We introduce Adaptive Filter Attention (AFA). AFA is a novel attention mechanism that directly integrates a learnable dynamic model into the calculation of attention weights. Instead of directly comparing queries and keys, we model the input sequence as discrete observations of a linear stochastic differential equation (SDE). Simultaneously, we assume a continuous-time linear time-invariant system with a diagonalizable state matrix and noise covariance, efficiently propagating uncertainty through the dynamics from keys to queries using the closed-form solution of the differential Lyapunov equation. Attention naturally emerges as a maximum-likelihood solution for filtering the trajectory of this linear SDE, and the attention weights correspond to robust residual-based reweighting of the propagated query-key precision. Furthermore, by constraining the system dynamics and noise, we obtain a simplified variant with the same computational and memory complexity as standard attention. With zero attenuation and process noise and a small-angle approximation, we recover the complex-valued generalization of common dot-product attention using rotational position encoding.
