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In layman's terms, this seems to mean that given a certain unedited LLM output, plus complete information about the LLM, they can determine what prompt was used to create the output. Except that in practice this works almost never. Am I understanding correctly?
No, it's about the distribution being injective, not a single sampled response. So you need a lot of outputs of the same prompt, and know the LLM, and then you should in theory be able to reconstruct the original prompt.
"And hence invertible" <- does every output embedding combination have an associated input ? Are they able to construct it or is this just an existence result ?
I don't think they're claiming surjectivity here. They're just saying the mapping is injective, so for a given output there should be a unique input to construct it.
What definition of invertible doesn't include surjectivity?
"And hence invertible" <- does every output embedding combination have an associated input ? Are they able to construct it or is this just an existence result ?
I remember hearing an argument once that said LLMs must be capable of learning abstract ideas because the size of their weight model (typically GBs) is so much smaller than the size of their training data (typically TBs or PBs). So either the models are throwing away most of the training data, they are compressing the data beyond the known limits, or they are abstracting the data into more efficient forms. That's why…
Imagine that you have an a spreadsheet that dates from the beginning of the universe to its end. It contains two columns: the date, and how many days it has been since the universe was born. That's very big spreadsheet with lots of data in it. If you plot it, it creates a seemingly infinite diagonal line.
But it can be "abstracted" as Y=X. And that's what ML does.
I remember hearing an argument once that said LLMs must be capable of learning abstract ideas because the size of their weight model (typically GBs) is so much smaller than the size of their training data (typically TBs or PBs). So either the models are throwing away most of the training data, they are compressing the data beyond the known limits, or they are abstracting the data into more efficient forms. That's why…
Unfortunately, the reality is more boring. https://www.litcharts.com/lit/frankenstein/chapter-18 https://www.cliffsnotes.com/literature/frankenstein/chapter-... https://www.sparknotes.com/lit/frankenstein/sparklets/ https://www.sparknotes.com/lit/frankenstein/section9/ https://www.enotes.com/topics/frankenstein/chapter-summaries... https://www.bookey.app/freebook/frankenstein/chapter-18/summ... https://tcanotes.com/drama-frankenstein-ch-18-20-summary-ana... https://quizlet.com/content/novel-frankenstein-chapter-18 https://www.studypool.com/studyGuides/Frankenstein/Chapter_S... https://study.com/academy/lesson/frankenstein-chapter-18-sum... https://ivypanda.com/essays/frankenstein-by-mary-shelley-ana... https://www.shmoop.com/study-guides/frankenstein/chapter-18-... https://carlyisfrankenstein.weebly.com/chapters-18-19.html https://www.markedbyteachers.com/study-guides/frankenstein/c... https://www.studymode.com/essays/Frankenstein-Summary-Chapte... https://novelguide.com/frankenstein/summaries/chap17-18 https://www.ipl.org/essay/Frankenstein-Summary-Chapter-18-90...
I have not known an LLM to be able to summarise a book found in its training data, unless it had many summaries to plagiarise (in which case, actually having the book is unnecessary). I have no reason to believe the training process should result in "abstracting the data into more efficient forms". "Throwing away most of the training data" is an uncharitable interpretation (what they're doing is more sophisticated than that) but, I believe, a correct one.
I remember hearing an argument once that said LLMs must be capable of learning abstract ideas because the size of their weight model (typically GBs) is so much smaller than the size of their training data (typically TBs or PBs). So either the models are throwing away most of the training data, they are compressing the data beyond the known limits, or they are abstracting the data into more efficient forms. That's why…
Earlier quoted context omitted.
Edit: there are other clarifications, eg authors on X, so this comment is irrelevant. The birthday paradox relies on there being a small number of possible birthdays (365-366). There are not a small number of dimensions being used in the LLM. The GP argument makes sense to me.
It doesn't need a small number -- rather it relies on you being able to find a pairing amongst any of your candidates, rather than find a pairing for a specific birthday. That's the paradoxical part: the number of potential pairings for a very small number of people is much higher than one might think, and so for 365 options (in the birthday example) you can get even chances with far fewer than 365, and even far fewe…
Earlier quoted context omitted.
Edit: there are other clarifications, eg authors on X, so this comment is irrelevant. The birthday paradox relies on there being a small number of possible birthdays (365-366). There are not a small number of dimensions being used in the LLM. The GP argument makes sense to me.
It doesn't need a small number -- rather it relies on you being able to find a pairing amongst any of your candidates, rather than find a pairing for a specific birthday. That's the paradoxical part: the number of potential pairings for a very small number of people is much higher than one might think, and so for 365 options (in the birthday example) you can get even chances with far fewer than 365, and even far fewe…