Grokking shows that generalization can be a delayed phase transition

A few years ago, researchers at DeepMind described a phenomenon they called 'grokking': train a small transformer on a modular arithmetic task long past the point of memorization, and at some point generalization kicks in suddenly, like a phase transition. The training loss is already near zero; the test loss drops abruptly after thousands of additional gradient steps.

This is strange. Our usual understanding of neural network training imagines a smooth tradeoff between fitting and generalizing. Grokking suggests that's not always right — that the network can be in a memorization regime and a generalization regime that are genuinely different attractors, and that optimization can jump between them with enough time.

Mechanistic interpretability work has since identified the specific circuits that implement the generalization solution in these small models. The model learns modular addition by computing Fourier components. That's not how a human would approach the problem. It's not obvious that it's the simplest solution. It's what gradient descent found.

For independent ML researchers, grokking is a tractable phenomenon: you can reproduce the experiments with modest compute, the datasets are trivial to generate, and the behavior is robust. What other problem structures produce it? Does the delayed generalization timescale depend on the task's algebraic structure?