cayley

That completes your Cayley table and you can collect your paycheck and go home to wife and kids, because with 3 elements your Cayley has 9 slots.

But when you have 10,001 employees, your Cayley will have 100 million slots.

Even Arthur Cayley might have smirked at that one.

Could Cayley use Orly for a storage engine?

George Cayley figured out how to build an airplane in 1799, but it wasn't for another century until materials science and high power-to-weight ratio engines made the Wright Flyer possible.

Some of the things I like about cayley 1.

(I was into them before they were cool, of course.) I've only just started looking at Cayley but it looks like there are some significant differences between the projects.

The algorithm in the parent comment is not actually matrix exponentiation but the "fast doubling algorithm" in Minase's terminology, where you exponentiate the matrix algebraically using the Cayley-Hamilton theorem rather than using matrix multiplication.

"Adding employees" is simply a rule to fill the Cayley.

My "intuitive understanding" of this comes via an intuitive understanding of a paradoxical decomposition of the free group and its Cayley graph, which is flashed briefly in the video here[0] but sadly not discussed at length.

Unless you have a rule to fill those slots, you won't be able to fill the Cayley.

Wrote Halmos about his proof of the Hamelton-Cayley theorem and got back a nice answwer!

So it may turn out that LLMs have some place on the evolutionary path to AGI, or it could turn out they're a dead end like Cayley's ornithopters.