There is a real connection insofar as the internal space of an LLM is a vector space so things which hold for vector spaces hold for the internal space of an LLM. This is the power of abstract algebra. When an algebraic structure can be identified you all of a sudden know a ton of things about it because mathematicians have been working to understand those structures for a while.
The internal space of an LLM would also have things in common with how, say currents flow in a body of water because that too is a vector space. When you study this stuff you get this sort of zen sense of everything getting connected to everything else. Eg in one of my textbooks you look at how pollution spreads through the great lakes and then literally the next example looks at how drugs are absorbed into the bloodstream through the stomach and it’s exactly the same dynamic matrix and set of differential equations. Your stomach works the same as the great lakes on a really fundamental level.
The spaces being described here are a little more general than vector spaces, so some of things which are true about vector spaces wouldn’t necessarily work the same way here.
The internal space of an LLM would also have things in common with how, say currents flow in a body of water because that too is a vector space. When you study this stuff you get this sort of zen sense of everything getting connected to everything else. Eg in one of my textbooks you look at how pollution spreads through the great lakes and then literally the next example looks at how drugs are absorbed into the bloodstream through the stomach and it’s exactly the same dynamic matrix and set of differential equations. Your stomach works the same as the great lakes on a really fundamental level.
The spaces being described here are a little more general than vector spaces, so some of things which are true about vector spaces wouldn’t necessarily work the same way here.