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This uses the Convolve module for inference to do an average convolution on chunks and then grab every nth element based on the coarsening factor. It starts padded so it doesn't grab the first or last along a dimension like I was thinking. I just verified this.
The logic breaks if there is no midpoint (scaling factor thats not divisible by 4 — don't ask questions). So I just forced power of 2 for now. Which is excessive because technically anything thats a multiple of 4 (excluding 2) would work.