(Note: I don't actually think the consciousness question is the most important one in the near term. Where I think this line of reasoning gets really dangerous is when people use it to assert that LLMs can't or won't engage in certain behaviors no matter much they advance; this doesn't have anything to do with consciousness.)
Most people would expect that matrix multiplication is not conscious, and autocomplete is not conscious either.
We can't prove matrix multiplication isn't conscious, but it doesn't seem likely unless everything is conscious.
As a side note, that is why I find the idea that the brain is a quantum-classical hybrid computer appealing. And following the research developments is very interesting, to say the least.
“If LLMs are conscious, it means matrix multiplication is conscious” == “If humans are conscious it means cells are conscious”.
It’s possible for complex systems to have emergent properties not exhibited by any individual component of the system.
So for consciousness and LLMs it could be Qualia, lack of semantic understanding, lack of continuity in time, lack of a high degree of integrated causal feedback, etc.
Or perhaps those are just features of human consciousness but not integral to consciousness as a whole. To me this then implies panpsychism to some degree, which I'm alright with too.
But qualia are not directly measurable and the rest of the list only matters if those features are necessary for qualia, which we can't decide without such measurements or at least a strong theoretical model.