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Failing to Understand the Exponential, Again

julian.ac

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Re: Failing to Understand the Exponential, Again

#111

Post by Inufu »

hnlmorg wrote: post #30

Just because something exhibits an exponential growth at one point in time, that doesn’t mean that a particular subject is capable of sustaining exponential growth. Their Covid example is a great counter argument to their point in that covid isn’t still growing exponentially. Where the AI skeptics (or even just pragmatists, like myself) chime in is saying “yeah AI will improve. But LLMs are a limited technology that…

Author here.

The argument is not that it will keep growing exponentially forever (obviously that is physically impossible), rather that:

- given a sustained history of growth along a very predictable trajectory, the highest likelihood short term scenario is continued growth along the same trajectory. Sample a random point on an s-curve and look slightly to the right, what’s the most common direction the curve continues?

- exponential progress is very hard to visualize and see, it may appear to hardly make any progress while far away from human capabilities, then move from just below to far above human very quickly

Re: Failing to Understand the Exponential, Again

#112

Post by rmunn »

theptip wrote: post #98
crazygringo wrote: post #7

> Given consistent trends of exponential performance improvements over many years and across many industries, it would be extremely surprising if these improvements suddenly stopped. I'm sure people were saying that about commercial airline speeds in the 1970's too. But a lot of technologies turn out to be S-shaped, not purely exponential, because there are limiting factors. With LLM's at the moment, the limiting fac…

> 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 to fit more and more training data into the models. Now that all the meaningful training data has been fed in, further growth will come from one of two things: generating training data from one LLM to feed into another one (dangerous, highly likely to lead to "down the rabbit hole forever" hallucinations, and weeding those out is a LOT of work and will therefore contribute to slower growth), or else finding better ways to tweak the models to make better use of the available training data (which will produce growth, but much slower than what "Hey, we can slurp up the entire Internet now!" was producing in terms of rate of growth).

And yes, there is more training data available because the Internet is not static: the Internet of 2025 has more meaningful, human-generated content than the Internet of 2024. But it also has a lot more AI-generated content, which will lead into the rabbit-hole problem where one AI's hallucinations get baked into the next one's training, so the extra data that can be harvested from the 2025 Internet is almost certainly going to produce slower growth in meaningful results (as opposed to hallucinated results).

Re: Failing to Understand the Exponential, Again

#113

Post by breuleux »

Nevermark wrote: post #58
crazygringo wrote: post #7

> Given consistent trends of exponential performance improvements over many years and across many industries, it would be extremely surprising if these improvements suddenly stopped. I'm sure people were saying that about commercial airline speeds in the 1970's too. But a lot of technologies turn out to be S-shaped, not purely exponential, because there are limiting factors. With LLM's at the moment, the limiting fac…

Progress in information systems cannot be compared to progress in physical systems. For starters, physical systems compete for limited resources and labor. For another, progress in software vastly reduces the cost of improved designs. Whereas progress in physical systems can enable but still increase the cost of improved designs. Finally, the underlying substrate of software is digital hardware, which has been improv…

> Looking at information systems as far back as the first coordination of differentiating cells to human civilization is one of exponential improvement.

Under what metric? Most of the things you mention don't have numerical values to plot on a curve. It's a vibe exponential, at best.

Life and humans have become better and better at extracting available resources and energy, but there's a clear limit to that (100%) and the distribution of these things in the universe is a given, not something we control. You don't run information systems off empty space.

Re: Failing to Understand the Exponential, Again

#114

Post by TeMPOraL »

oofbey wrote: post #94
crazygringo wrote: post #7

> Given consistent trends of exponential performance improvements over many years and across many industries, it would be extremely surprising if these improvements suddenly stopped. I'm sure people were saying that about commercial airline speeds in the 1970's too. But a lot of technologies turn out to be S-shaped, not purely exponential, because there are limiting factors. With LLM's at the moment, the limiting fac…

There’s a key way to think about a process that looks exponential and might or might not flatten out into an S curve: reasoning about fundamental limits. For COVID it would obviously flatten out because there are finite humans, and it did when the disease had in fact infected most humans on the planet. For commercial airlines you could reason about the speed of sound or escape velocity and see there is again a natura…

> For computational intelligence, we have one clear example of an upper limit in a biological human brain. It only consumes about 25W and has much more intelligence than today’s LLMs in important ways. Maybe that’s the wrong limit?

It's a good reference point, but I see no reason for it to be an upper limit - by the very nature of how biological evolution works, human brains are close to the worst possible brains advanced enough to start a technological revolution. We're the first brain on Earth that crossed that threshold, and in evolutionary timescales, all that followed - all human history - happened in an instant. Evolution didn't have time yet to iterate on our brain design.

