in my FLOP era

where does 10^26 come from? :: blogtober 10/1/24

To challenge myself, I'm going to write a blog post every day in October. These might not be particularly long or good, and I might queue up a few blog posts in advance. “Blogtober” has been done before, and the general premise is to blog every day in October. Sort of like NaNoWriMo, except it seems like a more useful endeavor for my purposes. Each post will take about an hour - judge accordingly.

In light of SB 1047 flopping, I want to talk about the use of FLOPs in AI policy. Specifically, 10²⁶ FLOP. Where does that number come from?

Executive order 14110 specifies that reporting applies to “any model that was trained using a quantity of computing power greater than 10²⁶ integer or floating-point operations.”¹ SB 1047 would have applied to models that trained with 10²⁶ FLOP and cost over $100,000,000. The EU AI act applies to models trained with 10²⁵ FLOP. Where are these numbers coming from?

Jack Clark did a great writeup highlighting the difference between 10²⁵ and 10²⁶ in financial terms. A 10²⁵ training run would cost ~$10.4m, a 10²⁶ run would cost ~$104m. That seems suspiciously even. Did 10²⁶ as a threshold come from someone leaning back in their office chair and just going one order of magnitude higher than the current state of the art?

My best guess as to where 10²⁶ came from: 2023’s Frontier AI Regulation paper. It seemed like 10²⁶ FLOP as a threshold for regulation started appearing in 2023, and it was a notable paper. So I did a little CTRL+f snooping to see the context in which this number first appears, and I got this:

[50] links to an Our World in Data table listing the number of petaFLOP used to train some of the most notable AI systems. According to Our World in Data, the largest training run (at the time of publication) used 2.1 x 10²⁵ FLOP. Currently, the largest is 5 x 10²⁵ FLOP.

So, yes - 10²⁶ maybe was chosen because it was a bit beyond the state of the art at the time. Whether it’s still beyond the state of the art is harder to say. But it’s interesting how a number that perhaps started as a ballpark became codified in policy.

PS: for those curious, the correct nomenclature is FLOP when referring to quantity, and FLOP/s when referring to performance. h/t Lennart Heim

1. There are exceptions - eg if using biological sequence data, reporting starts at 10²³