That's a mischaracterization. Latent space is simply a (multidimensionally) sorted collection, it's only a piece of the pie. A massive amount of structure is held in the unembedding layer. Generative AI models are a very specific ordering, LLMs a very specific subset of that, and they're hardly the only users of the concept.
I get what the author is going for, and they're on the right track. There is something interesting going on with embedding spaces: When used as the substrate for a neural network, you can effectively treat them as a kind of continuous form of computation. That is, given two functions, you can trivially derive a function which sits exactly between those two, and do so ad infinitum, for any arbitrary program (in theory. Obviously everything materially accessible is finite.) This is only one such manipulation. You can deform a function in an unenumerable amount of ways. Think like a bezier curve path tool in something like Krita or Photoshop, but for a function. You can keep adding points and twist it to your heart's content.
It's wrong to focus on LLMs specifically, as well. This is a much, much broader topic than you realize. Most of the interesting stuff has nothing to do with language models at all. I get a huge chunk of the industry is currently having a stroke over LLMs being able to brute-force problem solving, but if we're to talk philosophy, theory, and so on, we have to get past the surface level misuse of Machine Translation's holy grail. That's like having a conversation about the potential of computation itself, but all you talk about is web browsers, using them interchangeably with "computer".
This article and your comment reminded me of something Stephen Wolfram was saying about "mining" the latent space of, in his case, cellular automata as a computational medium. A quick search yields this somewhat older talk: https://www.stephenwolfram.com/publications/mining-computati...
That phrasing and analogy stuck in my mind, of looking at the space of all possible programs as a resource to be explored for valuable nuggests of algorithms. Your description of interpolating between two functions gives me a similar perspective, of seeing algorithms not only as discrete and separate objects/processes, but "slices" of a larger space, the continuum of computation.
What the article is describing seems to me like "slices of semantic space", not just similar on the surface, but it's actually talking about the same space explored using different tools and lenses.
>Latent space is simply a (multidimensionally) sorted collection, it's only a piece of the pie.
I agree about the small piece of the pie, but I can't really see it as a sorted collection.
The essence of many dimensions is that you can head off in another direction that doesn't impact the relationship of other dimensions. It seems common to consider a latent space as a encoding of meaning. It is certainly a mapping of relationships, and I think there's some pretty good philosophy arguing that a set of relationships is synonymous with meaning.
A long distance view of LLMs is embeddings encode meaning, Attention finds relevant meanings, and the perceptron does the thinking on things that have meaning and are relevant to each other. The transformer is those things stacked to turn input latents into output latent with a different meaning relative to the input. Stack enough transformer layers to get lots of thinking about lots of meanings.
I'm not entirely convinced that embeddings are doing exactly the things that the ideas like the King - man + woman = Queen examples suggest. It seems to me that the number of dimensions are too low for that to allow a good combination of ideas.
I have wondered how things would look if you considered, instead of cosine difference have something like min(cosine_difference(dimension_mask_0)... cosine_difference(dimension_mask_n)).
The idea would be instead of dimensions being pure encodings of some group of meaning some dimensions are expendable.
Like if you had W,X,Y,Z dimensions and you wanted to encode the relationship between items if they all had identical circular dials with a thousand concepts written around the rim. and the dial faces were around WX,WY,WZ, XY, XZ, YZ, you could link any two concepts with any two dials.
In higher dimensions the combination of relationships possible become astronomical. and to me it seems intuitively more expressive for relationships than the weighting of some dimensions representing a vector that encodes a magnitude of a single concept.
I think you're running into difficulty because you're conflating 'sorting' with what we would call a total or linear ordering. Partial orders are non-linear, and allow you to form posets, which are isomorphic with DAGs. Then you have the broader family of orderings containing weak orders, preorders, strictness, etc. which make matters more complicated. Cyclic orders drop transitivity, for example, allowing you to describe directed graphs with cycles. The thing is that sorting also isn't strictly about orderings. It also encapsulates classification, which are a family of operations entirely distinct from order. There's overlap in the structural implications of some orderings and classifications, but they're also distinct categories (and both are important in ML.)
Dear Kevin: AI models don't contain all of human knowledge. They don't even contain, for example, the complete curricula of the least comprehensive K-12 program.
That's a mischaracterization. Latent space is simply a (multidimensionally) sorted collection, it's only a piece of the pie. A massive amount of structure is held in the unembedding layer. Generative AI models are a very specific ordering, LLMs a very specific subset of that, and they're hardly the only users of the concept.
