Fixed-neuron ReLU^k ridge functions form an exact finite-dimensional de Rham complex in any dimension, provided the lowest-order family is linearly independent.
Bernstein-Gelfand-Gelfand se- quences
3 Pith papers cite this work, alongside 210 external citations. Polarity classification is still indexing.
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representative citing papers
A variational functional E on Riemannian metrics vanishes precisely when geodesics realize prescribed unparametrised paths, and every conformal class on a surface admits a unique (up to homothety) conformally critical metric for E.
Explicit formulae for splitting operators, first BGG operators and prolongation connections on almost Grassmannian structures, plus geometric characterizations of parallel tractors and the induced geometry on zero loci of BGG solutions.
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Prescribing geodesics and a variational problem for Riemannian metrics
A variational functional E on Riemannian metrics vanishes precisely when geodesics realize prescribed unparametrised paths, and every conformal class on a surface admits a unique (up to homothety) conformally critical metric for E.
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Parallel (co-)tractors and the geometry of first BGG solutions on almost Grassmannian structures
Explicit formulae for splitting operators, first BGG operators and prolongation connections on almost Grassmannian structures, plus geometric characterizations of parallel tractors and the induced geometry on zero loci of BGG solutions.