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Conservation Laws from Data Symmetry in Neural Networks
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conservation-laws-from-data-symmetry-in-neural-networks-cd3f547c·1 events·first seen 7d agoAliases: Conservation Laws from Data Symmetry in Neural Networks
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Conservation laws from data symmetry in neural network gradient-flow training
A new arXiv preprint investigates whether intrinsic symmetries in training data produce conserved quantities during gradient-flow training of neural networks. The authors prove that for analytic, non-polynomial loss functions, data symmetries generically do not induce additional integrals of motion, but for MSE loss, data augmentation can yield extra conserved quantities. They introduce a framework of 'tensorizable networks'—architectures including linear, polynomial, and Lightning Attention networks—where parameter and input dependence can be separated via an intermediate representation.