Feature Lottery? A Bifurcation Theory of Concept Emergence

In three linesBifurcation theory to detect in real time the emergence of structured representations in neural networks. A dynamic ratio β(t)/βc(t) based on loss Hessian predicts four distinct transition regimes (SAE on Pythia, SSL CIFAR, arithmetic grokking). At 5% of training, early atom purity predicts final convergence with 12x baseline improvement.

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