[hansvm]

Not only is there a rough order, they explicitly require the ability to meaningfully embed data into the reals, and the performance gains come from assuming those embeddings have simple delta distributions. I wouldn't be surprised if the technique is worse than useless when that assumption is violated.

Edit: I don't have time right now, but a toy example I like to throw at these kinds of problems is mapping primes to their indices (e.g. 2->0, 3->1, 5->2, ...). General-purpose learning algorithms can usually make a little headway with it, but not much, and only with substantial resources thrown at the problem. I'd be shocked if that toy example were any faster with their solution than a b-tree.

[xucheng]

Due to the prime number theorem, your toy example actually has a very good approximated mapping.

[hansvm]

Kind of. Appropriately normalizing the primes with some kind of function based on log(log(n)) would probably allow the article's technique to perform well (still struggling on larger primes -- you can't avoid needing a lot of bits to express those gaps), but it's precisely the shifting density which makes the problem hard to learn with any standard algorithm, and I don't think theirs would be an exception since they explicitly rely on gaps drawn from some fixed distribution.