Grokking arises from gradual amplification of a Fourier-based circuit in the weights followed by removal of memorizing components.
and Tegmark, Max and Williams, Mike , title =
5 Pith papers cite this work, alongside 24 external citations. Polarity classification is still indexing.
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abstract
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. We find on transformers the grokking phase stays closer to the memorization phase (compared to the comprehension 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.
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background 1representative citing papers
In grokking modular arithmetic, weight direction portably carries circuit identity across independent runs while weight norm only sets susceptibility to overwrite and a weak delay effect.
Random Matrix Theory detects overfitting via growing Correlation Traps in weight spectra during the anti-grokking phase of neural network training.
Grokking delay on Collatz prediction is a decoder access bottleneck after early encoder structure learning, with numeral base as a strong inductive bias on learnability.
Proposes a two-gradient-field model with candidate order parameters alpha_dagger and kappa_c to unify phase transitions across learning theory and non-equilibrium chemistry.
citing papers explorer
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Progress measures for grokking via mechanistic interpretability
Grokking arises from gradual amplification of a Fourier-based circuit in the weights followed by removal of memorizing components.
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Cross-Trajectory Chimera Interventions Reveal Dissociable Roles of Weight Magnitude and Direction in Grokking
In grokking modular arithmetic, weight direction portably carries circuit identity across independent runs while weight norm only sets susceptibility to overwrite and a weak delay effect.
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Detecting overfitting in Neural Networks during long-horizon grokking using Random Matrix Theory
Random Matrix Theory detects overfitting via growing Correlation Traps in weight spectra during the anti-grokking phase of neural network training.
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The Long Delay to Arithmetic Generalization: When Learned Representations Outrun Behavior
Grokking delay on Collatz prediction is a decoder access bottleneck after early encoder structure learning, with numeral base as a strong inductive bias on learnability.
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Phase Transitions in Driven Informational Systems: A Two-Field Perspective on Learning Theory and Non-Equilibrium Chemistry
Proposes a two-gradient-field model with candidate order parameters alpha_dagger and kappa_c to unify phase transitions across learning theory and non-equilibrium chemistry.