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Receptive Field and Parameter Efficiency of Stacked Convolutions

Stacking multiple small convolutions provides the same receptive field as a single larger convolution while improving parameter efficiency and increasing depth. For example, applying two successive 3imes33 imes 3 convolutions touches the same input pixels as a single 5imes55 imes 5 convolution. However, while a single 5imes55 imes 5 convolution requires 25c225 \cdot c^2 parameters (where cc is the number of channels), three successive 3imes33 imes 3 convolutions use a comparable number of parameters (39c2=27c23 \cdot 9 \cdot c^2 = 27 \cdot c^2) while providing an even larger receptive field. This analysis demonstrated that deep and narrow networks significantly outperform their shallow and wide counterparts, establishing stacked 3imes33 imes 3 convolutions as a gold standard in deep learning architecture design.

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Updated 2026-05-13

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