For Monte Carlo Tree Search, I think this could be useful for estimating how deeply to search a position. Higher meta-uncertainty -> more search.

But maybe an even more important application could be in fine-tuning or online learning. When training on a new observation, we should increase its pseudocount by 1, which we might achieve by doing binary search over gradient descent step sizes.

It looks like there was an issue with the formatting. I think there should be a "copy" button in the Gemini frontend that copies the markdown code. That should work better than "select all." You can still edit your article after posting to fix it.

I decided to go with KaTrain for now. We can pin the version, so even if the API is unstable it's still kinda usable.

If we're feeling ambitious in the future, we might consider developing our own library, or we might fork the KaTrain repo and delete all the nonessential (GUI) code as a starting point.

In regular perturbation theory, we assume the solution can be expressed as a regular power series in the small parameter ε for ε sufficiently small.

This statement confused me a bit, and I wonder if it's a mistake. I think it should just say "...expressed as a power series..." rather than as a "regular" power series.