Grokking › Limitations and Ongoing Questions

Several aspects of grokking remain poorly understood. Grokking is reproducible in controlled settings, but its practical significance for day-to-day large-scale training remains actively debated.

The basic unresolved question is whether we can predict whether and when grokking will occur given a specific model trained on a given dataset under a particular setup. We can make qualitative predictions such as "more regularization speeds grokking" or "more data helps", but we cannot make reliable quantitative predictions. We cannot generally predict whether grokking will happen at step 50,000 or 500,000, or whether it will happen at all. This limits the practical usefulness of grokking insights for tasks where extended training runs are expensive. Without reliable predictors, you cannot know in advance whether the extra training cost is justified.

The relationship between grokking in small toy tasks and training dynamics in large practical models remains deeply unclear. Large language models train on natural language with far messier structure than modular arithmetic. Whether grokking insights transfer to these settings is an open question that the research community has not reached consensus on. Some researchers argue that continued training with regularization improves generalization in large language models, and that early stopping during pretraining may leave capability on the table. Others argue that the phenomena are fundamentally different at scale, because the clean two-solution competition in grokking tasks has no direct analog in large models where millions of tasks are entangled.

There are also significant computational implications to grapple with. If useful capabilities emerge only after extended training, we should consider using longer training runs in practice. However, training large models is enormously expensive, which makes it hard to justify continued training when visible metrics have plateaued for many thousands of steps. Better understanding of when grokking will occur could help justify these extended training investments, but such understanding remains elusive. The absence of reliable predictors for grokking means practitioners cannot easily distinguish between a model that is in a pre-grokking plateau and a model that has simply converged.

Another important limitation is that grokking has been primarily studied in settings where both the memorization and algorithmic solutions are readily identifiable and their competition is clean. In practical tasks, the set of possible solutions is far more complex, with many partial solutions, locally optimal configurations, and mixed representations that do not cleanly separate into "memorization" and "algorithm" categories. Whether the clean theoretical frameworks developed for modular arithmetic translate to this messier setting is an open question that requires both theoretical and empirical work to answer.

The competing theoretical frameworks cover circuit formation and representation learning, as well as compression and phase transitions. They all give partial explanations, but a unified theory that predicts grokking from first principles remains elusive. These frameworks are not mutually exclusive. Circuit formation can be viewed as a consequence of representation learning; compression can be seen as the goal that drives both circuit formation and representation reorganization; phase transitions describe the dynamics at a statistical physics level while leaving the mechanism open. Progress in mechanistic interpretability may eventually give clearer answers through direct observation of internal representations as they emerge during grokking. We will encounter this approach in later chapters on model analysis.

Grokking has been studied primarily in controlled settings with small models and clean algorithmic tasks. The degree to which these results generalize to the messy, large-scale training settings of practical NLP remains an empirical question. Its practical significance for day-to-day model training remains debated. At minimum, grokking shows that the relationship between training time and generalization is more complex than classical theory suggests, so extended training with appropriate regularization may be useful for tasks with underlying algorithmic structure. A stronger claim, that grokking is a basic feature of neural-network learning that explains capability development in large language models, remains unproven.