Comment by adam_arthur

2 days ago

Information density of the prompt is the most important factor in my experience.

And interestingly, LLMs seem particularly bad at writing prompts for other LLMs for this reason (you can guide them to be more dense, just speaking by default).

Conciseness is usually a byproduct of information density though.

Lexical-priming->semantic-space-constraint;specialized-lexis+=sharp distributional-signature;∴ tight concept-cluster; generic-lexis->diffuse-activation, broad candidate-set;Attention-heads key/query-match domain-tokens;"Hamiltonian"->{operator,eigenstate,quantum,energy}->register+domain locked;Net:constrained-decoding,vocab=soft-prior over output-distribution; register-matching;#taskdef=decompress->continue

  • Information density of the interpretability of the intent from the perspective of a human (or human-like).

    If the intent is not easy to understand, it's information sparse. Because it takes a lot of CPU (or brainpower) to interpret.

    You can run gzip on an English sentence to make it more textually dense, but clearly it is not more information dense in this context.

    • I’d buy a ticket to ride the philosophical “human-like” comment with you, but I think you might have made an incorrect assumption. The model did not take longer to “decompress” the prompt than it would take for any other prompt of equal token length. If you run it with thinking enabled you might be mistaking that output as some kind of necessary gunzip step, but it’s not. Disable thinking and try again.

      The prompt was also “easier to understand”, purely in the sense that the response is more or less guarantee to be what I wanted it to say, which was the point behind the demonstration. I went into more detail on it in another comment around here.

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  • Chatbot expanded this into something that made sense, but I've no idea if it's what you meant. There's an irony there somewhere.

    • It’s what I meant, which is what I meant. Hah. The prompt and the explanation were both to illustrate the importance of domain specific lexical complexity, which is not quite the same as “information density” or necessarily “conciseness” as the OP was attributing their prompting success. It’s not that they’re wrong though. Information density requires some level of jargon and removal of unnecessary filler or scaffolding words, so my example prompt was both information dense and concise as they might say, but that’s the result, not the target. That’s confusing, but it breaks into two clearer pieces:

      1. Information density is subjective, lexical complexity is how you measure it. The OP is talking “weight”, I’m talking “mass and gravity.” One of them will get you the other in most situations, so for the causal physicist it doesn’t matter, but if you’re getting into tweaking the universe then your mental model and approach matters significantly. My comment right now could be seen by some as being information dense, since I’m staying roughly on topic and tossing many concepts out, but “lexical complexity” might be the most lexical complexity in the whole thing and taken word-for-word I’m sure less than 1% of it is domain specific. “The program must use parallel processing on the CPU.” That seems decently information dense, but “the” is found in nearly every block of text ever written, “program” - are we talking television? Theater?, “must” is no better than “the”, and so on. Compare it to “#include <immintrin.h>“

      2. Most people don’t realize how far that goes with LLMs. The vocabulary it has is dictated by the words in the conversation. If I ask you “what time is it?” you don’t respond “shoelace” because you’d sound crazy, although you could say it if you wanted, but the model absolutely won’t say it because that word literally does not exist yet. The end result feels the same, but the difference matters and it’s why it’s suggested not to use negating instructions. For example: “Do not mention elephants.” Well that mathematically wasn’t possible until you said it. Not having the word in the list of possibilities is a lot better than hoping it adheres to the “do not mention” part. My example prompt took that same idea from the opposite direction. The model must respond, it will be grammatically complete and coherent, and as much as possible the only words it has are the ones tightly associated with making my point for me. It didn’t ramble about baking a chocolate cake because it can’t, and making that the case is the goal with prompting, not specifically density. Word density > language density; feels similar, very different.

      Perhaps this comment itself is the irony you were seeking. I spent several meandering paragraphs and included analogies to drive home the point that you should focus on the words that matter most.

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> LLMs seem particularly bad at writing prompts for other LLMs for this reason

Claude is terrible at this! Probably for the same reason that its writing style in prose is so annoying and full of claudisms.