action proposals.[]{data-label="fig2:3"}](context){width="44.00000%"}

With the learned and mixed Gaussian kernels, we calculate the weighted sum of the feature map based on the values in Gaussian curve and obtain the aggregated feature $F$. Specifically, given the weighting coefficients $W^j_{t}$ of Gaussian kernel $G^j_{t}$ at center location $t$ in $j$-th layer, the aggregated feature for proposal $P^j_{t}$ is formulated as $$\label{Eq2:2}\small
\begin{split}
&F^j_t = \frac{1}{T^j}\sum\nolimits_{i=0}^{T^j-1} W^j_t[i] \cdot f_i, \\
\end{split}$$ where the representation $F^j_{t}$ is further exploited for the action classification and temporal boundary regression.

The above Gaussian pooling mechanism inherently takes the contextual contributions around each action proposal into account. In contrast to the manual extension plus average-pooling strategy to capture video context information (left part of Figure \[fig2:3\]), ours provides an elegant alternative to adaptively learn the weighted representation (right part of Figure \[fig2:3\]) based on the importance.

Network Optimization
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Given the representation of each proposal from Gaussian pooling, three 1D convolutional layers are utilized in parallel to predict action classification scores, localization parameters and overlap parameter, respectively. Action classification scores $\mathbf{y^a}=[y^a_0, y^a_1, ..., y^a_{C}]$ indicate the probabilities belonging to $C$ action classes plus one “background” class. Localization parameters $(\Delta c, \Delta w)$ denote temporal offsets relative to default center 