location $a_c$ and width $a_w$, which are leveraged to adjust the temporal coordinate $$\label{Eq2:6}\small
       \begin{split}
              \varphi_c = a_c + \alpha_1 a_w \Delta c ~~~{\rm{and}} ~~~\varphi_w = a_w \exp{(\alpha_2 \Delta w)}~,
       \end{split}$$ where , are refined center location and width of the proposal. The $\alpha _1$, $\alpha _2$ are utilized to control the impact of temporal offsets. In particular, we define an overlap parameter $y_{ov}$ to represent the precise IoU prediction of the proposal, which benefits the proposal re-ranking in prediction.

In the training stage, we accumulate all the proposals from Gaussian pooling and produce the action instances through prediction layer. The overall training objective in our GTAN is formulated as a multi-task loss by integrating action classification loss ($L_{cls}$) and two regression losses, i.e., localization loss ($L_{loc}$) and overlap loss ($L_{ov}$): $$\label{Eq2:9}
       \small
       {L} = {L}_{cls} + \beta {L}_{loc} + \gamma {L}_{ov},$$ where and are the trade-off parameters. Specifically, we measure the classification loss $L_{cls}$ via the softmax loss: $$\label{Eq2:5}\small
L_{cls} = -\sum\limits_{n=0}^{C}I_{n=c}\log(y^a_{n}),$$ where indicator function $I_{n=c}=1$ if $n$ equals to ground truth action label $c$, otherwise $I_{n=c}=0$. We denote $g_{iou}$ as the IoU between default temporal boundary of this proposal and its corresponding closest ground truth. If the of 