I'm allergic to latent space because I've yet to find any meaning to it beyond poetics, I develop an acute allergy when it's explicitly related to visually dimensional ideas like clustering.
I'll make a probably bad analogy: does your mindmap place things near each other like my mindmap?
To which I'd say, probably not, mindmaps are very personal, and the more complex we put on ours, the more personal and arbitrary they would be, and the less import the visuals would have
ex. if we have 3 million things on both our mindmaps, it's peering too closely to wonder why you put mcdonalds closer to kids food than restaurants, and you have restaurants in the top left, whereas I put it closer to kids foods, in the top mid left.
It would make sense for the human mental latent spaces to also converge. The reason is that the latent space exists to model the environment, which is largely shared among humans.
Why would that matter? The absolute orientation of the mind map doesn't matter - maybe my map is actually very close to yours, subject to some rotation and mirroring?
More than that, I'd think a better 2D analogy for the latent space is a force-directed graph that you keep shaking as you add things to it. It doesn't seem unlikely for two such graphs, constructed in different order, to still end up identical in the end.
Thirdly:
> if we have 3 million things on both our mindmaps, it's peering too closely to wonder why you put mcdonalds closer to kids food than restaurants, and you have restaurants in the top left, whereas I put it closer to kids foods, in the top mid left.
In 2D analogy, maybe, but that's because of limited space. In 20 000 D analogy, there's no reason for our mind maps to meaningfully differ here; there's enough dimensions that terms can be close to other terms for any relationship you could think of.
> there's no reason for our mind maps to meaningfully differ here
Yes there is.
If you think all training runs converge to the same bits given the same output size, I would again stress that the visual dimensions analogy is poetics and extremely tortured.
If you're making the weaker claim that generally concepts sort themselves into a space and they're generally sorted the same way if we have the same training data. Or rotational symmetry means any differences don't matter. Or location doesn't matter at all...we're in poetics.
Something that really sold me when I was in a similar mindset was word2vec's king - man + woman = queen wasn't actually real or in the model. Just a way of explaining it simply.
Another thought from my physics days: try visualizing 4D. Some people do claim to, after much effort, but in my experience they're unserious, i.e. I didn't see PhDs or masters students in my program claiming this. No one tries claiming they can see in 5D.
Yes, I'm making the weaker claim that concepts would generally sort themselves into roughly equivalent structures, that could be mapped to each other through some easy affine transformations (rotation, symmetry, translation, etc.) applied to various parts of the structures.
Or, in other words, I think absolute coordinates of any concept in the latent space are irrelevant and it makes no sense to compare them between two models; what matters is the relative position of concepts with respect to other concepts, and I expect the structures to be similar here for large enough datasets of real text, even if those data sets are disjoint.
(More specific prediction: take a typical LLM dataset, say Books3 or Common Crawl, randomly select half of it as dataset A, the remainder is dataset B. I expect that two models of the same architecture, one trained on dataset A, other on dataset B, should end up with structurally similar latent spaces.)
> Something that really sold me when I was in a similar mindset was word2vec's king - man + woman = queen wasn't actually real or in the model. Just a way of explaining it simply.
Huh, it seems I took the opposite understanding from word2vec: I expect that "king - man + woman = queen" should hold in most models. What I mean by structural similarity could be described as such equations mostly holding across models for a significant number of concepts.
I think you are hung up on the visual representation.
Last week, the post about jailbreaking ChatGPT(?) talked about turning off a direction in possibility-space to disable the "I'm sorry, but I can't..." message.
In a regular program, it would be a boolean variable, or a single ASM instruction.
And you could ask the same thing. "How does my program have an off switch if there aren't enough values to store all possible meanings of "off"? Does my off switch variable map to your off switch variable?"
And the answer would be yes, or no, or it doesn't matter. It's a tool/construct.
I mean, it's mostly about how close concepts are to each other, and to some extent how different concepts are placed on a given axis. Of course the concept space is very high-dimensional so it's not very easy to visualise without reducing the dimensions, but because we mostly care about distance that reduction is not particularly lossy, but it does mean that top-left vs bottom right doesn't mean much, it's more that mcdonalds is usually closer to food than it is to, say, gearboxes (and that a representation that doesn't do that probably doesn't understand the concepts very well).
I'll make a probably bad analogy: does your mindmap place things near each other like my mindmap?
To which I'd say, probably not, mindmaps are very personal, and the more complex we put on ours, the more personal and arbitrary they would be, and the less import the visuals would have
ex. if we have 3 million things on both our mindmaps, it's peering too closely to wonder why you put mcdonalds closer to kids food than restaurants, and you have restaurants in the top left, whereas I put it closer to kids foods, in the top mid left.