Learning Broken Symmetries with Approximate Invariance
This addresses the challenge of handling broken symmetries in neural network training for domains like particle physics, where detector asymmetries or varying resolutions break ideal symmetries, offering a solution that is incremental in improving upon existing constrained methods.
The paper tackled the problem of broken symmetries in real-world data, where exact symmetries are idealized and standard methods like data augmentation or equivariant networks fail, by proposing a dual-subnet model that balances constrained and unconstrained learning; in a toy example demonstrating Lorentz invariance violation, the model learned as rapidly as symmetry-constrained networks while overcoming their performance limitations.
Recognizing symmetries in data allows for significant boosts in neural network training, which is especially important where training data are limited. In many cases, however, the exact underlying symmetry is present only in an idealized dataset, and is broken in actual data, due to asymmetries in the detector, or varying response resolution as a function of particle momentum. Standard approaches, such as data augmentation or equivariant networks fail to represent the nature of the full, broken symmetry, effectively overconstraining the response of the neural network. We propose a learning model which balances the generality and asymptotic performance of unconstrained networks with the rapid learning of constrained networks. This is achieved through a dual-subnet structure, where one network is constrained by the symmetry and the other is not, along with a learned symmetry factor. In a simplified toy example that demonstrates violation of Lorentz invariance, our model learns as rapidly as symmetry-constrained networks but escapes its performance limitations.