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Failing to Understand the Exponential, Again

julian.ac

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Re: Failing to Understand the Exponential, Again

#121

Post by LegionMammal978 »

theptip wrote: post #115
LegionMammal978 wrote: post #108

Earlier quoted context omitted.

> The point is, why predict that the growth rate is going to slow exactly now? What evidence are you going to look at? Why predict that the (absolute) growth rate is going to keep accelerating past exactly now? Exponential growth always assumes a constant relative growth rate, which works in the fiction of economics, but is otherwise far from an inevitability. People like to point to Moore's law ad nauseam, but other…

> Why predict that the (absolute) growth rate is going to keep accelerating past exactly now? By following this logic you should have predicted Moore’s law would halt every year for the last five decades. I hope you see why this is a flawed argument. You prove too much. But I will answer your “why”: plenty of exponential curves exist in reality, and empirically, they can last for a long time. This is just how technol…

> By following this logic you should have predicted Moore’s law would halt every year for the last five decades. I hope you see why this is a flawed argument. You prove too much.

I do think it's continually amazing that Moore's law has continued in some capacity for decades. But before trumpeting the age of exponential growth, I'd love to see plenty of examples that aren't named "Moore's law": as it stands, one easy hypothesis is that "ability to cram transistors into mass-produced boards" lends itself particularly well to newly-discovered strategies.

> So I wouldn’t bet on exponential growth in AI capabilities for the next 10 years, but I would consider it very foolish to use pure induction to bet on growth stopping within 1 year.

Great, we both agree that it's foolish to bet on growth stopping within 1 year. What I'm saying that "growth doesn't stop" ≠ "growth is exponential".

A theory of "inertia" could just as well support linear growth: it's only because we stare at relative growth rates that we treat exponential growth as a "constant" that will continue in the absence of explicit barriers.

Re: Failing to Understand the Exponential, Again

#122

Post by vjerancrnjak »

There’s no exponential improvement in go or chess agents, or car driving agents. Even tiny mouse racing.

If there is, it would be such nice low hanging fruit.

Maybe all of that happens all at once.

I’d just be honest and say most of it is completely fuzzy tinkering disguised as intellectual activity (yes, some of it is actual intellectual activity and yes we should continue tinkering)

There are rare individuals that spent decades building up good intuition and even that does not help much.

Re: Failing to Understand the Exponential, Again

#123

Post by theptip »

rmunn wrote: post #112
theptip wrote: post #98

Earlier quoted context omitted.

> a lot of technologies turn out to be S-shaped, not purely exponential, because there are limiting factors. Yes of course it’s not going to increase exponentially forever. The point is, why predict that the growth rate is going to slow exactly now? What evidence are you going to look at? It’s possible to make informed predictions (eg “Moore’s law can’t get you further than 1nm with silicon due to fundamental physica…

NOTE IN ADVANCE: I'm generalizing, naturally, because talking about specifics would require an essay and I'm trying to write a comment. Why predict that the growth rate is going to slow now? Simple. Because current models have already been trained on pretty much the entire meaningful part of the Internet. Where are they going to get more data? The exponential growth part of the curve was largely based on being able t…

> Where are they going to get more data?

This is a great question, but note that folks were freaking out about this a year or so ago and we seem to be doing fine.

We seem to be making progress with some combination of synthetic training datasets on coding/math tasks, textbooks authored by paid experts, and new tokens (plus preference signals) generated by users of the LLM systems.

It wouldn’t surprise me if coding/math turned out to have a dense-enough loss-landscape to produce enough synthetic data to get to AGI - though I wouldn’t bet on this as a highly likely outcome.

I have been wanting to read/do some more rigorous analysis here though.

This sort of analysis would count as the kind of rigorous prediction that I’m asking for above.

E2A: initial exploration on this: https://chatgpt.com/share/68d96124-a6f4-8006-8a87-bfa7ee4ea3...

Gives some relevant papers such as

https://arxiv.org/html/2211.04325v2#:~:text=3.1%20AI

Re: Failing to Understand the Exponential, Again

#124

Post by ottah »

rmunn wrote: post #112
theptip wrote: post #98

Earlier quoted context omitted.

> a lot of technologies turn out to be S-shaped, not purely exponential, because there are limiting factors. Yes of course it’s not going to increase exponentially forever. The point is, why predict that the growth rate is going to slow exactly now? What evidence are you going to look at? It’s possible to make informed predictions (eg “Moore’s law can’t get you further than 1nm with silicon due to fundamental physica…

NOTE IN ADVANCE: I'm generalizing, naturally, because talking about specifics would require an essay and I'm trying to write a comment. Why predict that the growth rate is going to slow now? Simple. Because current models have already been trained on pretty much the entire meaningful part of the Internet. Where are they going to get more data? The exponential growth part of the curve was largely based on being able t…

Alternative argument, there is no need for more training data, just better algorithms. Throwing more tokens at the problem doesn't solve the fact that training llms using supervised learning is a poor way to integrate knowledge. We have however seen promising results coming out of reinforcement learning and self play. Which means that anthropic and openais' bet on scale is likely a dead end, but we may yet see capability improvements coming from other labs, without the need for greater data collection.

