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

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.

Higher-order mutual information reveals synergistic sub-networks for multi-neuron importance

Quantifying which neurons are important with respect to the classification decision of a trained neural network is essential for understanding their inner workings. Previous work primarily attributed importance to individual neurons. In this work, we study which groups of neurons contain synergistic or redundant information using a multivariate mutual information method called the O-information. We observe the first layer is dominated by redundancy suggesting general shared features (i.e. detecting edges) while the last layer is dominated by synergy indicating local class-specific features (i.e. concepts). Finally, we show the O-information can be used for multi-neuron importance. This can be demonstrated by re-training a synergistic sub-network, which results in a minimal change in performance. These results suggest our method can be used for pruning and unsupervised representation learning.