Information-Theoretic Progress Measures reveal Grokking is an Emergent Phase Transition

Abstract: This paper studies emergent phenomena in neural networks by focusing on grokking where models suddenly generalize after delayed memorization. To understand this phase transition, we utilize higher-order mutual information to analyze the collective behavior (synergy) and shared properties (redundancy) between neurons during training. We identify distinct phases before grokking allowing us to anticipate when it occurs. We attribute grokking to an emergent phase transition caused by the synergistic interactions between neurons as a whole. We show that weight decay and weight initialization can enhance the emergent phase.