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The LLM approach is not dependent on system configurationsHow is it not dependent? Like, help me out here: I'm writing something up in vim on my FreeBSD system using the built-in dictionary capability, maybe I've got grammar too with LanguageTool via the ALE plugin. I've added various words to my good words list over time. I save it to a network drive and want to keep working on it and do some graphical formatting as well for output to a different audience with a different tool on an iPad for a flight. How does "the LLM approach" uniquely slot into vim and the iPad app. "Uniquely" as-in a way that you couldn't slot in a shared sync'd dictionary file or whatever else. What if one of the developers doesn't want to and I don't have time or (if it's closed source) can't? How does it help all the other different software I use that are still using their own thing?
If by "LLM approach" you specifically mean "I copy/paste into this whole other software, and that software is what I use from different platforms" well, that's nice but it's not an "LLM approach" it's a "copy/paste into different software" approach which again could be done with whatever.
I explicitly noted that non-determinism doesn't need to be flawless, only better than the deterministic solution on average.
But how do you know what the "average" is? You can't get that from a single shot. And what's the upside vs downside of false positives or false negatives or meaning changes/hallucinations? That's also a point of contention, particularly when it comes to any problem space (coding of course, but also law, medicine etc) where precision in language is important even 1% of the time. And you clearly have an intense personal issue here around grammar/spelling that is not universally shared. Which is fine, but the tradeoffs you're willing to make are also going to be personal. It's also going to vary, just as with using LLMs for coding, based on the user. Some people are sufficiently capable with language to realistically be able to expect to double check an LLM and mostly do fine. It's a lot riskier though for someone with a weak grasp to depend on.