Data symmetries generically do not induce conserved quantities in NN training for analytic non-polynomial losses, but can for MSE with tensorizable networks.
arXiv preprint arXiv:2603.29566 , year=
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For large monomial activation degree, critical points in deep fully-connected networks coincide exactly with subnetwork configurations where neurons are inactive or redundant.
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Conservation Laws from Data Symmetry in Neural Networks
Data symmetries generically do not induce conserved quantities in NN training for analytic non-polynomial losses, but can for MSE with tensorizable networks.
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Singular Learning and Occam's Razor in Deep Monomial Networks
For large monomial activation degree, critical points in deep fully-connected networks coincide exactly with subnetwork configurations where neurons are inactive or redundant.