In-context learning across the logistic family

Prior theoretical studies of in-context learning (ICL) in transformers have formulated task inference in a regression setting, where tasks are weight vectors in parameter space and the data are independently sampled from a known distribution. In contrast, time series prediction involves observations generated from an evolving latent system that can exhibit temporal dependencies while the available representation may only preserve part of the underlying state. We study ICL in transformers trained to perform next token prediction on trajectories generated by the logistic family. Using the logistic family as a controlled setting, we investigate how training-task diversity, context length, and observation resolution affect model performance while retaining the latent structure of the task. At a fixed trajectory budget, generalization to new maps emerges sharply beyond a critical level of training-task diversity. The resulting generalization structure depends on representation: finer resolutions require greater task diversity to generalize but attain lower limiting error. Under restricted training support, transfer is strongly asymmetric. Models trained on intervals containing chaotic dynamics often predict lower-complexity systems accurately, whereas reverse transfer is poor. Our results show that in-context generalization depends jointly on task diversity, observation representation, and the dynamical regimes represented during training.