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Towards Understanding Grokking: An Effective Theory of Representation Learning
Ziming Liu · Ouail Kitouni · Niklas S Nolte · Eric Michaud · Max Tegmark · Mike Williams

Wed Nov 30 09:00 AM -- 11:00 AM (PST) @ Hall J #227

We aim to understand grokking, a phenomenon where models generalize long after overfitting their training set. We present both a microscopic analysis anchored by an effective theory and a macroscopic analysis of phase diagrams describing learning performance across hyperparameters. We find that generalization originates from structured representations, whose training dynamics and dependence on training set size can be predicted by our effective theory (in a toy setting). We observe empirically the presence of four learning phases: comprehension, grokking, memorization, and confusion. We find representation learning to occur only in a "Goldilocks zone" (including comprehension and grokking) between memorization and confusion. Compared to the comprehension phase, the grokking phase stays closer to the memorization phase, leading to delayed generalization. The Goldilocks phase is reminiscent of "intelligence from starvation" in Darwinian evolution, where resource limitations drive discovery of more efficient solutions. This study not only provides intuitive explanations of the origin of grokking, but also highlights the usefulness of physics-inspired tools, e.g., effective theories and phase diagrams, for understanding deep learning.

Author Information

Ziming Liu (MIT)
Ouail Kitouni (MIT)
Niklas S Nolte (MIT)
Eric Michaud (University of California, Berkeley)
Max Tegmark (MIT)

Max Tegmark is a professor doing physics and AI research at MIT, and advocates for positive use of technology as president of the Future of Life Institute. He is the author of over 250 publications as well as the New York Times bestsellers “Life 3.0: Being Human in the Age of Artificial Intelligence” and "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality". His AI research focuses on intelligible intelligence. His work with the Sloan Digital Sky Survey on galaxy clustering shared the first prize in Science magazine’s “Breakthrough of the Year: 2003.”

Mike Williams (MIT)

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