Index Networks

M2O assumption assumes that all feature slices have contributions to each index slice. The local index function is defined by $l(\mathcal{X}): \mathbb{R}^{k\times k\times C}\rightarrow\mathbb{R}^{k\times k\times1}$. Compared to O2O DINs, the only difference in implementation is the use of standard convolution instead of group convolution, i.e., $M=C,N=1$ in Fig. \[fig:depthwise\_networks\].

Property and Model Complexity
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Both HINs and DINs have merits and drawbacks. Here we discuss some important properties of IndexNet. We also present an analysis of computational complexity.

Index maps generated by HINs and used by the $\mathcal{IP}$ and $\mathcal{IU}$ operators are related to spatial attention.

The holistic index map is shared by all feature slices, which means that the index map is required to be expanded to the size of $H\times W\times C$ when feeding into $\mathcal{IP}$ and $\mathcal{IU}$. This index map can be thought as a collection of local attention maps [@mnih2014recurrent] applied to individual local spatial regions. In this case, the $\mathcal{IP}$ and $\mathcal{IU}$ operators can also be referred to as “attentional pooling” and “attentional upsampling”. However, it should be noted that spatial attention has no pooling or upsampling operators like $\mathcal{IP}$ and $\mathcal{IU}$.

HINs are more flexible than DINs and more friendly for decoder 