Global $L^p$ Second Commutation Lemma

What the math gives to ML

The paper constructs H-distributions that record localized correlations between weakly convergent Lp sequences and their conjugate-dual sequences, resolved by Fourier direction. The transferable asset is a non-Hilbert-space directional multiplier pairing that detects persistent anisotropic oscillatory structure. A practical neural-network adaptation is a regularizer on activation and residual tensors that penalizes excessive concentration of this cross-spectrum in particular directions.