In terms of accuracy, it totally depends on the resolution needed. We can get >99% accuracy of L2 waaaaay faster with 1/10 of the memory overhead. For what we are doing that is the perfect trade off.
In terms of LSH, we tried projection hashing and quantization and were always disappointed.
Or is there actually some interesting hash-based neural algorithm lurking around somewhere?
Network based hashing is great to maximise information quality of the hash (compared to other LSH methods). It works to compress existing vectors super efficiently.
Very soon things like language embeddings will skip the vectors and instead networks output hashes directly. These are much faster as the network can learn where to use more bits where it needs resolution, as opposed to using floatXX for everything. It’s amazing to see it work, but not fully there yet.
No one measures vector distance using the hamming distance on binary representations. That's silly. We use L1 or L2, usually, and the binary encoding of the numbers is irrelevant.
It sounds like the LSH is maaaaybe equivalent to vector quantization. In which case this would be a form of regularization, which sometimes works well, and sometimes meh.