I get what the author is going for, and they're on the right track. There is something interesting going on with embedding spaces: When used as the substrate for a neural network, you can effectively treat them as a kind of continuous form of computation. That is, given two functions, you can trivially derive a function which sits exactly between those two, and do so ad infinitum, for any arbitrary program (in theory. Obviously everything materially accessible is finite.) This is only one such manipulation. You can deform a function in an unenumerable amount of ways. Think like a bezier curve path tool in something like Krita or Photoshop, but for a function. You can keep adding points and twist it to your heart's content.
It's wrong to focus on LLMs specifically, as well. This is a much, much broader topic than you realize. Most of the interesting stuff has nothing to do with language models at all. I get a huge chunk of the industry is currently having a stroke over LLMs being able to brute-force problem solving, but if we're to talk philosophy, theory, and so on, we have to get past the surface level misuse of Machine Translation's holy grail. That's like having a conversation about the potential of computation itself, but all you talk about is web browsers, using them interchangeably with "computer".
This article and your comment reminded me of something Stephen Wolfram was saying about "mining" the latent space of, in his case, cellular automata as a computational medium. A quick search yields this somewhat older talk: https://www.stephenwolfram.com/publications/mining-computati...
That phrasing and analogy stuck in my mind, of looking at the space of all possible programs as a resource to be explored for valuable nuggests of algorithms. Your description of interpolating between two functions gives me a similar perspective, of seeing algorithms not only as discrete and separate objects/processes, but "slices" of a larger space, the continuum of computation.
What the article is describing seems to me like "slices of semantic space", not just similar on the surface, but it's actually talking about the same space explored using different tools and lenses.
>Latent space is simply a (multidimensionally) sorted collection, it's only a piece of the pie.
I agree about the small piece of the pie, but I can't really see it as a sorted collection.
The essence of many dimensions is that you can head off in another direction that doesn't impact the relationship of other dimensions. It seems common to consider a latent space as a encoding of meaning. It is certainly a mapping of relationships, and I think there's some pretty good philosophy arguing that a set of relationships is synonymous with meaning.
A long distance view of LLMs is embeddings encode meaning, Attention finds relevant meanings, and the perceptron does the thinking on things that have meaning and are relevant to each other. The transformer is those things stacked to turn input latents into output latent with a different meaning relative to the input. Stack enough transformer layers to get lots of thinking about lots of meanings.
I'm not entirely convinced that embeddings are doing exactly the things that the ideas like the King - man + woman = Queen examples suggest. It seems to me that the number of dimensions are too low for that to allow a good combination of ideas.
I have wondered how things would look if you considered, instead of cosine difference have something like min(cosine_difference(dimension_mask_0)... cosine_difference(dimension_mask_n)).
The idea would be instead of dimensions being pure encodings of some group of meaning some dimensions are expendable.
Like if you had W,X,Y,Z dimensions and you wanted to encode the relationship between items if they all had identical circular dials with a thousand concepts written around the rim. and the dial faces were around WX,WY,WZ, XY, XZ, YZ, you could link any two concepts with any two dials.
In higher dimensions the combination of relationships possible become astronomical. and to me it seems intuitively more expressive for relationships than the weighting of some dimensions representing a vector that encodes a magnitude of a single concept.
I think you're running into difficulty because you're conflating 'sorting' with what we would call a total or linear ordering. Partial orders are non-linear, and allow you to form posets, which are isomorphic with DAGs. Then you have the broader family of orderings containing weak orders, preorders, strictness, etc. which make matters more complicated. Cyclic orders drop transitivity, for example, allowing you to describe directed graphs with cycles. The thing is that sorting also isn't strictly about orderings. It also encapsulates classification, which are a family of operations entirely distinct from order. There's overlap in the structural implications of some orderings and classifications, but they're also distinct categories (and both are important in ML.)
Dear Kevin: AI models don't contain all of human knowledge. They don't even contain, for example, the complete curricula of the least comprehensive K-12 program.
That's a really interesting claim, can you give an example of a question that could reasonably be on a K-12 exam that a frontier model can't answer?
Some math related to training on latents, not tokens:
https://arxiv.org/abs/2605.27734
Probably the most important thing I've read this month. The key concepts are valuable.
In future, to provide guard rails to models, we will build token flow pipes in mathematical sense. Sort of like Mathematical Engineering.
Infinite Craft is a web game based on combining two things using LLMs, but it's not clear how it works, whether latent space or something else.
I believe it's just giving a prompt to an LLM saying "combine these things ..."
[dead]
This post made me want to watch Everything Everywhere All at Once again
This is nonsensical AI slop with so many technical mistakes.