A neural network pruning system can sparsely prune neural network models using an optimizer based approach that is agnostic to the model architecture being pruned. The neural network pruning system can prune by operating on the parameter vector of the full model and the gradient vector of the loss function with respect to the model parameters. The neural network pruning system can iteratively update parameters based on the gradients, while zeroing out as many parameters as possible based a preconfigured penalty.