Super Weights don't generalize, and training them in isolation destroys the model.

Prior work found individual parameters whose removal collapses LLM performance by orders of magnitude. arXiv 2607.08733 shows the effect isn't universal across models, then tests the obvious corollary that Super Weight-aware training should work. It doesn't. Training 100 to 8,192 Super Weights in isolation drops OLMo-1B and OLMo-7B to random-guessing accuracy, and expanding to local neighborhoods doesn't rescue it. A clean negative result against a seductive intuition, and negative results this direct are rare enough to be worth reading.