Conservation Laws from Data Symmetry in Neural Networks
We explore whether intrinsic symmetries of the training data lead to conserved quantities during gradient-flow training of neural networks. Under the assumption that the loss function is analytic and non-polynomial, we prove that data symmetries generically do not induce any additional integrals of motion. For mean squared error (MSE) loss, on the other hand, there are situations in which data augmentation yields extra conserved quantities. We build a framework, utilizing \emph{tensorizable networks} to describe this phenomenon. Tensorizable networks are a family of architectures whose dependence on parameters and inputs can be separated using an intermediate representation. They include ...
| Authors | Jakob Galley, Vahid Shahverdi, Axel Flinth |
|---|---|
| Primary category | cs.LG |
| Published | 9 June 2026 |
| Last updated at source | 9 June 2026 |
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