In-context learning (ICL) is an emergent capability of pretrained transformers that allows models to generalize to previously unseen tasks after seeing only a few examples. We investigate empirically the conditions necessary on the pretraining distribution for ICL to emerge and generalize out-of-distribution. We find that as task diversity increases, transformers undergo a transition from a specialized solution, which exhibits ICL only within the pretraining task distribution, to a solution which generalizes out of distribution to the entire task space.

Next we analyze ridge regression under concept shift, a form of distribution shift in which the input-label relationship changes at test time. We derive an exact expression for prediction risk in the thermodynamic limit. Our results reveal a phase transition between weak and strong concept shift regimes and nonmonotonic data dependence of test performance even when double descent is absent. Our theoretical results are in good agreement with experiments based on transformers; under concept shift, too long context length can be detrimental to generalization performance of next token prediction.