The Symmetry of Differential Neural Tangent Kernel under the Orthogonal Group

The paper studies the symmetry properties of the differential neural tangent kernel (DNTK) for overparameterized physics‑informed neural networks. It shows that the infinite‑width DNTK is invariant under the orthogonal group for both two‑layer and deep networks, regardless of activation or bias. The authors further prove that integral operators induced by group‑orbit operators share spectra and that the fixed DNTK exhibits zonal symmetry on the unit sphere, enabling derivation of eigenvalue decay rates for shallow RePU networks with zero bias.

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