I had a weird thought about LLMs and some math this week (and art!) Bear with me, I’ll try not to be too obscure or mathy (I’ve been joking recently that I want to make a t-shirt that says “stochasticity preferentially imperils metacognition” - now that’s obscure!)
Part of the process of training an LLM is to create an embedding of the training data. This is a mapping from each data point to a vector in a high-dimensional “latent space”. Current state of the art is embedding vectors with roughly 100K dimensions to them - a very high dimensional space indeed! We don’t really have good physical intuition for this kind of object - we can understand that, say, when you go from two dimensions (flat plane) to three (space) you can make different kinds of connections because you have the extra dimension (like a bridge going over a road, instead of there being an intersection). And geometry changes - the max number of equidistant points in any space is N+1 on the number of dimensions (so, in 3d space, its a tetrahedron, in 2d it’s a triangle etc, optimal sphere packing changes…ok, enough math). So, you can have weird structures like 100K points that are all the “Same distance” from each other for example.
The latent space of an LLM is a mapping of semantics (meaning). Vectors that are nearby in the space have similar meaning, and in some spaces, you can do math meaningfully on the vectors - for example, taking the vector for “king”, subtracting the vector for “man” and adding the vector for “woman” gets the vector for “queen” if the embedding is rich enough.
So, some of what we are doing when we prompt an LLMs is “guiding” it to look at a particular part of the latent space. That’s why things like “ask a dumb question, get a dumb answer” work, and why some of the counterintuitive things like promising a tip have impact - you’re directing the LLMs attention to part of the space.
Here’s the weird idea: what if art (human art, like in galleries, etc) is satisfying to us because it’s pointing our attention to unused or unusual parts of our own internal latent spaces? Or highlighting an unusual, high dimensional connection we weren’t aware of? Maybe that’s why we like it, and why art tends to feel “oblique” - you have to combine some unusual vectors to find an unusual part of the space. Banksy is “high art” + “street art” + “high competence” + “guerilla” + “anti-capitalist” and that’s all a strange part of the space.
I don’t know if this is really what’s happening, but I suspect something like it is. I think this is why we are annoyed when art is dumb - we expected to be taken on a ride but got pointed to a predictable, familiar part of the space. Or some art is very challenging - it shows connections between things we thought were farther apart.