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Why Permutation Symmetry Complicates Neural Network Merging

Neural networks don't average well, and the culprit is permutation symmetry. When two models learn the same task, their weights often sit in arrangements that look different but behave identically. Averaging them naively breaks the symmetry, producing a merged model that loses performance. This post unpacks that tension with clarity, connecting the math to practical model merging challenges. It's a worthwhile read for anyone exploring why weight averaging fails and what that means for building more reliable AI systems.