$w_{t}$ as a linear combination of previous region of attention $w_{t-1}$ and the anticipated region of attention at next fixation $L(w_{t-1})$, weighted by the predicted fixation probability $f^p_{t-1}$: $$w_t = f^p_{t-1}\cdot w_{t-1} + (1-f^p_{t-1})\cdot L(w_{t-1})$$

Finally, an attention map $G^a_t$ is computed as the weighted sum of the latent representation $F^S_{t}$ at frame $t$ by using the resulting channel weight vector $w_t$: $$G^a_t= \sum_{c=1}^{n} w_t[c] \cdot F^S_{t}[c]$$ where $[c]$ denotes the c-th dimension/channel of $w_t$/$F^S_{t}$ respectively.

Late Fusion
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We build the late fusion module (LF) on top of the saliency prediction module and the attention transition module, which takes $G^s_t$ and $G^a_t$ as input and outputs the predicted gaze map $G_t$. $$G_t = LF(G^s_t, G^a_t)$$ Finally, a predicted 2D gaze position $g_t$ is given as the spatial coordinate of maximum value of $G_t$.

Training
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For training gaze prediction in saliency prediction module and late fusion module, the ground truth gaze map $\hat{G}$ is given by convolving an isotropic Gaussian over the measured gaze position in the image. Previous work used either Binary Cross-Entropy loss [@kuen2016recurrent], or KL divergence loss [@zhang2017deep] between the predicted gaze map and the ground truth gaze map for training neural networks. However, these loss 