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Recent studies have shown that skeletonization (pruning parameters) of networks \textit{at initialization} provides all the practical benefits of sparsity both at inference and training time, while only marginally degrading their performance. However, we observe that beyond a certain level of sparsity (approx $95\%$), these approaches fail to preserve the network performance, and to our surprise, in many cases perform even worse than trivial random pruning. To this end, we propose an objective to find a skeletonized network with maximum {\em foresight connection sensitivity} (FORCE) whereby the trainability, in terms of connection sensitivity, of a pruned network is taken into consideration. We then propose two approximate procedures to maximize our objective (1) Iterative SNIP: allows parameters that were unimportant at earlier stages of skeletonization to become important at later stages; and (2) FORCE: iterative process that allows exploration by allowing already pruned parameters to resurrect at later stages of skeletonization. Empirical analyses on a large suite of experiments show that our approach, while providing at least as good a performance as other recent approaches on moderate pruning levels, provides remarkably improved performance on higher pruning levels (could remove up to $99.5\%$ parameters while keeping the networks trainable). Code can be found in https://github.com/naver/force.