Failing to Understand the Exponential, Again

So the author is in a clear conflict of interest with the contents of the blog because he's an employee of Anthropic. But regarding this "blog", showing the graph where OpenAI compares "frontier" models and shows gpt-4o vs o3-high is just disingenuous, o1 vs o3 would have been a closer fight between "frontier" models. Also today I learned that there are people paid to benchmark AI models in terms of how close they are to "human" level, apparently even "expert" level whatever that means. I'm not a LLM hater by any means, but I can confidently say that they aren't experts in any fields.

Maybe when we get updating models. Right now, they are trained, and released, and we are using that static model with a context window. At some point when we have enough processing to have models that are always updating, then that would be plastic. I'm supposing.

> When just a few years ago, having AI do these things was complete science fiction!

This is only because these projects only became consumer facing fairly recently. There was a lot of incremental progress in the academic language model space leading up to this. It wasn't as sudden as this makes it sound.

The deeper issue is that this future-looking analysis goes no deeper than drawing a line connecting a few points. COVID is a really interesting comparison, because in epidemiology the exponential model comes from us understanding disease transmission. It is also not actually exponential, as the population becomes saturated the transmission rate slows (it is worth noting that unbounded exponential growth doesn't really seem to exist in nature). Drawing an exponential line like this doesn't really add anything interesting. When you do a regression you need to pick the model that best represents your system.

This is made even worse because this uses benchmarks and coming up with good benchmarks is actually an important part of the AI problem. AI is really good at improving things we can measure so it makes total sense that it will crush any benchmark we throw at it eventually, but there will always be some difference between benchmarks and reality. I would argue that as you are trying to benchmark more subtle things it becomes much harder to make a benchmark. This is just a conjecture on my end but if something like this is possible it means you need to rule it out when modeling AI progress.

There are also economic incentives to always declare percent increases in progress at a regular schedule.

Will AI ever get this advanced? Maybe, maybe even as fast as the author says, but this just isn't a compelling case for it.

> I'm sure people were saying that about commercial airline speeds in the 1970's too.

They'd be wrong, of course - for not realizing demand is a limiting factor here. Airline speeds plateaued not because we couldn't make planes go faster anymore, but because no one wanted them to go faster.

This is partially economical and partially social factor - transit times are bucketed by what they enable people to do. It makes little difference if going from London to New York takes 8 hours instead of 12 - it's still in the "multi-day business trip" bucket (even 6 hours goes into that bucket, once you add airport overhead). Now, if you could drop that to 3 hours, like Concorde did[0], that finally moves it into "hop over for a meet, fly back the same day" bucket, and then business customers start paying attention[1].

For various technical, legal and social reasons, we didn't manage to cross that chasm before money for R&D dried out. Still, the trend continued anyway - in military aviation and, later, in supersonic missiles.

With AI, the demand is extreme and only growing, and it shows no sign of being structured into classes with large thresholds between them - in fact, models are improving faster than we're able to put them to any use; even if we suddenly hit a limit now and couldn't train even better models anymore, we have decades of improvements to extract just from learning how to properly apply the models we have. But there's no sign we're about to hit a wall with training any time soon.

Airline speeds are inherently a bad example for the argument you're making, but in general, I don't think pointing out S-curves is all that useful. As you correctly observe:

> But a lot of technologies turn out to be S-shaped, not purely exponential, because there are limiting factors.

But, what happens when one technology - or rather, one metric of that technology - stops improving? Something else starts - another metric of that technology, or something built on top of it, or something that was enabled by it. The exponent is S-curves on top of S-curves, all the way down, but how long that exponent is depends on what you consider in scope. So, a matter of accounting. So yeah, AI progress can flatten tomorrow or continue exponentially for the next couple years - depending on how narrowly you define "AI progress".

Ergo, not all that useful.

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[0] - https://simpleflying.com/concorde-fastest-transatlantic-cros...

[1] - This is why Elon Musk wasn't immediately laughed out of the room after proposing using Starship for moving people and cargo across the Earth, back in 2017. Hopping between cities on an ICBM sounds borderline absurd for many reasons, but it also promised cutting flight time to less than one hour between any two points on Earth, which put it a completely new bucket, even more interesting for businesses.

Somewhat missed by many comments proclaiming that it’s sigmoidal is that sigmoid curves exhibit significant growth after it stops looking exponential. Unless you think things have already hit a dramatic wall you should probably assume further growth.

We should probably expect compute to get cheaper at the same time, so that’s performance increases with lowering costs. Even after things flatline for performance you would expect lowering costs of inference.

Without specific evidence it’s also unlikely you randomly pick the point on a sigmoid where things change.