Grokking and Delayed Generalization

The original grokking paper, publicly submitted in January 2022, studies small algorithmically generated datasets. In some experiments, a network fits the training data while held-out performance remains poor, then generalizes after substantially more optimization. This separates fitting observed examples from learning behavior that transfers to unseen examples of the underlying task. It does not mean that every model has near-zero validation accuracy during an initial plateau or that memorization must always disappear completely. The original study varies dataset sizes and optimization choices, including weight decay. Its findings concern those setups rather than a unique universal explanation of generalization. Progress Measures for Grokking via Mechanistic Interpretability investigates small transformers trained on modular addition. The studied algorithm uses Fourier structure and trigonometric identities to represent addition through circular relationships. The researchers examine activations and weights and use Fourier-space ablations to test their account. They describe memorization, circuit formation, and cleanup phases, with generalizing structure emerging before the visible jump in test accuracy. Weight decay removes memorization components during the studied cleanup process. This is more specific than a story in which the entire algorithm appears suddenly at the accuracy jump. Modular tasks offer exact labels: for example, adding six and five modulo seven gives four because eleven leaves remainder four after division by seven. The original paper also reports increasing optimization requirements as training datasets become smaller. Such controlled experiments motivate further research, but do not establish that a large deployed model will eventually improve if trained indefinitely.