Grokking: Why Neural Networks Suddenly Generalise Long After Memorising

Train a small neural network on modular arithmetic and watch the curves. Training accuracy hits 100 percent quickly. Test accuracy sits near chance for a long time. Then, after thousands more steps with no change in the training data, test accuracy jumps to near 100 percent as well. Nothing in the data changed. Nothing in the task changed. The network grokked.

Grokking is the delayed, sudden transition from memorisation to generalisation. It was first noticed clearly on small algorithmic tasks, but the mechanism behind it - a slow competition between a memorising solution and a generalising solution, decided by regularisation and optimisation dynamics - matters far beyond toy arithmetic. It is a warning against judging a model too early, and a window into how networks build internal structure.

The setup: a task that can be memorised or understood

The classic grokking setup is modular addition.…