Grokking: Delayed Generalization Phase Transitions in Neural Networks and LLMs

Summary

This forum post introduces grokking, a phenomenon in neural network training where delayed generalization occurs as a phase transition: after a period of overfitting and memorization, continued training causes the model to shift toward structured understanding, such as algorithmic circuits or trigonometric representations. The post explains that in LLM pretraining, this manifests as local, asynchronous grokking, with mechanisms involving numerical stability (softmax collapse), shifts in optimization dynamics, and competition among circuits. It notes that 2024-2025 research has deepened the numerical and phase-transition perspectives and confirmed grokking's existence in real LLMs. Practical takeaways are included: researchers can monitor loss on data subsets and internal pathway evolution during pretraining as a cheap generalization indicator, while practitioners may extend training with stronger regularization to induce better generalization, and should pay attention to numerical precision optimizations such as the Muon optimizer.