Neural posterior estimation of the neutrino direction in IceCube using transformer-encoded normalizing flows on the sphere
Abstract
IceCube is a cubic-kilometer-scale neutrino detector located at the geographic South Pole. A precise directional reconstruction of IceCube neutrinos is vital for associations with astronomical objects. In this context, we discuss neural posterior estimation of the neutrino direction via a transformer encoder that maps to a normalizing flow on the 2-sphere. It achieves a new state-of-the-art angular resolution for the two main event morphologies in IceCube - tracks and showers - while being significantly faster than traditional B-spline-based likelihood reconstructions. All-sky scans can be performed within seconds rather than hours, and take constant computation time, regardless of whether the posterior extent is arc-minutes or spans the whole sky. We utilize a combination of $C^2$-smooth rational-quadratic splines, scale transformations and rotations to define a novel spherical normalizing-flow distribution whose parameters are predicted as a whole as the output of the transformer encoder. We test several structural choices diverting from the vanilla transformer architecture. In particular, we find dual residual streams, nonlinear QKV projection and a separate class token with its own cross-attention processing to boost test-time performance. The angular resolution for both showers and tracks improves substantially over the whole trained energy range from 100 GeV to 100 PeV. At 100 TeV deposited energy, for example, the median angular resolution improves by a factor of $1.3$ for throughgoing tracks, by a factor of $1.7$ for showers and by a factor of $2.5$ for starting tracks compared to state-of-the art likelihood reconstructions based on B-splines. While previous machine-learning (ML) efforts have managed to obtain competitive shower resolutions, this is the first time an ML-based method outperforms likelihood-based muon reconstructions above 100 GeV.
Authors 100
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Department of Physics , Loyola University Chicago , Chicago , IL 60660 , USA
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Deutsches Elektronen-Synchrotron DESY
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Deutsches Elektronen-Synchrotron DESY , Platanenallee 6 , D-15738 Zeuthen , Germany
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Dept. of Physics and Astronomy , University of Canterbury , Private Bag 4800 , Christchurch , New Zealand
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Université Libre de Bruxelles , Science Faculty CP230 , B-1050 Brussels , Belgium
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Niels Bohr Institute , University of Copenhagen , DK-2100 Copenhagen , Denmark
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Dept. of Physics , TU Dortmund University , D-44221 Dortmund , Germany
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Dept. of Physics and Astronomy , University of Kansas , Lawrence , KS 66045 , USA
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Bartol Research Institute and Dept. of Physics and Astronomy , University of Delaware , Newark , DE 19716 , USA
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Department of Physics , Marquette University , Milwaukee , WI 53201 , USA
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Department of Physics and Laboratory for Particle Physics and Cosmology , Harvard University , Cambridge , MA 02138 , USA
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Department of Physics and Astronomy , University of Utah , Salt Lake City , UT 84112 , USA
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Deutsches Elektronen-Synchrotron DESY
Affiliation as printed
Deutsches Elektronen-Synchrotron DESY , Platanenallee 6 , D-15738 Zeuthen , Germany
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Affiliation as printed
Bartol Research Institute and Dept. of Physics and Astronomy , University of Delaware , Newark , DE 19716 , USA
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Dept. of Physics and Astronomy , Michigan State University , East Lansing , MI 48824 , USA
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South Dakota School of Mines and Technology
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Physics Department , South Dakota School of Mines and Technology , Rapid City , SD 57701 , USA
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University of California, Irvine
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Dept. of Physics and Astronomy , University of California , Irvine , CA 92697 , USA
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Department of Physics and Astronomy , University of Utah , Salt Lake City , UT 84112 , USA
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University of California, Berkeley
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Dept. of Physics , University of California , Berkeley , CA 94720 , USA
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Affiliation as printed
Dept. of Astronomy , Ohio State University , Columbus , OH 43210 , USA
Dept. of Physics and Center for Cosmology and Astro-Particle Physics , Ohio State University , Columbus , OH 43210 , USA
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Affiliation as printed
Fakultät für Physik & Astronomie , Ruhr-Universität Bochum , D-44780 Bochum , Germany
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Affiliation as printed
III. Physikalisches Institut , RWTH Aachen University , D-52056 Aachen , Germany
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Affiliation as printed
Dept. of Physics and Astronomy , Uppsala University , Box 516 , SE-75120 Uppsala , Sweden
