Do note that the orthogonality thesis is a hypothesis, not something we have demonstrated. Weak versions of it (e.g. it is possible to have an intelligent agent with arbitrary goals) are more likely to be true than stronger versions (e.g. intelligent agents we build will have goals uniformly selected from the space of all possible goals).
> Scholars have interpreted Cassius Dio's wording to indicate that the fire did not actually destroy the entire Library itself, but rather one or more Library warehouses near the docks.[87][81][8][89] Whatever damage Caesar's fire may have caused, evidently the Library was not completely destroyed.[87][81][8][89][3] The geographer Strabo (c. 63 BC – c. 24 AD) mentions visiting the Mouseion, the larger research institution to which the Library was attached, in around 20 BC, several decades after Caesar's fire, indicating that it either survived the fire or was rebuilt soon afterwards.[87][8] Nonetheless, Strabo's manner of talking about the Mouseion shows that it was nowhere near as prestigious as it had been a few centuries prior. It is unknown whether this was due to historical decline or catastrophic destruction.[8] Despite mentioning the Mouseion, Strabo does not mention the Library separately, perhaps indicating that it had been so drastically reduced in stature and significance that Strabo felt it did not warrant separate mention.[8] It is unclear what happened to the Mouseion after Strabo's mention of it.[60]
> Further evidence for the Library's survival after 48 BC comes from the fact that the most notable producer of composite commentaries during the late first century BC and early first century AD was a scholar who worked in Alexandria named Didymus Chalcenterus, whose epithet Χαλκέντερος (Chalkénteros) means "bronze guts".[90][87] Didymus is said to have produced somewhere between 3,500 and 4,000 books, making him the most prolific known writer in all of antiquity.[90][82] He was also given the nickname βιβλιολάθης (Biblioláthēs), meaning "book-forgetter" because it was said that even he could not remember all the books he had written.[90][91] Parts of some of Didymus' commentaries have been preserved in the forms of later extracts and these remains are modern scholars' most important sources of information about the critical works of the earlier scholars at the Library of Alexandria.[90] Lionel Casson states that Didymus' prodigious output "would have been impossible without at least a good part of the resources of the library at his disposal".[87]
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.