You are conflating how it works with what the goal is.. If someone asks "how does a human run fast?" you don't say "you get a stop watch and ask them to run as

You are conflating how it works with what the goal is.. If someone asks "how does a human run fast?" you don't say "you get a stop watch and ask them to run as fast as they can and then look at the time and figure out how to get there quicker". There is a whole explanation involving biomechanics.... And if you understand how the biomechanics work, you might be able to answer how a human can jump high too. To make it even more concrete.... I have an LLM where I removed the last layer and fine tuned on a classification problem and the last layer now only has two outputs rather than vocab size outputs. The goal is binary classification. The output is not a completion of an idea or anything of the sort. It's still an LLM. It still works the same way all the way up until the last layer. The weights are the same all the way up to the last layer. It works because an LLM has to create a rich understanding of how a bunch of concepts work together.