The Column That Doesn't Fit

Pooling is the one stage of a convolutional network with nothing to learn in it. A small window sweeps the grid, and every stop is replaced by a single summary number — either the largest value lying under the window, or the mean of the values lying under it.

Task: write pool2d(grid, size, stride, mode), returning the pooled grid with every value rounded to 4 decimal places.

• grid is a rectangular list of rows of numbers, and size is the side of the square window.
• stride is how far the window moves between stops, applied the same way across and down.
• mode is "max" (keep the largest value in the window) or "avg" (keep the mean of the window).
• The window may never hang off the edge. Only stops where the whole window sits on real values are visited, so a side of length $n$ offers $\lfloor (n - \texttt{size}) / \texttt{stride} \rfloor + 1$ of them, and a leftover row or column that cannot hold a full window is never looked at.
• The windows are not obliged to tile. stride == size sets them edge to edge, and a smaller stride makes consecutive windows overlap — legal, and it must work.

The pooling layer you will actually meet is size = 2, stride = 2, which halves each side and so quarters the number of positions. Everything else here is that same sweep with the knobs turned — and it is the identical sweep a convolution performs, which is why the two shrink a grid by exactly the same formula.