Thanks a lot for the detailed reply, it was better than I had hoped for :)

So knowledge transfer is something incredibly specific and much more narrow than what I thought. They don't transfer concepts by generalization, but they compress knowledge instead, which I assume the difference is, that generalization is much more fluid, while compression is much more static, like a dictionary where each key has a probability to be chosen, and all the relationships are frozen, and the only generalization that happens, is the generalization which is an expression of the training method used, since the training method freezes it's "model of the world" into the weights so to say? So if the training method itself cannot generalize, but only compress, why would the resulting model that the training method produces? Is that understood correctly?

Does there exist a computational model, which can be used to analyse a training method and put a bound on the expressiveness of the resulting model?

It's fascinating that the emergent ability of models disappear if you measure them differently. Guess the difference is that "emergent abilities" are kinda nonsensical, since they have no explanation of causality (i.e. it "just" happens), and just seeing the model getting linearly better with training fits into a much more sane framework. That is, like you said, when your success metric is measuring discretely, you also see the model itself as discrete, and it hides the continuous hill climbing you would otherwise see the model exhibit with a different non-discrete metric.

But the model still gets better over time, so would you expect the model to get progressively worse on a more generalized metric, or does it only relate to the spikes in the graph that they talk about? IE, they answer the question of "why" jumps in performance are not emergent, but they don't answer why the performance keeps increasing, even if it is linear, and whether it is detrimental to other less related tasks?

And if you wanted to test "emergent" wouldn't it be more interesting to test the model on tasks, which would be much more unrelated to the task at hand? That would be to test generalization, more so as we see humans see it? So it wouldn't really be emergence, but generalization of concepts?

It makes sense that it is more straightforward to refute a claim by using contradiction. Would it be good practice for papers, to try and refute their own claims by contradiction first? I guess that would save a lot of time.

It's interesting about the knowledge leakage, because I was thinking about the concept of world simulations and using models to learn about scenarios through simulations and consequence. But the act of creating a model to perceive the world, taints the model itself with bias, so the difficulty lies in creating a model which can rearrange itself to get rid of incorrect assumptions, while disconnecting its initial inherent bias. I thought about models which can create other models etc, but then how does the model itself measure success? If everything is changing, then so is the metric, so the model could decide to change what it measures as well. I thought about hard coding a metric into the model, but what if the metric I choose is bad, and we are then stuck with the same problem of bias as well. So it seems like there are only two options, it either converges towards total uncontrollability or it is inherently biased, there's doesn't seem to be any in-between?

I admit I'm trying to learn things about ML I just find general intelligence research fascinating (neuroscience as well), but the more I learn, the more I realize I should really go back to the fundamentals and build up. Because even things which seem like they make sense on a surface level, really has a lot of meaning behind them, and needs a well-built intuition not from a practical level, but from a theoretical level.

From the papers I've read which I find interesting, it's like there's always the right combination of creativity in thinking, which sometimes my intuition/curiosity about things proved right, but I lack the deeper understanding, which can lead to false confidence in results.