I find the overlap between cryptography and machine learning really interesting. Today I noticed the Johnson–Lindenstrauss lemma appearing in both.
The lemma shows how to project a finite set of high-dimensional points into a lower-dimensional space while approximately preserving the distances between them.
Google Research's TurboQuant uses Quantized Johnson–Lindenstrauss as part of its approach to compressing KV caches and high-dimensional vectors. TurboQuant is also used in Gemma 4 inference implementations. Gemma 4 is a model I abliterated, which makes that connection particularly interesting to me.
In cryptography, LaBRADOR uses a modular Johnson–Lindenstrauss projection to help check bounds on vector norms. It is a lattice-based succinct proof system that can be used to aggregate Falcon signatures.
The same mathematical idea, in two very different applications.
While studying LaBRADOR, I found this excellent lecture on the JL lemma by @mkwoot: