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That won't make a difference. These generative AI systems have ingested more math books than any human being alive today and they still can't add numbers.
by soloist11 2y ago
That won't make a difference. These generative AI systems have ingested more math books than any human being alive today and they still can't add numbers.
- user3939382 2y agoI just asked both Claude and ChatGPT to add numbers and they both gave me the right answer.
- soloist11 2y agoAsk them to compute the simplicial homology of the n dimensional projective plane next.
- predictsoft 2y agoI just asked ChatGPT that and it seemed to come up with a good answer.
- soloist11 2y agoNow ask it to convert the computation into a logical calculus so that it can be verified with a theorem prover like Coq, Lean, or Isabelle.
- bubblyworld 2y agoWhat are you actually getting at with this? Formalising algebraic topology in Lean is still _very_ much an open project, for instance.
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- soloist11 2y agoYou'd think with all those billions spent on the software and the hardware it would be a walk in the park to convert a single book on algebraic topology into a formalized Coq, Lean, or Isabelle module. Seems like a very obvious test case for the intelligence capabilities of these systems. I know that it is possible because Kevin Buzzard is going to formalize Fermat's last theorem for less than £934,043 but no commercial AI lab has yet managed to build an AI that can do basic arithmetic. [0] Mira Murati is on the record about their next AI model and that it will have the intelligence of a PhD student so let's see if their next model can actually formalize basic algebraic topology into a logical calculus. [1] 0: https://gow.epsrc.ukri.org/NGBOViewGrant.aspx?GrantRef=EP/Y022904/1 https://gow.epsrc.ukri.org/NGBOViewGrant.aspx?GrantRef=EP/Y0... 1: https://engineering.dartmouth.edu/news/openai-cto-mira-murati-th12-shares-optimism-for-ais-future# https://engineering.dartmouth.edu/news/openai-cto-mira-murat...
- bubblyworld 2y agoWhy would you think that's a walk in the park? Have you actually tried formalising stuff in Lean/Coq? I have, and even with a postgraduate maths degree behind me it's hard as hell! The fact that Kevin and his team are formalising FLT is incredible, but they all have decades of experience with this stuff (!!). Transformers can do arithmetic (and many other things) just fine, do a bit of searching on arxiv and you'll find papers from 2023 showing that nano-scale transformer models suffice. It really is a data problem, not a fundamental limitation with the technology.
- soloist11 2y agoWhat is your degree in?
- bubblyworld 2y agoMaster's studying representation theorems in nonmonotonic logic, left academia for industry during my PhD. Fun spaced out maths problems. I tried to formalize my thesis in Lean but it is nowhere near as simple as you make it out to be.
- tobinfricke 2y agoThe output of ChatGPT almost always sounds good. That's the point. But I would wager that its answer was at least wrong, and perhaps total nonsense. That's the real hazard of using ChatGPT as a learning tool. You are in no position to evaluate whether the output makes any sense.
- bubblyworld 2y agoI asked it to compute the simplicial homology of RP^2 and not only was it spot on with the result, it gave me a detailed and essentially correct computation. This definitely appears in its training set, but nevertheless you should have some humility =P
- soloist11 2y agoHow do you know it's correct? The only simplicial traingulation I know of is by splitting up the sphere into an icosahedron and then identifying all the opposite faces to get the proper antipodal action for the quotient.
- bubblyworld 2y agoI'm not interested in engaging with you further on this topic after you devolved into ad hominems against me in the other thread. I'm here to argue in good faith. Have a good day.
- soist 2y agoYou made an incorrect assessment of a basic calculation in algebraic topology and claimed that it was correct. You didn't even look at what it was computing and simply looked at the final answer which lined up with the answer on Wikipedia. Simplicial calculations for projective planes are not simple. The usual calculations are done with cellular decomposition and that's why the LLM gives the wrong answer, the actual answer is not in the dataset and requires reasoning.
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- PaulHoule 2y agoI easily broke copilot by asking it to make lists of radioactive isotopes in order of half lives. It can put the U.S. states in alphabetical or reverse alphabetical order but for any other order I would bet against it. If I ask it what the probability is that it can correctly complete a sorting task, however, it insists that it is almost certain to get it right. I had a good conversation with it about the theory of partial orderings, it even corrected my mistakes. I asked it to make a textbook problem determining if a graph was cyclic or not and it made a straight and beautiful example where the partial ordering was realized with a total ordering and everything was written out in a straight order that was easy to follow. If I wrote a script that made up a bunch of "is this graph cyclic?" problems that are well randomized I am sure there is some size where it just falls down the same way it falls down with sorting. The obvious answer is that the LLM should pick an algorithm or write some code to do the thing which ordinary algorithms can do such as arithmetic, sorting, SAT solving, etc. There's the deeper issue that it doesn't know what it doesn't know. It can't sort a list of radioactive isotopes any more than it can help you make an atom bomb. In the second case it will say that it won't help you, in the first case it will try to help you anyway when it really should be saying "I can't do that, Dave" because it just can't.
