Ok, so I am just trying to understand the basic concepts in the paper and put it in my own words: It seems that the primary idea is that quantization precision

Ok, so I am just trying to understand the basic concepts in the paper and put it in my own words: It seems that the primary idea is that quantization precision is more important where there is a high density of neighbors. I.e. at the edges the quantized sections (buckets) could be large since there are few items there, but at high density areas, the buckets should be much smaller in order to have an even distribution of objects per bucket as possible. Therefore, the overall effectiveness of a Quantization loss function should not be evaluated on a sum of squared error (that assumes the vector space has consistent linear value), but should rather consider the densities of the vector space and use that as a weight of the errors at different regions. To me it seems analogous to a hash set, where the goal would be to have even distribution (same number of items in every bucket). We want to quantize space so that every position has about the same number of items.