During the public Kaggle competition “IceCube – Neutrinos in Deep Ice”, thousands of reconstruction algorithms were created and submitted, aiming to estimate the direction of neutrino events recorded by the IceCube detector. Here we describe in detail the three ultimate best, award-winning solutions. The data handling, architecture, and training process of each of these machine learning models is laid out, followed up by an in-depth comparison of the performance on the Kaggle datatset. We show that on cascade events in IceCube above 10 TeV, the best Kaggle solution is able to achieve an angular resolution of better than 5 $$^{\circ }$$  <math> <mmultiscripts> <mrow></mrow> <mrow></mrow> <mo>∘</mo> </mmultiscripts> </math>  , and for tracks correspondingly better than 0.5 $$^{\circ }$$  <math> <mmultiscripts> <mrow></mrow> <mrow></mrow> <mo>∘</mo> </mmultiscripts> </math>  . These results indicate that the Kaggle solutions perform at a level comparable to the current state-of-the-art in the field, and that they may even be able to outperform existing reconstruction resolutions for certain types of events.

United States

Habib Bukhari

India

Dipam Chakraborty

Germany

Philipp Eller

Japan

Takuya Ito

Maxim Shugaev

Rasmus Ørsøe

IceCube – Neutrinos in Deep Ice

The Bannai–Ito algebra can be defined as the centralizer of the coproduct embedding of <math><mrow><mi>osp</mi></mrow><mo>(</mo><mn>1</mn><mo>|</mo><mn>2</mn><mo>)</mo></math> in <math><mrow><mi>osp</mi></mrow><msup><mrow><mo>(</mo><mn>1</mn><mo>|</mo><mn>2</mn><mo>)</mo></mrow><mrow><mo>⊗</mo><mi>n</mi></mrow></msup></math>. It will be shown that it is also the commutant of a maximal Abelian subalgebra of <math><mi>o</mi><mo>(</mo><mn>2</mn><mi>n</mi><mo>)</mo></math> in a spinorial representation and an embedding of the Racah algebra in this commutant will emerge. The connection between the two pictures for the Bannai–Ito algebra will be traced to the Howe duality which is embodied in the <math><mi>P</mi><mi>i</mi><mi>n</mi><mo>(</mo><mn>2</mn><mi>n</mi><mo>)</mo><mo>×</mo><mrow><mi>osp</mi></mrow><mo>(</mo><mn>1</mn><mo>|</mo><mn>2</mn><mo>)</mo></math> symmetry of the massless Dirac equation in <math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msup></math>. Dimensional reduction to <math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math> will provide an alternative to the Dirac–Dunkl equation as a model with Bannai–Ito symmetry.