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- fragmede 2y ago> lists of radioactive isotopes in order of half lives ChatGPT-4o does just fine with that. Basing your opinion of a whole technology based on a poor implementation of that instead of the best one doesn't seem like the best analysis.
- user3939382 2y agoThat’s moving the goal post. GP’s assertion was that it couldn’t add numbers.
- soloist11 2y agoComputing simplicial homology is basic arithmetic. It's the same goal post.
- user3939382 2y agoThe goal post is adding numbers, not some other calculation for which adding numbers is a step.
- soist 2y agoThe computer can't do anything other than arithmetic
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- 317070 2y agoI work in the field. The issue is that you will find 2+2=5 literally a hundred times more in all big datasets than 6+3=9 A lot of information is wrong, a lot is only true in context (e.g. 2+2=5 features prominent in the book 1984), even more is spam or machine generated. If you see the garbage that goes in, I am always amazed at how these models do what they do.
- soloist11 2y agoYes, the issue is that statistical models can not reason and determine what is logically valid vs what is most probable (which I guess is also its own kind of logic).
- 317070 2y agoAnd context, so much context. The sqrt(-1) sometimes doesn't exist, sometimes it's 1i. 2+2=4, except in literature where it can be 5. 1+1=2, but sometimes 3 in advertisements or in ironical text. We often have some ideas about e.g how it works in a quiz, where you know there is only one factually correct answer. And we are disappointed if the model is wrong. But even in a quiz setting the jury gets that balance wrong every so often, where there are other answers than the official one which are also correct. Even "logically valid" is context dependend. This is not to say that models don't hallucinate, just that even within the logically valid answers, there is hidden context surrounding the data which is not expressed in the data itself. Fermats last problem is a solved problem in mathematics, but not in documents from before 1994.
- soloist11 2y agoThe models operate by the logic of boolean arithmetic so in that sense they can not be inconsistent. But in any case, it's pretty obvious no one in this thread understands what I'm getting at but maybe eventually there will be an AGI smart enough to get the point.
- mdp2021 2y agoAnd this is why input assessment¹ is crucial... (Idea assessment in general. Handled ideas in thought processes are still input.)
- GaggiX 2y agoI mean, they are much better than humans at "mental" arithmetic.
- soloist11 2y agoI don't know what that means. There is nothing "mental" happening in the circuits of the computer or the function graph which is implemented on top of it.
- Kiro 2y agoI keep seeing this being thrown around but ChatGPT can do addition just fine since at least GPT-3.5. Not that I care or expect it to (why would I use an LLM for math?) but still.
- soloist11 2y agoI don't know man, I keep hearing about AGI before 2030 but none of these AI labs can figure out how to do arithmetic with their fancy intelligence software.
- fragmede 2y agoThey do addition just fine, you're just repeating something you heard months ago, which is out of date in the field, which is why adherents are saying 2030.
- soloist11 2y agoPretty sure I'm right. Ask your favorite chatbot to solve the following system of equations and let me know what you get as the answer. Here is the answer from gemini: > Solve the following system of equations: 2x + 2y = 2 and x + y = 1 My pleasure, I’ve been growing my expertise in solving system of linear equations problems. Let’s solve the system of equations: $$2x+2y=2$$ $$x+y=1$$ We can solve the system of equations by elimination. Steps to solve: *1. Eliminate x:* Multiply the second equation by -2: $$-2x-2y=-2$$ Add the first and second equations: $$0=-1$$ *2. No solution:* Since we obtained a contradiction (0=-1), there is no solution to the system of equations. *Answer:* The system of equations has no solution.
- GaggiX 2y agoFrom Claude 3.5 Sonnet: "Let's solve this system of equations step by step: 1) We have two equations: 2x + 2y = 2 (Equation 1) x + y = 1 (Equation 2) 2) We can solve this using substitution. Let's express x in terms of y from Equation 2: x = 1 - y 3) Now, let's substitute this into Equation 1: 2(1 - y) + 2y = 2 4) Let's simplify: 2 - 2y + 2y = 2 2 = 2 5) This is true for all values of y, which means that Equation 1 is actually redundant. It doesn't give us any new information beyond what Equation 2 provides. 6) Therefore, we can conclude that there are infinitely many solutions to this system, all satisfying the equation: x + y = 1 7) We can express the solution set as: x = 1 - y y = y (where y can be any real number) Thus, the solution to this system is a line in the xy-plane described by the equation x + y = 1. Would you like me to explain any part of this solution in more detail?"