A kinetic theory for the transition from memorization to in-context generalization

Transformer models pretrained on large amounts of language data display a powerful feature known as in-context learning (ICL): the ability to parse new information presented in the context with no additional updates to the synaptic weights in the network. Recent work shows that ICL emerges when models are trained on a sufficiently diverse set of tasks and the transition from memorization to generalization is sharp with increasing task diversity. One interpretation is that a network's limited capacity to memorize favors generalization. I will present our analysis of this transition using a small transformer applied to a synthetic ICL task. Using theory and numerical experiments, we show that the sub-circuits that memorize and generalize can be viewed as largely independent. The relative rates at which these sub-circuits learn explains the transition from memorization to generalization, rather than capacity constraints. We uncover a memorization scaling law, which determines the task diversity threshold at which the network generalizes. The theory quantitatively explains a variety of other ICL-related phenomena, including the long-tailed distribution of when ICL is acquired, the bimodal behavior of solutions close to the task diversity threshold, the influence of contextual and data distributional statistics on ICL, and the transient nature of ICL.