Recent work (Kalchbrenner et al., 2018) has demonstrated that sparsity in theparameters of neural networks leads to more parameter and floating-point oper-ation (flop) efficient networks and that these gains also translate into inferencetime reductions. There is a large body of work (Molchanov et al., 2017; Zhu &Gupta, 2017; Louizos et al., 2017; Li et al., 2016; Guo et al., 2016) on variousways ofpruningnetworks that require dense training but yield sparse networksfor inference. This limits the size of the largest trainable model to the largesttrainable dense model. Concurrently, other work (Mocanu et al., 2018; Mostafa& Wang, 2019; Bellec et al., 2017), have introduced dynamic sparse reparameter-ization training methods that allow a network to be trained while always sparse.However, they either do not reach the accuracy of pruning, or do not have a fixedFLOP cost due to parameter re-allocation during training. This work introducesa new method that does not require parameter re-allocation for end-to-end sparsetraining that matches and even exceeds the accuracy of dense-to-sparse methods.We show that this method requires less FLOPs to achieve a given level of accu-racy than previous methods. We also provide some insights into why static sparsetraining fails to find good minima and dynamic reparameterization succeeds.