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Re:Understanding the Limitations of Mathematical Reasoning i... by parsimo2010 on Friday October 11, 2024 @10:27AM (#41809764)
I won't take a strong stance on whether or not LLMs actually do reasoning, but I will say that this decrease in performance is similar to what I see in college freshmen (I'm currently teaching a calculus course in which almost half of the students took AP calc in high school). They perform well on simple questions. Requiring students to chain multiple steps together, even simple steps, results in decreased accuracy and higher variance (I have no data on whether this decrease is linear or not, as the paper assumes that the decrease should be linear with the number of steps). We see similar results with adding unrelated statements into a problem- many students are trained to make sure to use all given information in solving a problem- if you leave out something that the instructor gives you, then you probably forgot to do something important.

So while I don't take a stance on what an LLM does should be considered reasoning, I do think that SOTA LLMs like GPT-4o perform about as good as high school graduates in America with average intelligence. In other words, average Americans exhibit similar limitations on their reasoning as good LLMs. Which on the one hand is a little disappointing to me in terms of the human performance but is kind of good news for LLMs- they aren't doing graduate-level research but they are already capable of helping a large portion of the population.

Re:Understanding the Limitations of Mathematical Reasoning i... by skydhash on Friday October 11, 2024 @10:44AM (#41809916)
Not to disparage American school system (my country’s is worse) but it’s very much easy mode. I know that not everyone is suited to academic excellence, but it’s definitely easier to learn when young. I do believe too much hand holding actively harm learning.
Re:Understanding the Limitations of Mathematical Reasoning i... by BriggyDwiggs42 on Friday October 11, 2024 @10:51AM (#41809981)
I don’t think the issue with American schools is that there’s too much hand holding. If anything, it’s the opposite; teachers at drastically underfunded schools don’t have any time to help the students of their 50 person class through the confused curriculum.
Re:Understanding the Limitations of Mathematical Reasoning i... by skydhash on Friday October 11, 2024 @11:34AM (#41810408)
Here, we have to go through 4 state exams just to get to university. The first when you’re 11, the second at 14, then two consecutive ones at 17 and 18. There’s a national curriculum that the exams will be about, although the schools are free to add to it. So however you feel about the school or the teacher, you have to master the subjects enough to go through. And that means paying attention in class, cram before it, or hoping you can cheat. We have our own problem too, but the consensus among all the people I know that have moved to the US is that classes are easy there. Not a bad thing per se (better explanation, better understanding instead of rote memorizing).
Re:Understanding the Limitations of Mathematical Reasoning i... by BriggyDwiggs42 on Saturday October 12, 2024 @02:46AM (#41816981)
Yeah you’ll never convince me that one-time exams are a good system to determine the rest of a student’s life, but I don’t disagree our schools are much easier. I’m just arguing the issue is less on a behavior of teachers level and more on a funding and incentives level. If I recall correctly, one issue is that schools are incentivized to lower educational standards to prevent students from repeating grades so that that receive more funding.
Re:Understanding the Limitations of Mathematical Reasoning i... by exoverito on Friday October 11, 2024 @04:53PM (#41813628)
Baltimore would be a counterexample. They spend $22k per student, with a student-teacher ratio of 15 to 1. This still results in remarkably poor performance, with only 8% of students proficient in math and 22% in reading.

Culture and genetics would be next obvious explanations.

Re:Understanding the Limitations of Mathematical Reasoning i... by mdp2021 on Friday October 11, 2024 @05:02PM (#41813703)
> obvious explanations

I'd want to assess a few lessons first.

