$3 \times D^j$ feature map cell, and the value is constrained within the range $(0,1)$ through a sigmoid operation. The weights of the Gaussian kernel $G^j_{t}$ are defined as $$\label{Eq2:1}\small
\begin{split}
&W^j_t[i] = \frac{1}{Z}\exp(-\frac{(p_i-\mu_t)^2}{2{\sigma^j_{t}}^2})~, \\
&s.t.~~~p_i = \frac{i}{T^j},~ \mu_t = \frac{t}{T^j}~,\\
&~~~~~~~~i \in \{0,1,...,T^j-1\},~~~~ t \in \{0,1,...,T^j-1\},
\end{split}$$ where $Z$ is the normalizing constant. Taking the spirit from the theory that the $\sigma^j_{t}$ could be considered as a measure of width (Root Mean Square width, RMS) in Gaussian kernel $G^j_{t}$, we utilize $\sigma^j_{t}$ as the interval measure of action proposal $P^j_{t}$. Specifically, the $\sigma^j_{t}$ can be multiplied with a certain ratio to represent the default temporal boundary: $$\label{Eq2:3}\small
a_c = (t+0.5)/T^{j},~~~~a_w = r_d \cdot 2\sigma^j_{t}/T^{j},$$ where $a_c$ and $a_w$ are the center location and width of default temporal boundary and $r_d$ represents temporal scale ratio. The $W^j_t$ is also utilized for feature aggregation with a pooling mechanism to generate action proposals, which will be elaborated in Section \[sec:3.4\].

![Visualization of Gaussian Kernel Grouping.[]{data-label="fig2:2"}](grouping_camera){width="34.00000%"}

Compared to the conventional 1D convolutional anchor layer which fixes the temporal scale as $1/T^j$ in $j$-th layer, ours employs the dynamic temporal scales by leveraging the learned Gaussian kernel of each proposal to explore the action 