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Equation 5 · A History of Small and On-Device AI

What does this equation mean?

DK⋅DK⋅M⋅N⋅DF⋅DFD_K \cdot D_K \cdot M \cdot N \cdot D_F \cdot D_F

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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DKD_K

Symbol D_K

DKD_K is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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MM

Symbol M

M is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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NN

Symbol N

N is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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DFD_F

Symbol D_F

DFD_F is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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multiplication

multiplication

Multiply the quantities on either side.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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What the article says around this equation

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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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 cost, and its ratio to the standard cost, directly:

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