The present disclosure provides systems and methods for modification (e.g., pruning, compression, quantization, etc.) of artificial neural networks based on estimations of the utility of network connections (also known as “edges”). In particular, the present disclosure provides novel techniques for estimating the utility of one or more edges of a neural network in a fashion that requires far less expenditure of resources than calculation of the actual utility. Based on these estimated edge utilities, a computing system can make intelligent decisions regarding network pruning, network quantization, or other modifications to a neural network. In particular, these modifications can reduce resource requirements associated with the neural network. By making these decisions with knowledge of and based on the utility of various edges, this reduction in resource requirements can be achieved with only a minimal, if any, degradation of network performance (e.g., prediction accuracy).