arXiv:2607.21355 2026 Regularization 1 ideas extracted · analyzed Aug 30, 2026
The paper introduces a nonlocal variational energy in which points in a zero phase are rewarded according to their distance from the zero-phase boundary, rather than merely rewarding the amount of zero mass. This distinguishes isolated zeros from geometrically coherent, deep zero regions and supplies a principled way to encourage contiguous inactive regions. A promising neural-network transfer is a differentiable distance-to-boundary regularizer on nonnegative CNN feature maps, producing spatially structured sparsity that can be pruned or skipped at inference. The paper does not provide a direct neural-network theorem, so the engineering claim should be tested empirically against L1 and group-sparsity baselines.
Add a nonlocal regularizer to nonnegative CNN feature maps that rewards activation-zero pixels lying deep inside a contiguous zero region. Unlike L1 sparsity, this penalizes isolated holes and favors block-like inactive areas that are more amenable to spatial skipping, channel gating, or structured pruning.