What are you talking about it asymptoped at 5 units. It cant be described as exponential until it is exponential otherwise its better described as linear or polynomial if you must.
Exponential growth is always exponential, not just if it suddenly starts to drastically increase in the arbitrarily choosen view scale.
A simple way, to check wether data is exponential, is to visualize it in loc-scale, and if it shows there a linear behavior, it has a exponential relation.
Exponential growth means, that the values change by a constant ratio, contrary to linear growth where the data changes by a constant rate.
I have at this point absolutely no idea anymore, what you want to tell me.
Would you care to rephrase your statement, on which we are disagreeing, so we can back on track and have a constructive discussion.
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.
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.
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.
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.
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.
This is precisely a property of exponential growth, that it can take (seemingly) very long until it starts exploding.
What are you talking about it asymptoped at 5 units. It cant be described as exponential until it is exponential otherwise its better described as linear or polynomial if you must.
Exponential growth is always exponential, not just if it suddenly starts to drastically increase in the arbitrarily choosen view scale.
A simple way, to check wether data is exponential, is to visualize it in loc-scale, and if it shows there a linear behavior, it has a exponential relation.
Exponential growth means, that the values change by a constant ratio, contrary to linear growth where the data changes by a constant rate.
There’s no point in arguing with OP, he’s doubling down at an exponential rate (or was it linear).
That’s what I said. Exponential growth is always exponential.
Iykyk
Close enough chat gpt
I have at this point absolutely no idea anymore, what you want to tell me. Would you care to rephrase your statement, on which we are disagreeing, so we can back on track and have a constructive discussion.
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.
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.
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.
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.
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.