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Equation 6 · Part 12 · A History of Small and On-Device AI

Numerator: D_K × D_K × M × D_F × D_F + M × N × D_F × D_F

DK⋅DK⋅M⋅DF⋅DF+M⋅N⋅DF⋅DFDK⋅DK⋅M⋅N⋅DF⋅DF=1N+1DK2\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}
DK⋅DK⋅M⋅DF⋅DF+M⋅N⋅DF⋅DFD_K \cdot D_K \cdot M \cdot D_F \cdot D_F + M \cdot N \cdot D_F \cdot D_F

What this part means

The complete quantity above the fraction bar.

Its job in the formula

DKD_K × DKD_K × M × DFD_F × DFD_F + M × N × DFD_F × DFD_F occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

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 DKD_K ×\times DKD_K kernel, M input channels, N output channels and a DFD_F ×\times DFD_F feature map, a standard convolution costs DKD_K ⋅\cdot DKD_K ⋅\cdot M ⋅\cdot N ⋅\cdot DFD_F ⋅\cdot DFD_F multiply-adds. The paper gives the depthwise separable replacement’s…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

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