Comments on What underlying principle is at play for how objective or subjective a natural language instruction is?
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What underlying principle is at play for how objective or subjective a natural language instruction is?
I am interested in exploring a series of prompts for a large language model which move from instructions which have a clear-cut "correct result", such as the instruction to capitalize every letter "S" in some sentence, to questions which may have a few acceptable results, to questions which are more open-ended and subjective.
I would like to think of some analytical framework which makes it clear exactly what is changing, presumably semantically, as we shift along that gradient. I can't see it clearly in my mind at the moment.
My guess is it could be modeled using information theory, and I can expand on how.
Post
The question alludes to at least three correlated, but quite distinct dimensions.
- Objectivity/subjectivity
- Room for model's creativity (information theoretical)
- Crispness of the boundary between "correct" and "incorrect" productions.
To define them, introduce an additional agent, perhaps a human, acting as a referee. The referee observes of the interaction between the prompt and the model's production and eventually marks the model's performance with a percentage of "correctness": 0 for an incorrect production, 100 for a correct production.
Crispness of correctness - Crisp (black-and-white) prompts will mostly solicit productions scored 0 or 100. Fuzzy (gray area) prompts will mostly solicit productions scored somewhere in between. There's no single most popular measure of fuzziness, but you could pick one from literature or invent your own.
Room for creativity - For a crisp prompt, define this as the logarithm of the number of 100% correct productions for a given prompt. For a fuzzy prompt, you might need something like weighted entropy and/or a "minimum correctness cut-off threshold".
Objectivity/subjectivity seems to relate to a population of referees. An objective prompt will solicit correlated marks from different referees, whereas for a subjective prompt, it's conceivable that different referees will prefer different productions. Ultimately, you can measure that correlation. But the concept is population-dependent.
It's not unusual to see one of those dimensions used as a proxy for another. If the competitors are people and not language models, and you need a very high degree of objectivity, it often helps if all the prompts are crisp and the room for creativity is zero - that is, if each prompt has exactly one correct production. Such limitations don't deliver any objectivity in themselves, but they make it easier to evaluate objectivity using a population of assessors.
I'm afraid that none of those three dimensions are of primarily linguistic nature, or at least I cannot quite see the connection (and a better answer might be able to point one out).
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