I am reading the HTM whitepaper and I am having trouble finding some definition of the input space. The paper talks about “natural center over the input region” and distance from this center (“higher values near the center”, page 34), but never actually tells what the input region is. Is it a metric space? Is it a vector space? Is it an Euclidean space? Other thing I am missing is what is the distribution from which we select inputs of a column. Is it uniform over the whole space of inputs?

That paper is old and outdated. See our recent papers here. Also, there is HTM School, which has an entire video about the input space.

Thanks, I will check it out.