Re: Failing to Understand the Exponential, Again

#115

Post by theptip »

LegionMammal978 wrote: post #108
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…

> 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 technology works; some exponential process kicks off, then eventually is rate-limited, then if we are lucky another S-curve stacks on top of it, and the process repeats for a while.

Reality has inertia. My hunch is you should apply some heuristic like “the longer a curve has existed, the longer you should bet it will persist”. 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.

And to be clear, I think these heuristics are weak and should be trumped by actual physical models of rate-limiters where available.

Re: Failing to Understand the Exponential, Again

#116

Post by emporas »

Nevermark wrote: post #58
crazygringo wrote: post #7

> Given consistent trends of exponential performance improvements over many years and across many industries, it would be extremely surprising if these improvements suddenly stopped. I'm sure people were saying that about commercial airline speeds in the 1970's too. But a lot of technologies turn out to be S-shaped, not purely exponential, because there are limiting factors. With LLM's at the moment, the limiting fac…

Progress in information systems cannot be compared to progress in physical systems. For starters, physical systems compete for limited resources and labor. For another, progress in software vastly reduces the cost of improved designs. Whereas progress in physical systems can enable but still increase the cost of improved designs. Finally, the underlying substrate of software is digital hardware, which has been improv…

>[..] to first metabolic cycles, cells, multi-purpose genes, modular development genes, etc.

One example is when cells discovered energy production using mitochondria. Mitochondria add new capabilities to the cell, with (almost) no downside like: weight, temperature-sensitivity, pressure-sensitivity. It's almost 100% upside.

If someone tried to predict the future number of mitochondria-enabled cells from the first one, he could be off by 10^20 less cells.

I am writing a story the last 20 days, with that exact story plot, have to get my stuff together and finish it.

Re: Failing to Understand the Exponential, Again

#117

Post by senordevnyc »

coldtea wrote: post #39

> People notice that while AI can now write programs, design websites, etc, it still often makes mistakes or goes in a wrong direction, and then they somehow jump to the conclusion that AI will never be able to do these tasks at human levels, or will only have a minor impact. When just a few years ago, having AI do these things was complete science fiction! Both things can be true, since they're orthogonal. Having AI…

Except it’s not been five years, it’s been at most three, since approximately no one was using LLMs prior to ChatGPT’s release, which was just under three years ago. We did have Copilot a year before that, but it was quite rudimentary.

And really, we’ve had even less than that. The first large scale reasoning model was o1, which was released 12 months ago. More useful coding agents are even newer than that. This narrative that we’ve been using these tools for many years and are now hitting a wall doesn’t match my experience at all. AI-assisted coding is way better than it was a year ago, let alone five.

Re: Failing to Understand the Exponential, Again

#118

Post by mrshu »

credit_guy wrote: post #62

I think the author of this blog is not a heavy user of AI in real life. If you are, you know there things AI is very good at, and thing AI is bad at. AI may see exponential improvements in some aspects, but not in other aspects. In the end, those "laggard" aspects of AI will put a ceiling on its real-world performance. I use AI in my coding for many hours each day. AI is great. But AI will not replace me in 2026 or i…

The author is an AI researcher at Anthropic: https://www.julian.ac/about/

He likely has his substantial experience using AI in real life (particularly when it comes to coding).

Re: Failing to Understand the Exponential, Again

#119

Post by senordevnyc »

credit_guy wrote: post #62

I think the author of this blog is not a heavy user of AI in real life. If you are, you know there things AI is very good at, and thing AI is bad at. AI may see exponential improvements in some aspects, but not in other aspects. In the end, those "laggard" aspects of AI will put a ceiling on its real-world performance. I use AI in my coding for many hours each day. AI is great. But AI will not replace me in 2026 or i…

How much better is AI-assisted coding than it was in September 2023?

Re: Failing to Understand the Exponential, Again

#120

Post by ttoinou »

marginalia_nu wrote: post #50
_fizz_buzz_ wrote: post #21

Earlier quoted context omitted.

That is even true for covid for obvious reasons, because Covid runs out of people it can infect at some point.

Infectious diseases rarely see actual exponential growth for logistical reasons. It's a pretty unrealistic model that ignores that the disease actually needs to find additional hosts to spread, the local availability of which starts to go down from the first victim.

Yes the model where the S curves comes out is extremely simplified. Looking at covid curves we could have well said it was parabolic, but that’s much less worrisome
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