arXiv:2607.01458 2026 Regularization 1 ideas extracted · analyzed Aug 30, 2026
The paper gives a sharp, dimension-independent lower bound on the growth of Minkowski sums of finite sets inside an integer hypercube: combining n supports cannot produce an arbitrarily small output support relative to the input supports. This is transferable to sparse neural computation and discrete representation learning, where repeated additive composition can suffer from support collapse or excessive overlap. The useful asset is the explicit exponent p, which converts measured input support sizes into a principled minimum target for the composed support rather than an ad hoc diversity coefficient. The most direct experiment is a support-growth regularizer for sparse convolutional or discrete-code layers, using exact or sampled sumset cardinalities and a straight-through gradient estimator.
Apply the paper's sharp sumset lower bound to the active discrete supports of multiple additive branches in a sparse neural layer. Penalize cases where the support of the combined output is smaller than the mathematically guaranteed minimum implied by the branch supports, discouraging destructive overlap and representational collapse.