Depthwise Separable Convolution: MobileNet's Efficiency Trick (2D)

Kernel Size K

Feature-Map Shape

Input channels C_in 32

Output channels C_out 64

Spatial size N×N 32

Cost — Standard Conv

Multiply-accumulates

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Parameters

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Cost — Depthwise Separable

Multiply-accumulates

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Parameters

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Speedup vs. standard

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Drag empty canvas to pan, scroll to zoom. The fanned cards are the C_in channel stack; the gold outline is the sliding K×K window.

How it works

A standard convolution layer slides a K×K×C_in filter across the feature map, and does this once per output channel — every output pixel mixes all input channels and all kernel taps in one step:

FLOPs_std = N·N · K·K · C_in · C_out
Params_std = K·K · C_in · C_out

MobileNet's depthwise separable convolution factors that into two cheaper stages:

1) Depthwise: one K×K filter PER channel, no channel mixing
   FLOPs_dw = N·N · K·K · C_in

2) Pointwise: a 1×1 convolution that mixes channels
   FLOPs_pw = N·N · C_in · C_out

FLOPs_ds = FLOPs_dw + FLOPs_pw
Speedup  = FLOPs_std / FLOPs_ds ≈ 1 / (1/C_out + 1/K²)

Kernel size K — a larger receptive field makes the standard filter's cost grow with K², while only the depthwise stage feels that cost.
C_in / C_out — the pointwise 1×1 stage carries all the channel-mixing cost; more output channels widen the gap to standard convolution.
Spatial size N — both approaches scale the same way with resolution (N²), so it cancels out of the speedup ratio.
The sliding gold window shows the same K×K window mechanic both approaches share — the difference is purely in how many multiply-accumulates happen at each window position.

Real-world relevance: this factoring is the core trick behind MobileNet, EfficientNet and most on-device vision models — it typically cuts compute by 8–9× with only a small accuracy cost, which is why phones can run real-time image classification.

Input feature-map stack Sliding K×K window Standard conv cost Depthwise cost Pointwise (1×1) cost

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