[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.