Languages as designed latent spaces

Summary

This post is an edited version of a Mastodon thread I wrote recently. I have been thinking recently about how language is a high entropy latent space and what that means. Latent spaces are sort of magic: they don’t just reduce the dimensionality of a higher dimensional space, they also constrain it such that arbitrary movement in the latent space maps to some meaningful position in the higher dimensional space. Think about how almost any textual prompt you give to an image generator results in a picture with recognisable shape and form, yet the vast majority of the possible images are basically just random noise. Language is, obviously, like this. Once you’ve learned to conquer the basic structural rules like syntax, grammar, and basic pattern matching of words with similar semantic clustering, movement within it almost always produces ‘meaningful’ (read: intelligible, not philosophically meaningful) results. Consider how an articulate human being can fairly easily produce passable bullshit in a field with which they have no experience simply by reading a little of the field’s jargon and improvising, but would utterly fail to demonstrate practical ability in the field. Language as technology One way to think about this is that language is a tool that makes conceptual reasoning easy: once you have the basic rules laid down, it’s almost more difficult to produce an output that doesn’t carry some meaning than it is to produce an output that does. Consider a strongly-typed programming language like Rust, Haskell, Lean, whatever: like human language, almost every well-typed transformation of the code corresponds to some meaningful change. In the same way that programmers can ‘bounce off’ the barriers of a type system to avoid bugs, a user of human languages can ‘bounce off’ conceptual barriers that would otherwise lead to them producing unintelligible nonsense, simply by following the grammatical rules of the language. However: the map is not the territory. For every wel...