetic, hadronically decaying particles using machine-learning techniques, J. Instrum. 15, P06005 (2020).
  113. D. E. Soper and M. Spannowsky, Finding physics signals with shower deconstruction, Phys. Rev. D 84, 074002 (2011).
  114. D. E. Soper and M. Spannowsky, Finding top quarks with shower deconstruction, Phys. Rev. D 87, 054012 (2013).
  115. D. E. Soper and M. Spannowsky, Finding physics signals with event deconstruction, Phys. Rev. D 89, 094005 (2014).
  116. D. F. de Lima, P. Petrov, D. Soper, and M. Spannowsky, Quark-gluon tagging with shower deconstruction: Unearthing dark matter and Higgs couplings, Phys. Rev. D 95, 034001 (2017).
  117. A. J. Larkoski and E. M. Metodiev, A theory of quark vs. gluon discrimination, J. High Energy Phys. 10 (2019) 014.
  118. G. Kasieczka, S. Marzani, G. Soyez, and G. Stagnitto, Towards machine learning analytics for jet substructure, J. High Energy Phys. 09 (2020) 195.

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Phys. Rev. D 103, 036020– Published 26 February, 2021
  • Received 14 November 2020
  • Accepted 5 February 2021
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