Global Sub-Sampled Attention

Global Sub-Sampled Attention, or GSA, is a local attention mechanism used in the Twins-SVT architecture.

A single representative is used to summarize the key information for each of $m \times n$ subwindows and the representative is used to communicate with other sub-windows (serving as the key in self-attention), which can reduce the cost to $\mathcal{O}(m n H W d)=\mathcal{O}\left(\frac{H^{2} W^{2} d}{k_{1} k_{2}}\right)$. This is essentially equivalent to using the sub-sampled feature maps as the key in attention operations, and thus it is termed global sub-sampled attention (GSA).

If we alternatively use the LSA and GSA like separable convolutions (depth-wise + point-wise). The total computation cost is $\mathcal{O}\left(\frac{H^{2} W^{2} d}{k_{1} k_{2}}+k_{1} k_{2} H W d\right) .$ We have:

$$\frac{H^{2} W^{2} d}{k_{1} k_{2}}+k_{1} k_{2} H W d \geq 2 H W d \sqrt{H W} $$

The minimum is obtained when $k_{1} \cdot k_{2}=\sqrt{H W}$. Note that $H=W=224$ is popular in classification. Without loss of generality, square sub-windows are used, i.e., $k_{1}=k_{2}$. Therefore, $k_{1}=k_{2}=15$ is close to the global minimum for $H=W=224$. However, the network is designed to include several stages with variable resolutions. Stage 1 has feature maps of $56 \times 56$, the minimum is obtained when $k_{1}=k_{2}=\sqrt{56} \approx 7$. Theoretically, we can calibrate optimal $k_{1}$ and $k_{2}$ for each of the stages. For simplicity, $k_{1}=k_{2}=7$ is used everywhere. As for stages with lower resolutions, the summarizing window-size of GSA is controlled to avoid too small amount of generated keys. Specifically, the sizes of 4,2 and 1 are used for the last three stages respectively.