Growing Winning Subnetworks, Not Pruning Them: A Paradigm for Density Discovery in Sparse Neural Networks

The lottery ticket hypothesis suggests that dense networks contain sparse subnetworks that can be trained in isolation to match full-model performance. Existing approaches-iterative pruning, dynamic sparse training, and pruning at initialization-either incur heavy retraining costs or assume the target density is fixed in advance. We introduce Path Weight Magnitude Product-biased Random growth (PWMPR), a constructive sparse-to-dense training paradigm that grows networks rather than pruning them, while automatically discovering their operating density. Starting from a sparse seed, PWMPR adds edges guided by path-kernel-inspired scores, mitigates bottlenecks via randomization, and stops when a logistic-fit rule detects plateauing accuracy. Experiments on CIFAR, TinyImageNet, and ImageNet show that PWMPR approaches the performance of IMP-derived lottery tickets-though at higher density-at substantially lower cost (~1.5x dense vs. 3-4x for IMP). These results establish growth-based density discovery as a promising paradigm that complements pruning and dynamic sparsity.