Receptive field through a stack

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Problem

A one-dimensional stack has a width- $3$ convolution with stride $1$ , width- $2$ pooling with stride $2$ , and a width- $3$ convolution with stride $1$ , all without padding. For input length $32$ , compute the final length, final receptive-field width, and spacing of adjacent final receptive-field centers in input coordinates.

Reveal answer or reference solution

The lengths are

32\to30\to15\to13.

Track the receptive-field width $r$ and input jump $j$ from $(1,1)$ using

r_{\text{new}}=r+(k-1)j,\qquad j_{\text{new}}=js.

The sequence is

(1,1)\to(3,1)\to(4,2)\to(8,2).

Thus, the final length is $13$ , the receptive-field width is $8$ , and the center spacing is $2$ .

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Receptive field through a stack

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