Re:Understanding the Limitations of Mathematical Reasoning i... by BriggyDwiggs42 on Saturday October 12, 2024 @02:35AM (#41816952)
Genetics lmao come on man.
Re:Understanding the Limitations of Mathematical Reasoning i... by imtringued on Saturday October 12, 2024 @06:02AM (#41817947)
The mean IQ score is 100... Unless you are in some elite school for the top 10% it is not reasonable to use genetics as a justification. It sounds more like a thinly veiled form of specifically American racism.
Re:Understanding the Limitations of Mathematical Reasoning i... by mncharity on Saturday October 12, 2024 @09:30AM (#41818927)
An instructional challenge at the Ivy end, is incoming students having had such clear teachers, that they lack the attitudes and skills for wrestling with information to extract understanding.
Re:Understanding the Limitations of Mathematical Reasoning i... by hintymad on Friday October 11, 2024 @05:39PM (#41814034)
> Not to disparage American school system (my country’s is worse) but it’s very much easy mode

I used to be very upset about how low the bar of the US school has when it comes to STEM subjects. There was a meme that contrasted the difference between maths in 1970s and 2010s. In the meme kids used to learn how to find the area of an irregular shape, while now the kids are asked to color a regular shape.

But then I made peace, as I realized that the US people simply didn't think that it was that important to push everyone to be good at STEM -- just some level of general understanding is good enough. To most people, the level of STEM as in IIT's JEE or in various national entrance exams in Eastern European countries is for elite students. The US school systems would rather have kids spend more time on sports, on ECs, on APs of kids' own choices, and etc. That's really just different trade offs. For parents like me, that means I don't have to worry about ECs, but I'll have to find tutors, serious tutoring schools like AOPS, and private teachers for STEM subjects. Or if my kids are truly talented, I'll guide them to find the right study groups, summer camps, and college courses.

I used to feel pain as I believed that the students in the middle, which were the majority, would be left behind. But I realized, especially after I've got kids, that the majority of the students were not into STEM anyway. If they had a choice, they'd rather spend time watching YouTube channels and hang out with their friends.

Re:Understanding the Limitations of Mathematical Reasoning i... by debit-freak on Friday October 11, 2024 @10:51AM (#41809986)
> In other words, average Americans exhibit similar limitations on their reasoning as good LLMs.

It's not even clear this is a good example of "reasoning". You can progress all the way through multi-variable calculus with just decent pattern-matching, variable-substitution, and rote memorization of sufficient lists of rules. I imagine for "reasoning" ability to apply you need to be able to detect incoherency and reject an approach—and incoherency detection seems to be a big missing ingredient right now (...which many humans lack, too!).

On the other side—any such ability would cripple a chatbot's ability to answer questions about the real world as our world is characterized (via description with informal language) by incoherent and contradictory concepts that can only be resolved through good-faith interpretation of the questioner. A large mark of intelligence (in the colloquial sense, not the IQ sense) is the ability to navigate both worlds.

Re:Understanding the Limitations of Mathematical Reasoning i... by richerram on Friday October 11, 2024 @11:03AM (#41810112)
This, it is like when I hear interviews of PHDs talking about AI and they mention something like "AI will be smarter than humans", I am like "really?, where have you been all this time?, do you smart people ever leave your labs and go see the real world?, LLMs are already smarter that the huge majority of Humans in this planet, what are you talking about?"
Re:Understanding the Limitations of Mathematical Reasoning i... by zeroonetwothree on Friday October 11, 2024 @11:16AM (#41810232)
This must be some bizarre definition of “smarter”.
Re:Understanding the Limitations of Mathematical Reasoning i... by kkzz99 on Friday October 11, 2024 @04:22PM (#41813350)
I don't think you know how "smart" the average human is.
Re:Understanding the Limitations of Mathematical Reasoning i... by richerram on Sunday October 13, 2024 @01:11AM (#41825323)
I know it won't be in the holistic or deep philosophical way but even by just predicting the next token without any real sense of the real world LLMs are already capable of simulating basic reasoning which a lot of people lacks, I mean even the 7B llama2 model can tell you the Earth ain't flat... go figure.
Re:Understanding the Limitations of Mathematical Reasoning i... by lupire on Friday October 11, 2024 @03:22PM (#41812636)
Can an AI walk and chew gum at the same time?
Re:Understanding the Limitations of Mathematical Reasoning i... by lukeschlather on Friday October 11, 2024 @06:21PM (#41814417)
I think the answer to this question might actually be yes, but I think there are plenty of things humans can do while walking that AI can't do at all. At least, not yet.
Re:Understanding the Limitations of Mathematical Reasoning i... by goatlover on Friday October 11, 2024 @04:43PM (#41813530)
Smarter than people in generating text, or smarter in oerforming all the other things people do as they go about their lives?
Re:Understanding the Limitations of Mathematical Reasoning i... by MVissers on Friday October 11, 2024 @05:18PM (#41813853)
They are starting to be smarter at both analyzing images and speech as well. They’re still behind on simple reasoning (eg. O1-preview), but it’s catching up quickly.

