This paper proposes Hyperflux, a network pruning technique to reduce the inference latency and power consumption of neural networks. While existing pruning methods rely primarily on empirical results, Hyperflux is a conceptually robust L0 pruning approach that estimates the importance of each weight as the gradient response (flux) to weight removal. A global pressure term continuously guides all weights toward pruning, and weights critical for accuracy automatically regrow according to the flux. In this paper, we present and experimentally validate several properties naturally derived from the Hyperflux framework and design a sparsity-controlled scheduler by deriving a generalized scaling law equation describing the relationship between final sparsity and pressure. Experimental results demonstrate state-of-the-art results on the CIFAR-10 and CIFAR-100 datasets using ResNet-50 and VGG-19.