space. This makes it possible to conduct the search using differentiable methods and greatly improves the search speed.

Attention Cell Search Space {#sec-searchspace}
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We aim to search for spatiotemporal attention cells, which can be seamlessly inserted into a wide range of backbone networks, e.g., I3D [@carreira2017quo] or S3D [@xie2018rethinking], to improve the performance on video understanding tasks.

Formally, an attention cell takes a 4D feature map of shape $(T, H, W, C)$ as input and outputs a feature map of the same shape. $T, H$, and $W$ are the temporal dimension, height, and width of the feature map, respectively. $C$ denotes the number of channels. The output of an attention cell is enforced to have the same shape as its input by design, so that the discovered attention cells can be easily inserted after any layers in any existing backbone networks.

An attention cell is composed of $K$ primitive attention operations. The proposed attention cell search space consists of an operation level search space and a cell level search space (see Fig. \[fig-search-space\]). The operation level search space contains different choices to instantiate an individual attention operation. The cell level search space consists of different choices to compose the 