Phase Transitions in Attention: A Bayesian Theory of Copy Head Emergence
Attention is the key mechanism underlying in-context learning in transformers, and attention patterns have been observed empirically to emerge abruptly during training. We present a Bayesian theory of feature learning in attention; we then focus on how the copy subcircuit in the first layer of an induction head is learned by analyzing a single-layer softmax attention network trained on a copy task. We derive a closed-form posterior over the attention matrix and reduce it to a low-dimensional order parameter space. This reduction reveals a phase transition in the amount of training data, which we verify using both Bayesian sampling and standard training with Adam. We contrast our results w...
| Authors | Itay Lavie, Kirsten Fischer, Andrey Lekov et al. |
|---|---|
| Primary category | stat.ML |
| Published | 10 June 2026 |
| Last updated at source | 10 June 2026 |
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