One of the most surprising puzzles in neural network generalisation is
grokking: a network with perfect training accuracy but poor generalisation
will, upon further training, transition to perfect generalisation. We propose
that grokking occurs when the task admits a generalising solution and a
memorising solution, where the generalising solution is slower to learn but
more efficient, producing larger logits with the same parameter norm. We
hypothesise that memorising circuits become more inefficient with larger
training datasets while generalising circuits do not, suggesting there is a
critical dataset size at which memorisation and generalisation are equally
efficient. We make and confirm four novel predictions about grokking, providing
significant evidence in favour of our explanation. Most strikingly, we
demonstrate two novel and surprising behaviours: ungrokking, in which a network
regresses from perfect to low test accuracy, and semi-grokking, in which a
network shows delayed generalisation to partial rather than perfect test
accuracy.

一种最令人惊讶的神经网络概括性的难题是理解：一个在训练中完美的网络但在概括性上表现糟糕，经过进一步训练后会过渡到完美的概括性。我们提出了这样的观点：理解发生在任务允许概括性解和记忆化解的情况下，其中概括性解的学习速度较慢但更高效，用相同参数范数产生较大的对数后验概率。我们提出假设，记忆化电路在训练数据集越大时变得越不高效，而概括性电路则不会，这提示存在一个关键数据集大小，在这个大小上记忆化和概括性同样高效。我们提出并验证了有关理解的四个新的预测，为我们的解释提供了重要证据。最引人注目的是，我们展示了两种新的令人惊讶的行为：非理解，在这种情况下，网络从完美的测试准确性回退到低的测试准确性；半理解，在这种情况下，网络表现出对部分而不是完美的测试准确性的延迟概括。