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Technical University of Munich
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Physik-department , Technische Universität München , D-85748 Garching , Germany
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Deutsches Elektronen-Synchrotron DESY
Affiliation as printed
Deutsches Elektronen-Synchrotron DESY , Platanenallee 6 , D-15738 Zeuthen , Germany
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Affiliation as printed
Dept. of Physics and Astronomy , University of Rochester , Rochester , NY 14627 , USA
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University of Maryland, College Park
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Dept. of Physics , University of Maryland , College Park , MD 20742 , USA
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Affiliation as printed
Dipartimento di Fisica e Astronomia Galileo Galilei , Università Degli Studi di Padova , I-35122 Padova PD , Italy
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Affiliation as printed
Dept. of Physics and Astronomy , University of Kansas , Lawrence , KS 66045 , USA
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University of Maryland, College Park
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Dept. of Physics , University of Maryland , College Park , MD 20742 , USA
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Affiliation as printed
Dept. of Physics and Astronomy , University of Alabama , Tuscaloosa , AL 35487 , USA
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Deutsches Elektronen-Synchrotron DESY
Affiliation as printed
Deutsches Elektronen-Synchrotron DESY , Platanenallee 6 , D-15738 Zeuthen , Germany
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Karlsruhe Institute of Technology
Affiliation as printed
Karlsruhe Institute of Technology , Institute for Astroparticle Physics , D-76021 Karlsruhe , Germany
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Affiliation as printed
Department of Physics and Laboratory for Particle Physics and Cosmology , Harvard University , Cambridge , MA 02138 , USA
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Affiliation as printed
Dipartimento di Fisica e Astronomia Galileo Galilei , Università Degli Studi di Padova , I-35122 Padova PD , Italy
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Johannes Gutenberg University Mainz
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Institute of Physics , University of Mainz , Staudinger Weg 7 , D-55099 Mainz , Germany
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Affiliation as printed
Dept. of Physics and Astronomy , Uppsala University , Box 516 , SE-75120 Uppsala , Sweden
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Affiliation as printed
III. Physikalisches Institut , RWTH Aachen University , D-52056 Aachen , Germany
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University of Wisconsin–Madison
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Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center , University of Wisconsin-Madison , Madison , WI 53706 , USA
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Georgia Institute of Technology
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School of Physics and Center for Relativistic Astrophysics , Georgia Institute of Technology , Atlanta , GA 30332 , USA
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Dept. of Physics, Engineering Physics, and Astronomy , Queen's University , Kingston , ON K7L 3N6 , Canada
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Affiliation as printed
Department of Physics , University of Adelaide , Adelaide , 5005 , Australia
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University of Wisconsin–Madison
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Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center , University of Wisconsin-Madison , Madison , WI 53706 , USA
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Affiliation as printed
Department of Physics and Laboratory for Particle Physics and Cosmology , Harvard University , Cambridge , MA 02138 , USA
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Friedrich-Alexander-Universität Erlangen-Nürnberg · Massachusetts Institute of Technology · University of Nevada, Las Vegas
Affiliation as printed
Department of Physics & Astronomy , University of Nevada , Las Vegas , NV 89154 , USA
Nevada Center for Astrophysics , University of Nevada , Las Vegas , NV 89154, USA 34 Dept. of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA 35 Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany 36 Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 37 Dept. of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA 16802, USA 38 Dept. of Physics, Pennsylvania State University, University Park, PA 16802, USA 39 Vrije Universiteit Brussel (VUB), Dienst ELEM, B
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Affiliation as printed
Université Libre de Bruxelles , Science Faculty CP230 , B-1050 Brussels , Belgium
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University of Wisconsin–Madison
Affiliation as printed
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center , University of Wisconsin-Madison , Madison , WI 53706 , USA
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Affiliation as printed
Department of Physics and Astronomy , University of Utah , Salt Lake City , UT 84112 , USA
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University of Maryland, College Park
Affiliation as printed
Dept. of Physics , University of Maryland , College Park , MD 20742 , USA
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Affiliation as printed
Dipartimento di Fisica e Astronomia Galileo Galilei , Università Degli Studi di Padova , I-35122 Padova PD , Italy
