A Tale of Two Circuits: Grokking as Competition of Sparse and Dense SubnetworksDownload PDF

Published: 04 Mar 2023, Last Modified: 16 May 2023ME-FoMo 2023 PosterReaders: Everyone
Keywords: Grokking, Emergence, Parity, Phase Transitions
TL;DR: empirical findings on sparsity and subnetwork competition during grokking
Abstract: Grokking is a phenomenon where a model trained on an algorithmic task first overfits but, then, after a large amount of additional training, undergoes a phase transition to generalize perfectly. We empirically study the internal structure of networks undergoing grokking on the sparse parity task, and find that the grokking phase transition corresponds to the emergence of a sparse subnetwork that dominates model predictions. On an optimization level, we find that this subnetwork arises when a small subset of neurons undergoes rapid norm growth, whereas the other neurons in the network decay slowly in norm. Thus, we suggest that the grokking phase transition can be understood to emerge from competition of two largely distinct subnetworks: a dense one that dominates before the transition and generalizes poorly, and a sparse one that dominates afterwards.
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