Definition
Plain language
A small, central piece of code that does one critical job — on a graphics chip it's a fast math routine, and in a proof checker it's the trusted core that verifies every step.
As stated in the literature
On a GPU, a compute routine implementing a primitive operation (e.g., a CUDA kernel); writing fast custom kernels is a frequent optimization target for self-improving agents and is benchmarked by KernelBench. In a proof assistant like Lean, the kernel is instead the small, heavily-scrutinized trusted core that mechanically checks each proof step. Distinct from an OS kernel.
Also called: kernels, CUDA kernel, GPU kernel
Why it matters: Faster kernels can dramatically speed up training and inference, making them a prime target for agents that optimize their own performance.
For example, a custom kernel might multiply two matrices on a GPU far faster than the default code by squeezing the most out of the chip.
Heard on the show
“There's a language called Lean 4 where you write math as code, and a small, paranoid core program — the kernel — checks every logical step against a fixed set of rules.”Episode 188 — A Coding Agent Found a Hole in a Peer-Reviewed STOC Proof for Five Dollars