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M. Favoni, A. Ipp, D. Mueller, D. Schuh:
"Implementing gauge symmetry in machine learning models";
Talk: Strong and Electro-Weak Matter 2021, Paris, Frankreich; 2021-06-28 - 2021-07-02.

When applying machine learning to problems in field theory, the symmetries of the underlying theory are generally not preserved. Although neural networks can in principle approximate any function, it is a non-trivial task to let a neural network learn a particular symmetry just from training data alone.
In this talk I present our proposal of a manifestly gauge equivariant formulation of CNNs called lattice gauge equivariant convolutional neural networks (L-CNNs) [1]. These new types of neural networks exactly preserve lattice gauge symmetry and can be used to learn any gauge covariant function on the lattice. We show that in non-trivial regression tasks such as learning to compute particular Wilson loops, L-CNNs clearly outperform traditional CNNs. In addition, we show that our L-CNN models can be trained on data from small lattices while still performing well on larger lattices.

[1] ``Lattice gauge equivariant convolutional neural networks", M.~Favoni, A.~Ipp, D.~I.~Müller, D.~Schuh,
https://arxiv.org/abs/2012.12901

Project Head Gerhard Kahl:
Glasma-ML