No, exponential functions are that way. A feature of exponential functions is that it increases very slowly until the slope hits 1. We’re still on the slow part, we didn’t really have any way of knowing exactly the extreme increase will be.
Do you think that our current iteration of A.I. can have these kinds if gains? Like, what if the extreme increase happens beyond our lifetimes? or beyond the lifetime of our planet?
I think we can’t know, but LLMs definitely feel like a notable acceleration. Exponential functions are also, well, exponential. As X grows, X × X grows faster. The exponential part is gonna come from meta-models, coordinating multiple specialized models to complete complex tasks. Once we get a powerful meta-model, we’re off to the races. AI models developing AI models.
It could take 50 years, it could take 5, it could happen this Wednesday. We won’t know which development is going to be the one to tip us over the edge until it happens, and even then only in retrospect. But it could very well be soon.
An exponential function is a precise mathematical concept, like a circle or an even number. I’m not sure what you mean by “asymptote” here - an exponential function of the form y = k^x asymptotically approaches zero as x goes to negative infinity, but that doesn’t sound like what you’re referring to.
People often have bad intuition about how exponential functions behave. They look like they grow slowly at first but that doesn’t mean that they’re not growing exponentially. Consider the story about the grains of rice on a chessboard.
How about this, this is a real easy one.
What type of function is this:
There is a theorem that “all smooth functions are locally linear”. In other words, most “normal” functions are indistinguishable from a straight line on the graph if you zoom in far enough.
So that’s not just not an easy one, it is an impossible one.
They’re not saying that slow growth is definitely evidence it’s exponential. They’re saying that slow growth doesn’t prove that it isn’t exponential, which seemed to be what you were saying.
It’s always hard to identify exponential growth in its early stages.
Or you can just admit you dont have any data to quantify your assertion that AI advancement is exponential growth.
Ah, that’s a fair argument. LLMs growing exponentially is just an assertion being made and we’re supposed to believe that then the steep growth must be just around the corner.
But all over this post you’ve got heavily downvoted comments that sound like you are misunderstanding exponential functions rather than doubting that they’re the right model for this.
We might be on the steep part of an S function right now.
The exponential function has a single horizontal asymptote at y=0. Asymptotes at x=1 and x=-4 would be vertical. Exponential functions have no vertical asymptotes.
It’s exponential along its entire range, even all the way back to negative infinity.
Sure. Everything is exponential if you model it that way asymptote.
No, exponential functions are that way. A feature of exponential functions is that it increases very slowly until the slope hits 1. We’re still on the slow part, we didn’t really have any way of knowing exactly the extreme increase will be.
Do you think that our current iteration of A.I. can have these kinds if gains? Like, what if the extreme increase happens beyond our lifetimes? or beyond the lifetime of our planet?
I think we can’t know, but LLMs definitely feel like a notable acceleration. Exponential functions are also, well, exponential. As X grows, X × X grows faster. The exponential part is gonna come from meta-models, coordinating multiple specialized models to complete complex tasks. Once we get a powerful meta-model, we’re off to the races. AI models developing AI models.
It could take 50 years, it could take 5, it could happen this Wednesday. We won’t know which development is going to be the one to tip us over the edge until it happens, and even then only in retrospect. But it could very well be soon.
An exponential function is a precise mathematical concept, like a circle or an even number. I’m not sure what you mean by “asymptote” here - an exponential function of the form
y = k^xasymptotically approaches zero asxgoes to negative infinity, but that doesn’t sound like what you’re referring to.People often have bad intuition about how exponential functions behave. They look like they grow slowly at first but that doesn’t mean that they’re not growing exponentially. Consider the story about the grains of rice on a chessboard.
Its a horizontal asymtote. From x=1, as demonstrated in the graph, to around x=-4, where the asymtote is easily estimated by Y, it is 5 units.
Man just say you don’t understand functions and that’s it, you don’t have to push it
Tell me how im wrong. Or why did you even bother?
Or you can just admit you dont have any data to quantify your assertion that AI advancement is exponential growth. So youre just going off vibes.
Would you even admit that linear growth can grow faster than exponential growth?
Edit:
How about this, this is a real easy one.
What type of function is this:
There is a theorem that “all smooth functions are locally linear”. In other words, most “normal” functions are indistinguishable from a straight line on the graph if you zoom in far enough.
So that’s not just not an easy one, it is an impossible one.
And yet you want me to believe that because “exponential functions can have a slow build up” it is definitely exponental.
They’re not saying that slow growth is definitely evidence it’s exponential. They’re saying that slow growth doesn’t prove that it isn’t exponential, which seemed to be what you were saying.
It’s always hard to identify exponential growth in its early stages.
I do not.
See my other response to your pre-edit comment.
Ah, that’s a fair argument. LLMs growing exponentially is just an assertion being made and we’re supposed to believe that then the steep growth must be just around the corner.
But all over this post you’ve got heavily downvoted comments that sound like you are misunderstanding exponential functions rather than doubting that they’re the right model for this.
We might be on the steep part of an S function right now.
You can read. Read my comments.
The exponential function has a single horizontal asymptote at y=0. Asymptotes at x=1 and x=-4 would be vertical. Exponential functions have no vertical asymptotes.
I didnt say there are asymtotes at 1 and -4. I said at x=-4, the asymtote can be estimated by Y.