We introduce “instability analysis”, which assesses whether a neural network optimizes to the same, linearly connected minimum under different samples of SGD noise. We find that standard vision models become “stable” in this way early in training. From then on, the outcome of optimization is determined to within a linearly connected region. We use instability to study “iterative magnitude pruning” (IMP), the procedure used by work on the lottery ticket hypothesis to identify subnetworks that could have trained to full accuracy from initialization. We find that these subnetworks only reach full accuracy when they are stable, which either occurs at initialization for small-scale settings (MNIST) or early in training for large-scale settings (Resnet-50 and Inception-v3 on ImageNet).