Equivariance and generalization in neural networks
This work addresses the need for symmetry-aware neural networks in high-energy physics, offering incremental improvements in domain-specific applications.
The paper tackled the problem of improving neural network performance and generalization in high-energy physics tasks by incorporating translational equivariance, finding that equivariant architectures significantly outperformed non-equivariant ones in most regression and classification tasks, including on unseen physical parameters and lattice sizes.
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.