[docjay]

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

[adam_arthur]

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.

[docjay]

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.

[adam_arthur]

I say "human-like" in the sense that LLMs are fed in text data largely in the exact form (mapped to tokens) that humans read them.

Thus from first principles it's most likely that content which is more understandable to humans is also likely to be more understandable to LLMs. Of course they are still capable of interpreting very obscure structures too, but usually at the cost of cognitive performance.

I'm open to being wrong about this, and I'm sure it's being researched.

(Specifically for text representations)

To your point, at some level of intelligence an LLM will be able to infer the intent of your prompt consistently without thinking enabled, in which case interpretability to a human matters less. But for complex tasks you aren't likely to get optimal performance with prompts that are difficult for humans to understand. And yes, you'd see that with thinking enabled as it churns over thousands of tokens trying to "mentally expand" a compressed prompt.

Interesting discussion though!

[docjay]

It’s a lot of fun to compare human and LLM black boxes, but it’s important to keep in mind that we don’t need to know what it is to know what it isn’t, and we can use that to define the edges of the box. We don’t know how either of them work in certain ways, but we know they’re not magic that breaks both thermodynamics and every concept loosely correlated with “entropy” as a topic.

Intelligence requires thought/processing, and I think we can all agree on that part, even if we struggle to define intelligence itself. Increased thought or processing requires increased energy, and the universe agrees on that part. There’s no way around it, that’s the thermodynamics of computation and it holds for biological, digital, and as of yet undiscovered systems used by aliens at the edge of the observable universe. Having information means fighting entropy, and that requires energy. The more, the more.

If you give a dense LLM a 100 token long question about the nature of quantum mechanics or a 100 token long sequence of “-“ and limit it to N token responses to both, it will take exactly the same time and energy to provide both responses. If you resist the urge to turn temperature above 0.0 you’ll also get the exact same response for the same input tokens every time. A deterministic response to external stimulus is typically first broad stroke we use to separate thought capable entities from rocks, but even if we grant LLMs their own unique category of “thinking rock” we can see that prompt complexity and energy required to respond are always constant (per token), so the thermodynamics necessarily means there is not additional thought or computation. Physics demands it. That, again, is a deterministic response.

It has a seemingly endless range of potential responses, but it doesn’t. If you don’t add a random number generator, which is common practice, then you can directly map every possible input to every output. I’m pretty sure that’s why Anthropic removed the ability to change temperature on the latest models. They always forced some amount of non-deterministic responses, but it was a small amount and I actually used that fact to track changes in the model by mapping repeated responses.

Most people actually do have some experience with things that have an astronomical range of possible outputs, a nearly equal number of possible inputs, input and output are directly correlated, and input complexity does not change processing time per input unit. One example is a piano, but we don’t worry about confusing it with a complex note.

[flir]

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.

[docjay]

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.

[flir]

I've been starting with "write three paragraphs about X" when I want to talk about X, as a form of "priming the pump" - getting closer to the useful point in the phase space. After all, it doesn't matter who in the conversation generates the magic words, as long as they're present. I think your approach might be better. It's certainly enlightening. Thanks.

[docjay]

You, sir, are doing exactly the right thing and it works for the exact same reason that my prompt works. Whether my method is ‘better’ or not is probably a chocolate vs caramel debate.

What you might not have fully realized is that it’s exactly what enabling “thinking” does as well. That’s why that exists and it literally does what you’re doing as well: it primes the system. You say “light sensor and amplifier” and at some point it outputs “photodiode and transimpedance amplifier” - now you’re off into advanced responses. The thing is, if you knew it you could have just used those words in your question and received much the same response. “Thinking” exists to turn “So, I was wondering..” into academic prose that raises the probability of academic tokens in the response.

You can kind of cheat the system by doing the same thing for a fraction of the token cost by using something like Haiku to provide a comma separated list of advanced topics and jargon associated with {Your question}, then tack that onto your prompt to Opus with thinking disabled. Obviously easier if you’re using the API, but I’ve run hundreds of millions of tokens though that process and it’s consistently and measurably better than their default thinking. I believe that’s because Anthropic and OpenAI drank their own kool-aid and are treating it like a sentient being that needs to add “hmm…good question” so it feels more thinky about things ‘cause that’s how we do it. The fact that it isn’t, and doesn’t, is why I developed the example prompt I showed earlier; it’s an extreme play on the offloaded “thinking” I also use.

[mhjkl]

How do you make these compressed prompts like that