First of all, let me explain what "hapax legomena" is: it refers to words (and, by extension, concepts) that occurred just once throughout an entire corpus of text. An example is the word "hebenon", occurring just once within Shakespeare's Hamlet. Therefore, "hebenon" is a hapax legomenon. The "hapax legomenon" concept itself is a kind of hapax legomenon, IMO.
According to Wikipedia, hapax legomena are generally discarded from NLP as they hold "little value for computational techniques". By extension, the same applies to LLMs, I guess.
While "hapax legomena" originally refers to words/tokens, I'm extending it to entire concepts, described by these extremely unknown words.
I am a curious mind, actively seeking knowledge, and I'm constantly trying to learn a myriad of "random" topics across the many fields of human knowledge, especially rare/unknown concepts (that's how I learnt about "hapax legomena", for example). I use three LLMs on a daily basis (GPT-3, LLama and Gemini), expecting to get to know about words, historical/mythological figures and concepts unknown to me, lost in the vastness of human knowledge, but I now know, according to Wikipedia, that general LLMs won't point me anything "obscure" enough.
This leads me to wonder: are there LLMs and/or NLP models/datasets that do not discard hapax? Are there LLMs that favor less frequent data over more frequent data?
Is going trough text really that compuationally expensive? I guess the english language only uses a few thousand words frequently, plus some names and rare words. I'd imagine you can comfortably keep them in RAM next to a counter variable for each bucket. That should allow going through practically any book on earth on a regular computer, if I'm not mistaken. I'm not sure if that's I/O bound or CPU bound, but it shouldn't be that hard. It's something that gets taught in the first 3 semesters of computer science at university.
Regarding the hallucinations: There are two use-cases: If you want some creative output that doesn't need to be correct, you're fine. You'll be doing art like the people who manipulate electronic child toys and music instruments to coerce some strange sounds out of them. I think that's calles "circuit bending". You could also de-tune the parameters of an LLM, tinker around a bit and mess with the settings. Feed it random garbage prompts and see what it'll do. I guess that's an interesting arts project.
But if you want something that has to do with factuality or needs to be correct, the hallucinations will get in your way. A "hapax legomena" or unique word is a well-defined (objective) thing. It doesn't really help if the LLM returns some pretend answer. It might look interesting at first, but it won't be a unique word by real-world definition. And that's why I don't think an LLM can help in this case.
I've tried asking it the title and author of some children's story which I heard at a first communion ceremony at church. I tried googling that but all the church pages attribute the story to some random authors. So I tried asking Llama and ChatGPT but they wholehartedly make something up. I've tried like 20 times but all they return is made up and false. So it doesn't help. And I guess those more contemporary religous books just aren't in any dataset. And the LLM will just do something random in this case. As it'll do with everything that's rare or missing in the dataset (and it can't infer it).
Another thing I did (concerning language) is ask AI about idioms and figures of speech. Initially I did this because I'm not a native english speaker and figures of speech are very nice concepts. They can make your text more flowery or funny, and they always come with some interesting story of origin. But you have to learn and memorize them for later use, because they vary widely from country to country. And LLMs are really good at translating. And they indeed do well with that. And occasionally they'll hallucinate some idiom. Which can be hilarious. It won't be something that fits the definition of the term. But it definitely sparks my creativity at times. At least it makes me laugh.
And writing prose and longer stories with AI also shows their preference for likely things. They always try to push my stories towards some lame and common story arcs. Do super obvious plot twists. And lots of models (not all of them) always push towards resolving story arcs and an happy end. And it's difficult to impossible to overcome. It tends to get better with their size and "intelligence", but I don't think any of the current LLMs is close to being useful with that.
So summed up: You said in another comment, computer linguistics discards unique words because they have little value and additionally they get in the way. There is probably some reason to that, computer scientists generally aren't stupid and I suppose they tried, and put some thought into it. An LLM just can't make sense of the concept. It needs more training data to learn something. A unique word will just mess with the weights and shift them into some random direction. Likely degrading the LLM in some miniscule way. That's why they discard them. And even if they didn't do it, the LLM couldn't memorize a word if it's only there once. And if you put it into the dataset multiple times, an LLM could learn it... But it won't be unique anymore. So I don't see how it'd work. And also my experience tells me they generally don't do well with rare things.