Continuous Sparsification via Minimizing Movement

Continuous sparsification is a popular approach for finding efficient sparse subnetworks, optimizing soft masks before applying a hard Top-$K$ projection. However, existing methods typically regularize mask variables using flat Euclidean geometry, penalizing local rewirings and disruptive long-range relocations equally. To address this, we propose Continuous Sparsification via Minimizing Movement (CSMM), a geometry-aware framework that treats layer connectivity as a probability allocation on the simplex. By leveraging the minimizing-movement scheme, we regularize the temporal evolution of connectivity using flexible proximal penalty functions. This approach decouples task performance from structural evolution, allowing practitioners to impose specific geometric inductive biases on topology evolution. The experiment shows a promising result on CIFAR10 dataset under ResNet-20 architecture, offering a new approach on continuous sparsification.