Topology Is All You Need: Connectivity-Preserving Neural Network Pruning via Harmonic Participation Sieve

We introduce a topology-aware method for neural network weight pruning that achieves 40% sparsity with less than 1% accuracy loss on MNIST (97.80% → 96.90%), validated on NVIDIA A100, zero fine-tuning required. The method models the network as a graph where a BFS spanning tree permanently protects connectivity — no neuron ever becomes disconnected after pruning. A harmonic participation score ranks remaining weights by structural importance. Pruning low-score weights matches magnitude pruning (state of the art) up to 40% sparsity. Pruning high-score weights causes catastrophic failure (61 percentage-point accuracy drop at 30% sparsity), confirming the score correctly identifies critical connections. Primary application: post-training compression of large language models, reducing inference memory and compute by 40% without retraining. Same algorithm previously validated for 3D physics simulation (doi:10.5281/zenodo.20562846). Algorithm: PolyForm Noncommercial 1.0.0. Commercial licensing: lctrnc1@gmail.com