We explore the training dynamics of neural networks in a structured non-IID setting where documents are presented cyclically in a fixed, repeated sequence. Typically, networks suffer from catastrophic interference when training on a sequence of documents; however, we discover a curious and remarkable property of LLMs finetuned sequentially in this setting: they exhibit anticipatory behavior, recovering from the forgetting on documents before seeing them again. The behavior emerges and becomes more robust as the architecture scales up its number of parameters. Through comprehensive experiments and visualizations, we uncover new insights into training over-parameterized networks in structured environments.