Re: Failing to Understand the Exponential, Again

#125

Post by sdenton4 »

rmunn wrote: post #112
theptip wrote: post #98

Earlier quoted context omitted.

> a lot of technologies turn out to be S-shaped, not purely exponential, because there are limiting factors. Yes of course it’s not going to increase exponentially forever. The point is, why predict that the growth rate is going to slow exactly now? What evidence are you going to look at? It’s possible to make informed predictions (eg “Moore’s law can’t get you further than 1nm with silicon due to fundamental physica…

NOTE IN ADVANCE: I'm generalizing, naturally, because talking about specifics would require an essay and I'm trying to write a comment. Why predict that the growth rate is going to slow now? Simple. Because current models have already been trained on pretty much the entire meaningful part of the Internet. Where are they going to get more data? The exponential growth part of the curve was largely based on being able t…

Curiously, humans don't seem to require reading the entire internet in order to perform at human level on a wide variety of tasks... Nature suggests that there's a lot of headroom in algorithms for learning on existing sources. Indeed, we had models trained on the whole internet a couple years ago, now, yet model quality has continued to improve.

Meanwhile, on the hardware side, transistor counts in GPUs are in the tens of billions and still increasing steadily.

Re: Failing to Understand the Exponential, Again

#127

Post by dsr_ »

117 comments so far, and the word economics does not appear.

Any technology which produces more results for more inputs but does not get more efficient at larger scale runs into a money problem if it does not get hit by a physics problem first.

It is quite possible that we have already hit the money problem.

Re: Failing to Understand the Exponential, Again

#128

Post by theptip »

LegionMammal978 wrote: post #121
theptip wrote: post #115

Earlier quoted context omitted.

> Why predict that the (absolute) growth rate is going to keep accelerating past exactly now? By following this logic you should have predicted Moore’s law would halt every year for the last five decades. I hope you see why this is a flawed argument. You prove too much. But I will answer your “why”: plenty of exponential curves exist in reality, and empirically, they can last for a long time. This is just how technol…

> By following this logic you should have predicted Moore’s law would halt every year for the last five decades. I hope you see why this is a flawed argument. You prove too much. I do think it's continually amazing that Moore's law has continued in some capacity for decades. But before trumpeting the age of exponential growth, I'd love to see plenty of examples that aren't named "Moore's law": as it stands, one easy…

Sorry, to be clear I was making the stronger claim:

I would consider it very foolish to use pure induction to bet on _exponential_ growth stopping within 1 year.

I think you can easily find plenty of other long-lasting exponential curves. A good starting point would be:

https://en.m.wikipedia.org/wiki/Progress_studies

With perhaps the optimistic case as

https://en.m.wikipedia.org/wiki/Accelerating_change

This is where I’d really like to be able to point to our respective Manifold predictions on the subject; we could circle back in a year’s time and review who was in fact correct. I wager internet points it will be me :)

Concretely, https://manifold.markets/JoshYou/best-ai-time-horizon-by-aug...

Re: Failing to Understand the Exponential, Again

#129

Post by rmunn »

ottah wrote: post #124
rmunn wrote: post #112

Earlier quoted context omitted.

NOTE IN ADVANCE: I'm generalizing, naturally, because talking about specifics would require an essay and I'm trying to write a comment. Why predict that the growth rate is going to slow now? Simple. Because current models have already been trained on pretty much the entire meaningful part of the Internet. Where are they going to get more data? The exponential growth part of the curve was largely based on being able t…

Alternative argument, there is no need for more training data, just better algorithms. Throwing more tokens at the problem doesn't solve the fact that training llms using supervised learning is a poor way to integrate knowledge. We have however seen promising results coming out of reinforcement learning and self play. Which means that anthropic and openais' bet on scale is likely a dead end, but we may yet see capabi…

Better algorithms is one of the things I meant by "better ways to tweak the models to make better use of the available training data". But that produces slower growth than the jaw-droppingly rapid growth you can get by slurping pretty much the whole Internet. That produced the sharp part of the S curve, but that part is behind us now, which is why I assert we're approaching the slower-growth part at the top of the curve.

Re: Failing to Understand the Exponential, Again

#130

Post by rmunn »

theptip wrote: post #123
rmunn wrote: post #112

Earlier quoted context omitted.

NOTE IN ADVANCE: I'm generalizing, naturally, because talking about specifics would require an essay and I'm trying to write a comment. Why predict that the growth rate is going to slow now? Simple. Because current models have already been trained on pretty much the entire meaningful part of the Internet. Where are they going to get more data? The exponential growth part of the curve was largely based on being able t…

> Where are they going to get more data? This is a great question, but note that folks were freaking out about this a year or so ago and we seem to be doing fine. We seem to be making progress with some combination of synthetic training datasets on coding/math tasks, textbooks authored by paid experts, and new tokens (plus preference signals) generated by users of the LLM systems. It wouldn’t surprise me if coding/ma…

I am extremely confident that AGI, if it is achievable at all (which is a different argument and one I'm not getting into right now), requires a world model / fact model / whatever terminology you prefer, and is therefore not achievable by models that simply chain words together without having any kind of understanding baked into the model. In other words, LLMs cannot lead to AGI.
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