Mixed-norm Brascamp-Lieb inequalities
arXiv:2608.17952
2026
Regularization
1 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper proves a nonclassical mixed-norm Brascamp–Lieb inequality for a product of four nonnegative one-dimensional functions evaluated on different affine projections of a two-dimensional variable. The transferable asset is a deterministic multilinear stability bound: a structured product feature has bounded mixed norm in terms of the branch L1 masses, despite the factors depending on coupled coordinates. This suggests a normalized multilinear neural block or regularizer that controls cross-branch feature amplification without relying only on generic Frobenius penalties or LayerNorm. The most direct test is a four-branch latent interaction module with the theorem's affine projections and fractional exponents.
Ideas from this paper
Unverified
2026
Construct a four-branch neural interaction whose inputs are affine projections of a two-dimensional latent coordinate and whose output is the weighted product prescribed by the theorem. Normalize this product by the corresponding branch L1 masses, yielding a feature whose mixed norm is theoretically bounded up to the inequality constant. Use the normalized interaction as an architecture component or as a replacement for an unconstrained multiplicative fusion layer.
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