Itay Lavie

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 with linear attention and find that softmax attention exhibits a first-order phase transition while in linear attention an initial second-order phase transition is followed by a smooth, continuous evolution toward the structured attention pattern. Our work provides a first-principles theoretical account of the abrupt emergence of the copy subcircuit, reminiscent of the one observed in training large language models.

We study inductive bias in Transformers in the infinitely over-parameterized Gaussian process limit and argue transformers tend to be biased towards more permutation symmetric functions in sequence space. We show that the representation theory of the symmetric group can be used to give quantitative analytical predictions when the dataset is symmetric to permutations between tokens. We present a simplified transformer block and solve the model at the limit, including accurate predictions for the learning curves and network outputs. We show that in common setups, one can derive tight bounds in the form of a scaling law for the learnability as a function of the context length. Finally, we argue WikiText dataset, does indeed possess a degree of permutation symmetry.