What does this equation mean?

MobileNet, published by Howard and colleagues at Google fourteen months later, generalized the same idea into a reusable building block rather than one bespoke network. A standard convolutional layer filters and combines its inputs in a single step; MobileNet’s depthwise separable convolution splits that into a depthwise layer that filters each input channel on its own, followed by a 1×1 pointwise convolution that recombines the results [ 1 ] . For a $D_K$ $\times$ $D_K$ kernel, M input channels, N output channels and a $D_F$ $\times$ $D_F$ feature map, a standard convolution costs $D_K$ $\cdot$ $D_K$ $\cdot$ M $\cdot$ N $\cdot$ $D_F$ $\cdot$ $D_F$ multiply-adds. The paper gives the depthwise separable replacement’s cost, and its ratio to the standard cost, directly: $\frac{D_K \cdot D_K \cdot M \cdot D_F \cdot D_F + M \cdot N \cdot D_F \cdot D_F}{D_K \cdot D_K \cdot M \cdot N \cdot D_F \cdot D_F} = \frac{1}{N} + \frac{1}{D_K^2}$. With the near-universal 3$\times$3 kernel, that ratio works out to roughly an eighth to a ninth of the original computation, for what the paper reports as a small accuracy cost [ 1 ] . MobileNet then added two further dials rather than shipping one fixed shape: a width multiplier $\alpha$ that uniformly thins the number of channels at every layer, and a resolution multiplier that shrinks the input image, letting a developer choose a point on an accuracy-versus-latency curve instead of accepting whatever a single published checkpoint offered [ 1 ] . That is the detail worth keeping from this stage of the history: SqueezeNet showed that a deliberately designed structure could match a much larger network’s accuracy at a fraction of the parameters; MobileNet turned the same insight into a convolution that could be dropped into any architecture, with knobs that let one trained design be retargeted across a whole range of phones rather than retrained for each.