The Neural Pruning Law Hypothesis

Abstract

Network pruning is used to reduce inference latency and power consumption in large neural networks. However, most current pruning methods rely on ad-hoc heuristics that are poorly understood. We introduce Hyperflux, a conceptually-grounded pruning method, and use it to study the pruning process. Hyperflux models this process as an interaction between weight flux, the gradient's response to the weight's removal, and network pressure, a global regularization driving weights towards pruning. We postulate properties that arise naturally from our framework and find that the relationship between minimum flux among weights and density follows a power-law equation. Furthermore, we hypothesize the power-law relationship to hold for any effective saliency metric and call this idea the Neural Pruning Law Hypothesis. We validate our hypothesis on several families of pruning methods (magnitude, gradients, $L_0$), providing a potentially unifying property for neural pruning.