feature map share a holistic index map. By contrast, DINs learn an index function $I(\mathcal{X}):\mathbb{R}^{H\times W\times C}\rightarrow\mathbb{R}^{H\times W \times C}$, where the index map is of the same size as the feature map.

Since the index map generated by DINs can correspond to individual slices of the feature map, we can incorporate further assumptions into DINs to simplify the designs. If assuming that each slice of the index map only relates to its corresponding slice of the feature map, this is the One-to-One (O2O) assumption and *O2O DINs*. If each slice of the index map relates to all channels of the feature map, this leads to Many-to-One (M2O) assumption and *M2O DINs*. In O2O DINs, one can further consider sharing IndexNet. In the most simplified case, the same IndexNet can be applied to every slice of the feature map and can be shared across different downsampling/upsampling stages, like the $\max$ function. We name this IndexNet *Modelwise O2O DINs*. If IndexNet is stage-specific, i.e., only sharing indices in individual stages, we call this IndexNet *Shared Stagewise O2O DINs*. Finally, without sharing any parameter (each feature slice has its specific index function), we obtain the standard design, termed *Unshared Stagewise O2O DINs*. 