Because the opposite hypothesis, that 'winning tickets' can emerge from 'bad tickets' using stochastic gradient descent, implies that randomness doesn't push you back into the null space of the generalization curvature, which you can empirically observe that it almost always will, except for the same eigenvectors which tend to reinforce where there is strong alignment already, iteration after iteration. If you train a lot of small problems you can watch this happen just by looking at the angles between each update. Maybe that's the wrong explanation; I don't know. The practitioner take-away is that some initializations are just lucky/unlucky and you learn this quickly if you start a lot of small problems from scratch. Try stochastic BFGS and the frustration forces some inquiry. The paper is very experimental, which is great, but the conjecture itself is pointing roughly at some feature of SGD (i.e. "SGD seeks out and trains a subset of well-initialized weights.") without offering much direct explanation, for which I'm offering a hand-wavy viewpoint that also comes more from experience/frustration trying to optimize in ill-conditioned local curvatures. There may be a combinatorial way to look at 'lottery tickets', and that may be more productive than looking at it as eigenbasis pursuit, but it seems to me that it certainly might have something to do with that. Either way, the terms are irrelevant, and if it is true now, it was true before it got a name.