model

The definitions behind the math of LLMs.

This isn't true.

A neural network can do new things outside the training data. Random initialization sees to that.

Whether those things are useful is a different question, but it turns out that yes, some of those things are useful. It also turns out that in a large-enough LLM if you give it some kind of idea of what you see as useful then yes, it can pick out the newly useful things.

Random init only exists to make each neuron distinct from other neurons. The weight is still defined by the training data, without the training data, these random weight don't give us anything.

The second thing you said is basically what's called fine-tuning.

Yes you are right about random initilization of course. Long day here.

For the second: No, not fine tuning at all.

For one thing in-context learning is enough for learning novel tasks[1].

Secondly, it can do new things outside that data. LLMs build models of the world[2]. That means it can model novel behavior based on that internal representation.

[1] https://arxiv.org/abs/2005.14165

[2] https://arxiv.org/abs/2305.11169

Not sure what you're getting at, in any of the cases you said it needs to learn if it needs to do new things.

Maybe it can generalize outside of some learning task you gave it, but still it comes from the training data.

"Generalization" also comes with some luck, since these models most of the time output complete non-sense when it comes to tasks it "didn't learn" specifically. Just because you got lucky with the neuron connections doesn't mean it has what it takes to generalize anything.