This is not obvious to me! For example, if you locked me in a room with no information inputs, over time I may still become more intelligent by your measures. Through play and reflection I can prune, reconcile and generate. I need compute to do this, but not necessarily more knowledge.

LLMs are no longer trying to just reproduce the distribution of online text as a whole to push the state of the art, they are focused on a different distribution of “high quality” - whatever that means in your domain. So it is possible that this process matches a “better” distribution for some tasks by removing erroneous information or sampling “better” outputs more frequently.

While that is theoretically true, it misses everything interesting (kind of like the No Free Lunch Theorem, or the VC dimension for neural nets). The key is that the parent model may have been trained on a dubious objective like predicting the next word of randomly sampled internet text - not because this is the objective we want, but because this is the only way to get a trillion training points.

Given this, there’s no reason why it could not be trivial to produce a child model from (filtered) parent output that exceeds the child model on a different, more meaningful objective like being a useful chatbot. There's no reason why this would have to be limited to domains with verifiable answers either.

The latest models create information from base models by randomly creating candidate responses then pruning the bad ones using an evaluation function. The good responses improve the model.

It is not distillation. It's like how you can arrive at new knowledge by reflecting on existing knowledge.

Fine tuning an llm on the output of another llm is exactly how deepseek made its progress. The way they got around the problem you describe is by doing this in a domain that can be relatively easily checked for correctness, so suggested training data for fine tuning could be automatically filtered out if it was wrong.

> It is, of course not going to produce a “child” model that more accurately predicts the underlying true distribution that the “parent” model was trying to. That is, it will not add anything new.

Unfiltered? Sure. With human curation of the generated data it certainly can. (Even automated curation can do this, though its more obvious that human curation can.)

I mean, I can randomly developed fact claims about addition, and if I curate which ones go into a training set, train a model that reflects addition of integers much more accurately than the random process which generated the pre-curation input data.

Without curation, as I already said, the best you get is a distillation of the source model, which is highly improbable to be more accurate.

No one knows if the pigeon-hole principle applies absolutely exclusive to the ability to generalize outside of a training set.

That is the existential, $1T question.

No no no you don’t understand, the models will magically overcome issues and somehow become 100x and do real AGI! Any day now! It’ll work because LLM’s are basically magic!

Also, can I have some money to build more data centres pls?

> it's always true that training on the output of another model will result in a worse model.

Not convincing.

You can imagine model doing some primitive thinking and coming to conclusion. Then you can train another model on summaries. If everything goes well it will be coming to conclusions quicker. That's at least. Or it may be able solve more complex problems with the same amount of 'thinking'. It will be self-propelled evolution.

Another option is to use one model to produce 'thinking' part from known outputs. Then train another to reproduce thinking to get the right output, unknown to it initially. Using humans to create such dataset would be slow and very expensive.

PS: if it was impossible humans would be still living on the trees.

Not arguing with your point about training efficiency, but the degree to which R1 is a technical breakthrough changes if they were calling an outside API to get the answers, doesn't it?

It seems like the difference between someone doing a better writeup of (say) Wiles's proof vs. proving Fermat's Last Theorem independently.

Key point from your linked paper:

> We find that indiscriminate use of model-generated content in training causes irreversible defects in the resulting models

No one is training on indiscriminate synthetic data. It's very much discriminated, but still synthetic.