Your work looks more interesting to me now, even though cubic time and quadratic space in the number of dimensions are still a significant drag.
Consider: State-of-the-art models often work with dimensions 2-3 orders of magnitude greater than 64. For example, LLaMA 2 models operate on visible and hidden states on 4096 and 11008 dimensions, respectively.
Anyway, thank you again! I'm adding your paper to my reading list.