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arXiv · 2605.29351

Attention as In-Context Empirical Bayes: A Two-Stage View via Particle Dynamics

Matthew Smart·Soumya Ganguly·Nilava Metya·Alexandre V. Morozov·Anirvan M. Sengupta
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Abstract

We study minimal attention-only transformers under all-token corruption and show they admit a two-stage empirical Bayes interpretation. A single attention step computes a kernel-weighted posterior mean with respect to the empirical distribution defined by the context. Depth refines this distribution through particle dynamics (Stage 1), while a long-range skip-connection carries the noisy input as a query for posterior inference (Stage 2), revealing distinct statistical roles for depth and attention residuals. The framework isolates a minimal setting in which the context itself induces a depth-dependent energy landscape governing in-context inference. We show that effective denoising can emerge without an explicit noise schedule: a fixed kernel bandwidth and finite integration horizon suffice, yielding a principled depth-noise relationship. We further establish a posterior-mean recovery guarantee for a class of well-behaved priors, where the empirical estimator converges to the Bayes-optimal predictor under asymptotic conditions. Connecting these dynamics to reverse-diffusion limits, our results provide a statistical interpretation of attention as in-context inference via sample-based posterior estimation, without explicit density modeling.

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Matthew Smart, Soumya Ganguly, Nilava Metya, Alexandre V. Morozov, Anirvan M. Sengupta. 2026-05-28. Attention as In-Context Empirical Bayes: A Two-Stage View via Particle Dynamics. https://arxiv.org/abs/2605.29351

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