The sigmoids won't save you

philipallstar

But they do explain the improvement of AI driving 2017-2021 vs 2022-2026.

nathan_compton

A lot of words to say "The initial part of a sigmoidal curve is not very informative about the parameters of the sigmoid function in question."

andai

Well, curve shape aside, the high watermark might be lower than where it tapers off. https://news.ycombinator.com/item?id=46199723

BoredPositron

If you use the log scale you'll see that the time horizon of opus 4.6 was as expected...

gm678

I don't know what the Y-axis is supposed to be on that Wharton AI capabilities graph, but I am not really convinced that Opus 4.6 has more than double the intelligence/capability/whatever of GPT 5.1 Max.

devmor

"Exponentials all tend to become sigmoids but you can't predict exactly when" is a true statement, but I'm not sure it needed an article. This doesn't say much, and the author fights their own points a couple times, suggesting that they maybe didn't think through what they wanted to write until they were in the middle of writing it and started realizing their assumptions didn't match what they expected the data to say. I really don't get the point of what I just read.

addaon

https://xkcd.com/605/

inglor_cz

Hmmm, this is quite an interesting take by Scott. Lindy's Law is not actually a law and many exact minds will be provoked by the very name; it also fails spectacularly in certain contexts (e.g. lifetime of a single organism, though not necessarily existence of entire species). But at the same time, I am willing to take its invocation in the context of AI somewhat seriously. There is an international arms race with China, which has less compute, but more engineers and scientists. This sort of intellectual arms race does not exhaust itself easily. A similar space race in the 1950s and 1960s progressed from first unmanned spaceflight to a moonwalk in mere 12 years, which is probably less than what it takes to approve a bicycle lane in Chicago now.

krupan

News flash: predicting the future is hard

kubb

If the scary AI is so inevitable, why do you feel such an overwhelming need to convince people about that? Surely you can just wait a bit, and they'll see for themselves.

LarsDu88

I think an interesting thing about recent AI developments is that its all happening right as we hit the diminishing returns side of another "exponential that's actually a sigmoid" which is Moore's law. The naive expectation is that AI will slow down b/c Moore's law is coming to an end, but if you really think about the models and how they are currently implemented in silicon, they are still inefficient as hell. At some point someone will build a tensor processing chip that replaces all the digital matmuls with analogue logamp matmuls, or some breakthrough in memristors will start breaking down the barrier between memory and compute. With the right level of research funding in hardware, the ceiling for AI can be very high.

Brendinooo

> then what is their model? My mental model has been 3D computer graphics: doubling the polygon count had huge returns early on but delivered diminishing returns over time. Ultimately, you can't make something look more realistic than real. I don't know what the future holds, but the answer to the question "can LLMs be more realistic than real" will determine much about whether or not you think the curve will level off soon.

btilly

Lindy’s Law is an absolute gem, that I'm keeping. If we don't understand the fundamental limits to any particular kind of trend, our default assumption should be that it will continue for about as long as it has gone on already. We can, in fact, easily put a confidence interval on this. With 90% odds we're not in the first 5% of the trend, or the last 5% of the trend. Therefore it will probably go on between 1/19th longer, and 19 times longer. With a median of as long as it has gone on so far. This is deeply counterintuitive. When we expect something to last a finite time, every year it goes on, brings us a year closer to when it stops. But every year that it goes on properly brings the expectation that it will go on for a year longer still. We're looking at a trend. We believe that it will be finite. Our intuition for that is that every year spent, is a year closer to the end. But our expectation becomes that every year spent, means that it will last yet another year more! How can we apply that? A simple way is stocks. How long should we expect a rapidly growing company, to continue growing rapidly?

itkovian_

The other thing people don’t understand is exponential curves are self similar. The start of an exponential looks like an exponential. People always look at and think ‘well that’s it it’s exponential now, have missed it, can’t sustain’. Nope. Good example of this is number of submissions to neurips/icml/iclr. In 2017 that curve was exponential.

zkmon

The curve is a smoothed step curve (y=1 if x>1 otherwise 0). Nature doesn't allow any change to happen instantly at any degree of rate of change. The curveis just a manifestation a change with exponential smoothening of the sharp corners. For example, When a car starts, it's speed and acceleration become more than zero. But what about rate of change in higher degrees? It suddenly doesn't change from zero acceleration to non-zero. That means the car has a non-zero derivative at all degrees. In other words, the movement is exponential. The same thing happens in reverse when the car reaches a constant speed.

patrickmay

Stein's Law: "If something cannot go on forever, it will stop."

OscarCunningham

John D Cook gives more technical details here: "Trying to fit a logistic curve" https://www.johndcook.com/blog/2025/12/20/fit-logistic-curve...

janalsncm

> What if you don’t fully understand the process? AI forecasters know some things (like how data centers work and how much it costs to build them). But they’re unsure about other things (researchers keep inventing new paradigms of data generation that get over data walls, but for how long?), and other things are entirely opaque (What is intelligence really? Why do scaling laws work? Might they just stop working at some point?) Is there anything you can do here? This is the crux of the article. To a large extent continued progress depends on a stable increase in compute, an increase in training data, and an increase in good ideas to squeeze more out of both of them. One calculation you could do is a survival function: for each of the above, how long before it is disrupted? For example, China could crack down on AI or invade Taiwan. Or data centers become politically unpopular in the US. Or, we could run out of great ideas. Very hard to predict.

dsign

We did hit the sigmoid's plateau on airplane speed, but the applications of airplane speed are still coming (how fast can a Chinese company airship the PCB you ordered three minutes ago?). I expect the the same will happen with LLMs, though I also happen to believe things are just getting started on end capabilities.