Dynamical Kernel Attention: Estimating the Present from a Record of the Past

Peter Racioppo

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arXiv · 2610.24026

Dynamical Kernel Attention: Estimating the Present from a Record of the Past

Peter Racioppo

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Abstract

Standard self-attention compares tokens by similarity but does not account for how much of a past state survives to the present. We introduce Dynamical Kernel Attention (DKA), which derives attention from robust estimation of a latent state evolving under stochastic dynamics. As a past state decays toward equilibrium under the dynamics, the information it carries about the present vanishes, bounding the total evidence a head can draw. Unlike recency biases, DKA can abstain when relevant evidence is weak and guarantees a bounded error when old tokens are discarded. DKA preserves the parallel structure and computational cost of standard attention. We present the model and its theory; empirical evaluation is deferred to a subsequent version.

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Peter Racioppo. 2026-10-16. Dynamical Kernel Attention: Estimating the Present from a Record of the Past. https://arxiv.org/abs/2610.24026

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