Recurrent update step in a Sliding Window Attention (SWA). Animation of the equation \( S_t = \bar{A} S_{t-1} + U_t \) unfolding in real-time. The left matrix represents the previous state \( S_{t-1} \) without decay, while the right matrix shows the new input contribution \( U_t \). The center flow indicator highlights the integration process, culminating in the updated state \( S_t \).