I believe this has been extended to mean "on device", which is interesting. See Gerganov's article on Github [0]. I wrote about this here [1] where I made a contrast between the core and the edge. I think the term maps well to this meaning.

What I find more interesting is that in the classic "close network proximity", some parts of the world may not have benefited as much from that trend since the closest nodes of a global delivery network could be several countries away.

[0] https://github.com/ggerganov/llama.cpp/discussions/205

[1] https://medium.com/sort-of-like-a-tech-diary/consumer-ai-is-...