Induction Heads Interpolate N-Grams

• URL: http://arxiv.org/abs/2607.02800v1
• Date: Thu, 02 Jul 2026 22:19:26 GMT
• Title: Induction Heads Interpolate N-Grams
• Abstract summary: Induction heads are attention circuits believed to underlie in-context learning in transformers.<n>We study transformers trained on order-$k$ Markov chains and identify two complementary smoothing mechanisms.<n>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.
• Score: 29.939177622666858
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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