  Transformer models exhibit in-context learning: the ability to accurately
predict the response to a novel query based on illustrative examples in the
input sequence. In-context learning contrasts with traditional in-weights
learning of query-output relationships. What aspects of the training data
distribution and architecture favor in-context vs in-weights learning? Recent
work has shown that specific distributional properties inherent in language,
such as burstiness, large dictionaries and skewed rank-frequency distributions,
control the trade-off or simultaneous appearance of these two forms of
learning. We first show that these results are recapitulated in a minimal
attention-only network trained on a simplified dataset. In-context learning
(ICL) is driven by the abrupt emergence of an induction head, which
subsequently competes with in-weights learning. By identifying progress
measures that precede in-context learning and targeted experiments, we
construct a two-parameter model of an induction head which emulates the full
data distributional dependencies displayed by the attention-based network. A
phenomenological model of induction head formation traces its abrupt emergence
to the sequential learning of three nested logits enabled by an intrinsic
curriculum. We propose that the sharp transitions in attention-based networks
arise due to a specific chain of multi-layer operations necessary to achieve
ICL, which is implemented by nested nonlinearities sequentially learned during
training.
