Induction Heads Interpolate N-Grams

Researchers found that induction heads in transformers implement two smoothing mechanisms—soft context-matching and BOS token pseudo-counts—that interpolate n-gram estimates, enabling in-context learning to regularize rather than simply count. Trained transformers matched or outperformed classical count-based baselines on Markov chain tasks.

arXiv:2607.02800v1 Announce Type: new Abstract: Induction heads are attention circuits believed to underlie in-context learning in transformers, yet a precise characterization of the estimators they implement remains elusive. We study transformers trained on order-$k$ Markov chains and identify two complementary smoothing mechanisms. First, at finite attention-weight scale, the circuit implements a soft context-matching estimator: it aggregates contributions from exact and partial context matches, weighted exponentially by their overlap, and induces a data-dependent interpolation across context orders analogous to Jelinek-Mercer smoothing. Second, a beginning-of-sequence BOS token induces additive pseudo-counts, recovering Dirichlet-style smoothing. We construct a disentangled transformer implementing both mechanisms and show that trained transformers recover the predicted attention patterns. Across settings where pseudo-count smoothing is optimal or lower-order contexts provide structured evidence, trained transformers match or outperform classical count-based baselines. Our results bridge mechanistic interpretability of induction heads with classical statistical smoothing, revealing that transformers learn to regularize in-context estimation rather than simply count.