5 ms·
Someone asked if true intelligence requires a foundation of prior knowledge. This is the way I think about it. I = E / K where I is the intelligence of the sy
by owenpalmer 2y ago
Someone asked if true intelligence requires a foundation of prior knowledge. This is the way I think about it.
I = E / K
where I is the intelligence of the system, E is the effectiveness of the system, and K is the prior knowledge.
For example, a math problem is given to two students, each solving the problem with the same effectiveness (both get the correct answer in the same amount of time). However, student A happens to have more prior knowledge of math than student B. In this case, the intelligence of B is greater than the intelligence of A, even though they have the same effectiveness. B was able to "figure out" the math, without using any of the "tricks" that A already knew.
Now back to the question of whether or not prior knowledge is required. As K approaches 0, intelligence approaches infinity. But when K=0, intelligence is undefined. Tada! I think that answers the question.
Most LLM benchmarks simply measure effectiveness, not intelligence. I conceptualize LLMs as a person with a photographic memory and a low IQ of 85, who was given 100 billion years to learn everything humans have ever created.
IK = E
low intelligence * vast knowledge = reasonable effectiveness
- Woodi 2y agoYep, I aways liked encyclopedia. Wiki is good too :) What I would like to have in the future is SO answering-peoples accessible in real time via IRC. They have real answers NOW. They are even pedantic about their stuff !
- wangii 2y agoInteresting formulation! it captures the intuition of the "smartness" when solving a problem. However, what about asking good questions or proposing conjectures?
- hanspeter 2y agoAren't those solutions to problems as well? Find the best questions to ask. Find the best hypothesis to suggest.
- lorepieri 2y agoThere should be also a factor about resource consumption. See here: https://lorenzopieri.com/pgii/ https://lorenzopieri.com/pgii/
- spacebanana7 2y agoAlso perhaps a factor (with diminishing returns) for response speed? All else equal, a student who gets 100% on a problem set in 10 minutes is more intelligent than one with the same score after 120 minutes. Likewise an LLM that can respond in 2 seconds is more impressive than one which responds in 30 seconds.
- owenpalmer 2y ago> a student who gets 100% on a problem set in 10 minutes is more intelligent than one with the same score after 120 minutes According to my mathematical model, the faster student would have higher effectiveness, not necessarily higher intelligence. Resource consumption and speed are practical technological concerns, but they're irrelevant in a theorical conceptualization of intelligence.
- baq 2y agoIf you disregard time, all computers have maximal intelligence, they can enumerate all programs and compute answers to any decidable question.
- wouldbecouldbe 2y agoYeah speed is a key factor in intelligence. And actually one of the biggest differentiators in human iq measurements
- eru 2y agoHumans are a bit annoying that way, because it's all correlated. So a human with a better response time, also tends to give you more intelligent answers, even when time is not a factor. For a computer, you can arbitrarily slow them down (or speed them up), and still get the same answer.
- someothherguyy 2y agohttps://en.wikipedia.org/wiki/Fluid_and_crystallized_intelligence https://en.wikipedia.org/wiki/Fluid_and_crystallized_intelli...
- dmezzetti 2y agoWe should wait until it's released before we anoint it. It's disheartening to see how we keep repeating the same pattern that gives in to hype over the scientific method.
- lazide 2y agoThe scientific method doesn’t drive stock price (apparently).
- matusp 2y agoWell put. You ask LLMs about ARC-like challenges and they are able to come up with a list of possible problem formulations even before you show them the input. The models already know that they might expect various object manipulations, symmetry problem, etc. The fact that the solution costs thousands of dollars says to me that the model iterates over many solutions while using this implicit knowledge and feedback it gets from running the program. It is still impressive, but I don't think this is what the ARC prize was supposed to be about.
- curl-up 2y ago> while using this implicit knowledge and feedback it gets from running the program. What feedback, and what program, are you referring to?
- scotty79 2y agoBasically solutions that were doing well in arc just threw thousands of ideas at the wall and picked the ones that stuck. They were literally generating thousands of python programs, running them and checking if any produced the correct output when fed with data from examples. This o3 doesn't need to run python. It itself executes programs written in tokens inside it's own context window which is wildly inefficient but gives better results and is potentially more general.
- TheOtherHobbes 2y agoSo basically it's a massively inefficient trial-and-error leetcode solver which only works because it throws incredible amounts of compute at the problem. This is hilarious.
- scotty79 2y agoPrevious best specialized ARC solver was exactly that. This o3 thing might be a bit different because it's just chain of thought llm that can do many other things as well. It's not uncommon for people to have a handful of wrong ideas before they stumble upon a correct solution either.
- onemetwo 2y agoAn intelligent system could take more advantage of an increase of knowledge than a dumb one, so I should propose a simple formula: the derivative of efficiency with respect to knowledge is proportional to intelligence. $$ I = \frac{partial E}{partial K} \simeq \frac{\delta E}{\delta K} $$ In order to estimate $I$ you have to consider that efficiency and knowledge are task related, so you could take some weighted mean $sum_T C(E,K,T)*I(E,K,T)$ where $T$ is task category. I am thinking in $C(E,K,T)$ as something similar to thermal capacity or electrical resistance, the equivalent concept when applied to task. An intelligent agent in a medium of low resistance should fly while a dumb one would still crawl.
- owenpalmer 2y ago> An intelligent system could take more advantage of an increase of knowledge than a dumb one Why? > derivative of efficiency Where did your efficiency variable come from?
- onemetwo 2y agoWhy? I am using dumb as a low intelligence system. A more intelligent person can take advantage of new opportunities. Efficience variable: You are right that effectiveness could be better here because we are not considering resources like computer time and power.
- gardenhedge 2y agoWhere did someone ask that?
- scotty79 2y agoAs a kid I absolutely hated math and loved physics and chemistry because solving anything in math requires vast specific K. In comparison you can easily know everything there is to know about physics or chemistry and it's sufficient to solve interesting puzzles. In math every puzzle has it's own vast lore you need to know before you can have any chance at tackling it.
- owenpalmer 2y agoPhysics and chemistry require experimentation to verify solutions. With math however, any new knowledge can be intuited and proven from previous proofs, so yes, the lore goes deep!
- scotty79 2y agoDeep and wide. What was infuriating is that even if you learn lore necessary to solve one puzzle it's completely useless for other 99.
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