The Newton-Schulz iteration they use approximates setting all singular values of the matrix to 1. That computes the nearest orthogonal matrix under the Frobenius norm.
This is a decent derivation, if a little verbose, but I find myself doubting the disclaimer at the top:
> Disclaimer: no AI was used to write this. Any errors, awkward sentences, and weird tangents are 100% organic, free-range, and human-made.
If you're writing by hand and trying to avoid accusations of AI-generated content, it's really easy not to write bulleted lists where each item starts with a boldface summary like "A clean bijection in the middle." Or drive home a point with such pithy italicized mottos as "The complexity was never in the map. It was in the basis." If you didn't use AI in the writing here, you have trained yourself very well to write like an LLM.
No, this can't happen at temperature 0. The formula defining temperature-adjusted softmax isn't strictly defined at 0, but taking the limit (in the case where all logits are distinct) results in probability 1 being placed on the largest logit. Samplers will typically special case temperature 0 and pick the most likely token at each step.
A distribution with all probability mass on one outcome is deterministic, so in principle, setting temperature to 0 _should_ result in deterministic outputs. There are a few reasons it might not, but I don't think any of these apply when running a local model like the author did.
I'm not sure that analogy works: pretty much everyone agrees that there are some types of weapons civilians shouldn't be able to have, even though they might be very effective for resisting military tyranny.
Michael Spivak's Physics for Mathematicians has a lot of arguments like the one in the top answer here, answering questions about why the math of classical mechanics is the way it is.
Under the hood, yes, but Mythos had more relaxed safeguards and was/is only available to a subset of approved customers under Project Glasswing, similar to the situation with GPT-5.6 now.
I'm not sure it would be so easy to do it in a consistent, verifiable way. You can certainly prompt the LLM to work the ad into the conversation, but making sure it actually happens and is done in a way that the advertiser is going to be happy with is a lot harder.
I think what's going on with the complex logarithm is basically the same as the logarithm that outputs the set of all possible bases for a vector space. The complex logarithm produces a Z-torsor, and the basis logarithm produces a GL(V)-torsor. There's probably some way to represent a choice of branch cut as a part of the choice of the base of the complex logarithm, and similarly the choice of a specific basis as part of the choice of base of the vector space base logarithm.