$K$ operations to form a cell, i.e., the connectivity between the $K$ operations within a cell. We first introduce the operation level search space and then the cell level search space.

Operation Level Search Space
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An attention operation takes a feature map of shape $(T, H, W, C_{\text{in}})$ as input and outputs an attended featured map of shape $(T, H, W, C_{\text{out}})$. For an attention operation, $C_{\text{in}}$ and $C_{\text{out}}$ can be different. To construct an attention operation, we need to make two fundamental choices: the dimension to compute the attention weights and the type of the attention operation.

### Attention Dimension

For brevity, we term the dimension to compute the attention weights as *attention dimension*. In CNNs for video classification, previous work [@qiu2017learning; @xie2018rethinking; @feichtenhofer2019slowfast] has studied when to use temporal convolution (e.g., $3 \times 1 \times 1$), spatial convolution (e.g., $1 \times 3 \times 3$), and spatiotemporal convolution (e.g., $3 \times 3 \times 3$). It is also a valid question to ask for attention what is the right dimension to apply an attention operation to videos: temporal, spatial or spatiotemporal (temporal and spatial together). The choice of the attention dimension is important as computing attention weights for different 