Kazhdan's Property $(T)$ for Subspaces and Quotients of $L_p$-Spaces

What the math gives to ML

The paper proves a uniform spectral-gap inequality for isometric representations on closed subspaces of L_p, extending Hilbert-space property-T behavior to non-Hilbert feature geometries. The transferable asset is the quantitative principle that disagreement under a finite transformation set controls distance from the invariant feature subspace. This can become a group-augmentation regularizer for neural representations, with the power map x to x^m at even p providing a Hilbert-space proxy for implementation.