Convolutional Networks

CNN vs Fully Connected

Compare shared filters with independent dense weights.

y[r,c] = Σ input[r×stride+i−pad,c×stride+j−pad] × kernel[i,j]

0×1 + 0×0 + 1×-1 + 0×1 + 1×0 + 1×-1 + 1×1 + 1×0 + 1×-1

Output = -2

Output size = floor((input + 2×padding − kernel) / stride) + 1floor((5 + 2×0 − 3) / 1) + 1 = 3

Speed ×Step 0 / 8

Input channels1

Output filters8

Conv parameters = (K² × Cin + 1) × CoutCNN: 80 parameters; dense to same 3×3×8 output: 1872 parameters

Channels are tensor depth (for example R, G and B). A 2D convolution sums across channels; an RGB image does not require a spatial 3D convolution.

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CNN vs Fully Connected

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