Training identifies these dimensions in the training data and links it with each word/token. Then given a stream of such tokens, each with its own set of dimensions (which can be huge), and LLM predicts the dimensions that the next token is most likely to have...
formalisms come only after there is understanding of the phenomena and a specific need to communicate concepts across members of community - in a concise and commonly comprehensive way. my understanding is that education often fails to train understanding and jumps directly to formalisms. and this is right also for STEM schools, where it is presumed everyone has some innate inclination to the matter. but this presumption, in my experience as university teacher, is not entirely correct, and students are not universally prepared to express lack of understanding, and particularly when it is expected from them to rather indicate understanding.
it seems very weird, the concept, to reward the correct answer, while suppressing and discouraging the expression of misunderstanding or confusion. why is weird? because learning comes trough trial and error, and the error part is half of it. so we need to encourage people to express their errors or lack of understanding, so that we can then fill in the gaps and eventually stand on a common ground. sadly, many forums, HN included, does not cherish misunderstanding. our posts here mostly get upvoted whenever they cross a sort of threshold about the amount of truth in our writing, and not because of daring expressions of confusion.
On the other hand I deal with higher dimensions better than most, possibly because of my aphantasia.
Agreed, I don't think anyone has a good grasp on, say, 64K D, but we can do a bit better than just 3.
I mean, there are people with aphasia and hyperplasia - how do you prove actual 3D visualisation.
There are games that people play that need 4D visualisation to be able to do well and they perform at that.
But I don’t think it is possible for us. At least, for strict senses of visualization. I suspect that the architecture of our brains doesn’t support it. This is rather speculative because I don’t know basically any neuroscience, but I wonder if the whole “the brain is largely a very wrinkled surface (though with several layers to this surface), and the retinas are also surfaces” may have something to do with this. A retina in a eye-4-ball would have a 3D boundary (I.e. hypersurface), and I imagine that the amount of information that it would take in if it had an at all similar angular resolution, would be too great for our visual cortex to be able to represent all of it.
Of course, our vision only really has the high resolution it seems to everywhere in the narrow region we’re directly looking at, but still.
The trivial example that comes to mind is the character customization sliders in many video games.
That is why the scam works, because investors are humans...
Seeing LLMs for what they really are will also make it clear they are fundamentally unfit for a lot of tasks they are currently marketed for...
They're borderline useless and certainly potentially inadvertently malicious for writing, customer service, speech to text, writing large amounts of complex code, therapy, medical diagnostics... the list goes on
Sounds like you're part of the problem?
It's really a serious problem just eroding the fabric of society in real-time. Being complacent in it or believing in the promise is just wholly foolish and bad for everyone.
It's been several years now of LLMs only appeasing those with low expectations and inexperience. Unless the only goal was generating boilerplate or really sloppy proofs of concept, LLMs are a waste time for everyone else. This argument is so over already. We're all just hoping for a soft landing when the hangover really kicks in.
What domain?
"Amish do not view technology as evil, and individuals may petition for acceptance of a particular technology in the local community" - https://en.wikipedia.org/wiki/Amish_way_of_life#Use_of_moder...
See also https://thereader.mitpress.mit.edu/how-the-amish-let-technol... about some Amish use of cell phones with adapters to be more payphone/landline-like and https://news.ycombinator.com/item?id=21349989 was a discussion about the use of pneumatic machinery by the Amish.
Maybe you forgot that important tidbit?
People are using them because they're being shoved down their throats and they're complacent.
Software quality, maintainability, exploitability, morale, competency are all at all-time lows and just worsening.
It's really bad to defend this.
Then they removed the approve everything manually mode and I thought, maybe I'm the one out of touch, I should try vibe coding. I gave it a big spec of things to implement and I was pretty vague on the details, but I was kind of hoping that the AI would get it right anyway.
I noticed that when you let the AI just do its thing, you spend a lot of time staring at the screen waiting for it to finish. No wonder all these people are obsessed with parallel agents.
Anyway, after a while it produced the end result and it was pretty bad and I don't even mean the code. This was with gpt 5.6 Terra. Definitively not the type of "did a week's worth of work in one hour" type of deal.
Meanwhile if you guide it with your own technical skills the end result is a tireless code generator that operates at 80% of the quality of your own code but is only roughly 1.5x to 2x faster than doing it yourself. The biggest multipliers come from making the AI do things humans don't want to do, like writing a bunch of thorough tests but those don't translate into increased productivity, the opposite in fact. They translate into higher software quality but if you vibe the tests and don't review them, even that disappears.
i'm a worse programmer now because of it
I'm sure someone will point out something like the 4-color theorem as a counterargument. Where is that kind of theorem proving in this generation of AI? We seem to have hit a dead end rather quickly.