Oh, the space of possibilities is unimaginably vaster than that. Trillions of weights. But more combinations of those weights than there are electrons in the universe. So I think we could equally well speculate (and that's what we're both doing here, of course!) that all these things are simultaneously true:

1) Most configurations of LLM weights are indeed gibberish-producers (I agree with you here)

2) Nonetheless there is a vast space of combinations of weights that exhibit "intelligent" properties but in a profoundly alien way. They can still solve Erdos problems, but they don't see the world like us at all.

3) RL tends to herd LLM weights towards less alien intelligence zones, but it's an unreliable tool. As we just saw, with the goblins.

As a thought experiment, imagine that an alien species (real organic aliens, let's say) with a completely different culture and relation to the universe had trained an LLM and sent it to us to load onto our GPUs. That LLM would still be just as "intelligent" as Opus 4.7 or GPT 5.5, able to do things like solve advanced mathematics problems if we phrased them in the aliens' language, but we would hardly understand it.

Man, LLMs are really just astrology for tech bros. From randomness comes order.

I understand LLM architecture internals just fine. I can write you the attention mechanism on a whiteboard from memory. That doesn't mean I understand the emergent behaviors within SoTA LLMs at all. Go talk to a mechanistic interpretability researcher at Anthropic and you'll find they won't claim to understand it either, although we've all learned a lot over the last few years.

Consider this: the math and architecture in the latest generation of LLMs (certainly the open weights ones, almost certainly the closed ones too) is not that different from GPT-2, which came out in 2019. The attention mechanism is the same. The general principle is the same: project tokens up into embedding space, pass through a bunch of layers of attention + feedforward, project down again, sample. But, and here's the crux - if you'd told me in 2019 that an LLM in 2026 would have the capabilities that Opus 4.7 or GPT 5.5 have now (in math, coding, etc), I would not have believed you. That is emergent behavior ("grown, not made", as the saying is) coming out of scaling up, larger datasets, and especially new RL and RLVR training methods. If you understand it, you should publish a paper in Nature right now, because nobody else really does.

Also, I'm curious what you mean by "embed", the word implies a topographical mapping from "words" to some "high dimensional space". What are the topographical properties of words which are relevant for the task, and does the mapping preserve these?

circling back to the first point, are words continuous or discrete? is the space of all words differentiatable?

https://arxiv.org/html/2210.13382v5#abstract