arXiv:2608.23734 2026 Regularization 1 ideas extracted · analyzed Aug 29, 2026
This paper provides a Wasserstein gradient-flow model in which porous-medium diffusion counteracts attractive Newtonian or screened interaction, with a sharp critical exponent for avoiding concentration. The transferable asset is an explicit energy whose attractive component forms clusters while its density-power component penalizes singular collapse. A practical neural adaptation is a differentiable regularizer for low-dimensional embeddings, class prototypes, or mixture-of-experts router keys. The main falsifiable claim is that this regularizer can improve cluster structure or expert utilization while reducing embedding collapse at comparable task loss and compute.
Regularize learned low-dimensional embeddings or MoE prototypes with an aggregation-diffusion energy. The attractive term encourages compact, semantically coherent groups, while porous-medium diffusion creates density-dependent pressure that prevents points from collapsing into singular clusters.