QuadNorm: Resolution-Robust Normalization for Neural Operators
Normalization layers in neural operators usually compute statistics by uniformly averaging discrete grid values, making the normalization itself discretization-dependent and thereby a source of transfer error across different resolutions or meshes. To enable discretization robustness, we introduce a quadrature normalization family that replaces existing uniform averaging in normalization layers with numerical quadrature: QuadNorm and BlendQuadNorm. On endpoint-inclusive uniform grids, the proposed quadrature moments are $O(h^2)$-consistent across discretizations, meaning that their cross-resolution mismatch decays quadratically with grid spacing. A transfer-error bound then predicts how n...
| Authors | Bum Jun Kim, Makoto Kawano, Yusuke Iwasawa et al. |
|---|---|
| Primary category | cs.LG |
| Published | 8 May 2026 |
| Last updated at source | 8 May 2026 |
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