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Current methods for pruning neural network weights iteratively apply magnitude-based pruning on the model weights and re-train the resulting model to recover lost accuracy. In this work, we show that such strategies do not allow for the recovery of erroneously pruned weights. To enable weight recovery, we propose a simple strategy called cyclical pruning which requires the pruning schedule to be periodic and allows for weights pruned erroneously in one cycle to recover in subsequent ones. Experimental results on both linear models and large-scale deep neural networks show that cyclical pruning outperforms existing pruning algorithms, especially at high sparsity ratios. Our approach is easy to tune and can be readily incorporated into existing pruning pipelines to boost performance.