jl-lemma-dimension-bounds-log-n-epsilon

Summary

You can project data from any number of dimensions, even millions, down to a modest target space while keeping all pairwise distances roughly intact, and the size of that target space depends only on how many points you have and how much error you allow, not on the original dimensionality. This means the system can handle arbitrarily high-dimensional inputs without the computational cost blowing up, since the reduced dimension stays small no matter how large the source space is.