window partition

**Window Partition** is a **technique that divides a feature map or image into non-overlapping local windows for efficient self-attention** — computing attention independently within each window to reduce complexity from $O(N^2)$ to $O(w^2 cdot N/w^2) = O(N cdot w^2)$. **How Does Window Partition Work?** - **Partition**: Divide $H imes W$ feature map into $frac{H}{M} imes frac{W}{M}$ windows of size $M imes M$. - **Reshape**: Each window becomes a $M^2 imes C$ tensor (sequence of $M^2$ tokens). - **Attention**: Compute multi-head self-attention within each window independently. - **Unpartition**: Reshape back to $H imes W imes C$. **Why It Matters** - **Linear Complexity**: Attention cost scales linearly with image size (fixed $M^2$ attention per window). - **Local Inductive Bias**: Introduces locality similar to CNNs, which is beneficial for vision tasks. - **Foundation**: The base operation for Swin Transformer, Focal Transformer, and other window-based ViTs. **Window Partition** is **dividing the image into attention neighborhoods** — the fundamental operation that makes high-resolution Vision Transformers computationally practical.