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.
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It seems like what you are hinting at is the degree to which an instruction contains the context required to understand it, answer it, and evaluate the answer. Moreover, the question hints at an objective instruction being one that is almost completely self-contained in these aspects.
In the example you gave (Capitalize all letter S characters in a sentence), the prompt contains all the information about the subject acted upon, and, presumably, the computer the program is running on has the concept of characters/letters explicitly encoded into its operating system, including the concept of capitalization.
In this sense, LLM prompts already represent a small subset of natural language instructions. If we were in the same room, and I pointed to an object and told you to hand it to me, the instruction could be considered objective if we can both see the object, but it isn’t self-contained in the way it would need to be for an LLM because of the lack of shared context (assuming the LLM can’t see).
All this to say, I think the information you are looking for may be Contextual vs. Semantic in nature.
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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