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Affiliation as printed
Dept. of Astronomy , Ohio State University , Columbus , OH 43210 , USA
Dept. of Physics and Center for Cosmology and Astro-Particle Physics , Ohio State University , Columbus , OH 43210 , USA
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Affiliation as printed
Department of Physics and Laboratory for Particle Physics and Cosmology , Harvard University , Cambridge , MA 02138 , USA
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Affiliation as printed
Université Libre de Bruxelles , Science Faculty CP230 , B-1050 Brussels , Belgium
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Affiliation as printed
III. Physikalisches Institut , RWTH Aachen University , D-52056 Aachen , Germany
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University of Wisconsin–Madison
Affiliation as printed
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center , University of Wisconsin-Madison , Madison , WI 53706 , USA
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Affiliation as printed
Dept. of Physics and Astronomy , Michigan State University , East Lansing , MI 48824 , USA
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University of Wisconsin–Madison
Affiliation as printed
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center , University of Wisconsin-Madison , Madison , WI 53706 , USA
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Affiliation as printed
Dept. of Physics and Astronomy , Michigan State University , East Lansing , MI 48824 , USA
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Friedrich-Alexander-Universität Erlangen-Nürnberg · Massachusetts Institute of Technology · University of Nevada, Las Vegas
Affiliation as printed
Department of Physics & Astronomy , University of Nevada , Las Vegas , NV 89154 , USA
Nevada Center for Astrophysics , University of Nevada , Las Vegas , NV 89154, USA 34 Dept. of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA 35 Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany 36 Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 37 Dept. of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA 16802, USA 38 Dept. of Physics, Pennsylvania State University, University Park, PA 16802, USA 39 Vrije Universiteit Brussel (VUB), Dienst ELEM, B
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Affiliation as printed
Department of Physics and Astronomy , University of Utah , Salt Lake City , UT 84112 , USA
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Affiliation as printed
III. Physikalisches Institut , RWTH Aachen University , D-52056 Aachen , Germany
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Johannes Gutenberg University Mainz
Affiliation as printed
Institute of Physics , University of Mainz , Staudinger Weg 7 , D-55099 Mainz , Germany
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University of Wisconsin–Madison
Affiliation as printed
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center , University of Wisconsin-Madison , Madison , WI 53706 , USA
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Johannes Gutenberg University Mainz
Affiliation as printed
Institute of Physics , University of Mainz , Staudinger Weg 7 , D-55099 Mainz , Germany
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Technical University of Munich
Affiliation as printed
Physik-department , Technische Universität München , D-85748 Garching , Germany
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Technical University of Munich
Affiliation as printed
Physik-department , Technische Universität München , D-85748 Garching , Germany
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Affiliation as printed
Dept. of Physics , TU Dortmund University , D-44221 Dortmund , Germany
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Karlsruhe Institute of Technology
Affiliation as printed
Karlsruhe Institute of Technology , Institute for Astroparticle Physics , D-76021 Karlsruhe , Germany
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University of Wisconsin–Madison
Affiliation as printed
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center , University of Wisconsin-Madison , Madison , WI 53706 , USA
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Affiliation as printed
Department of Physics and Laboratory for Particle Physics and Cosmology , Harvard University , Cambridge , MA 02138 , USA
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University of Maryland, College Park
Affiliation as printed
Dept. of Physics , University of Maryland , College Park , MD 20742 , USA
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Affiliation as printed
Bartol Research Institute and Dept. of Physics and Astronomy , University of Delaware , Newark , DE 19716 , USA
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University of Maryland, College Park
Affiliation as printed
Dept. of Physics , University of Maryland , College Park , MD 20742 , USA
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University of Wisconsin–Madison
Affiliation as printed
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center , University of Wisconsin-Madison , Madison , WI 53706 , USA
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Affiliation as printed
Fakultät für Physik & Astronomie , Ruhr-Universität Bochum , D-44780 Bochum , Germany
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Deutsches Elektronen-Synchrotron DESY
Affiliation as printed
Deutsches Elektronen-Synchrotron DESY , Platanenallee 6 , D-15738 Zeuthen , Germany
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Affiliation as printed
III. Physikalisches Institut , RWTH Aachen University , D-52056 Aachen , Germany
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