Abstract
The crucial role played by the underlying symmetries of high energy physics and lattice field theories calls for the implementation of such symmetries in the neural network architectures that are applied to the physical system under consideration. In these proceedings, we focus on the consequences of incorporating translational equivariance among the network properties, particularly in terms of performance and generalization. The benefits of equivariant networks are exemplified by studying a complex scalar field theory, on which various regression and classification tasks are examined. For a meaningful comparison, promising equivariant and non-equivariant architectures are identified by means of a systematic search. The results indicate that in most of the tasks our best equivariant architectures can perform and generalize significantly better than their non-equivariant counterparts, which applies not only to physical parameters beyond those represented in the training set, but also to different lattice sizes.
Highlights
The past century has firmly established symmetries as a cornerstone of physics and especially of field theories, tracing back to Noether’s theorem [1]
The crucial role played by the underlying symmetries of high energy physics and lattice field theories calls for the implementation of such symmetries in the neural network architectures that are applied to the physical system under consideration
The results indicate that in most of the tasks our best equivariant architectures can perform and generalize significantly better than their non-equivariant counterparts, which applies to physical parameters beyond those represented in the training set, and to different lattice sizes
Summary
The past century has firmly established symmetries as a cornerstone of physics and especially of field theories, tracing back to Noether’s theorem [1]. In [7], group equivariant convolutional neural networks (G-CNNs) are proposed, which take care of the incorporation of translational, rotational and reflection symmetry in the architecture. Other proposals have been made in the context of lattice field theory, for example by designing a gauge equivariant normalizing flow [9, 10] and with the creation of specific layers that preserve gauge equivariance [11] In these proceedings, we focus on invariance under spacetime translations and study the impact of different choices of architectures that do or do not break translational symmetry, investigating in particular the generalization to different physical parameters and lattice sizes, as was discussed in our paper [12]
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