Obviously these models still have trouble interfacing with the real world.

Re:Understanding the Limitations of Mathematical Reasoning i... by ActorNightly on Friday October 11, 2024 @03:38PM (#41812825)
> I won't take a strong stance on whether or not LLMs actually do reasoning,

I don't understand why people are still confused about this. When these models fundamentally have a randomness parameter to make them appear like they are actually thinking instead of deterministically outputting information, it should be clear that there is no reasoning going on.

Re:Understanding the Limitations of Mathematical Reasoning i... by kkzz99 on Friday October 11, 2024 @04:19PM (#41813316)
"deterministally outputting information" neither do humans.
Re:Understanding the Limitations of Mathematical Reasoning i... by growthwtf on Friday October 11, 2024 @04:28PM (#41813403)
I don't see how the latter follows from the former.

Here's how I think about it: the fact that it can interpret the same words differently in different contexts alone shows that even on a temperature of 0 (i.e., lowest randomness possible) there could be something that possibly resembles reasoning happening.

It might be a mimicry of reasoning, but I don't think that having adjustable parameters on how random they are makes it any less of one.

I also don't see how that idea would fit in with the o1 models, which explicitly have "reasoning" tokens. Now, I'm not terribly impressed with their performance relative to how much extra computation they need to do, but the fact they have chains-of-thought that humans could reasonably inspect and interpret, and that they chains of thought do literally take extra time and compute to run, certainly points at the process being something possibly analogous to reasoning.

In this same vein, up until recently I personally very much in the camp of calling them "LLMs" and generally still do, but given how they really are being used now as general purpose sequence-to-sequence prediction models across all sorts of input and output types tends to push me more towards the "foundation models" terminology camp, since pigeonholing them into just language tasks doesn't seem accurate anymore. o1 was the turning point for me on this personally, since it is explicitly predicting and being optimized for correctness in the "reasoning tokens" (in scare quotes again since that's what openai calls it).

All that said, I personally think that calling what they do reasoning, and meaning it in the exact same way as how humans reason, is anthropomorphizing the models in a way that's not really useful. They clearly operate in ways that are quite different from humans in many ways. Sometimes that might imitate human reasoning, other times it doesn't.

But, the fact they have that randomness parameter seems to be to be totally unrelated to any of the above thoughts or merits about the models having reasoning abilities.

Re:Understanding the Limitations of Mathematical Reasoning i... by ActorNightly on Friday October 11, 2024 @06:17PM (#41814399)
>he fact that it can interpret the same words differently in different contexts alone shows that even on a temperature of 0 (

This is the problem with using loaded language like "reason" and "interpret". The model is not interpreting anything. All that is being done is a multdimentional map lookup with statistics.

> also don't see how that idea would fit in with the o1 models, which explicitly have "reasoning" tokens.

An LLM on top of an LLM (i.e using context to generate inputs to an LLM) is just a fancier LLM.

To really understand all of this, all you need to do is look at how Transformer works, namely the attention block. There is no such thing as Query, Key, and Value in the sense of how they are implied to be used. The may as well be called A,B,C, as they are all learned in training, and can be freely interchanged in naming. All you do for inference is multiply the output vector by A,B,C to get 3 matrices, then multiply them together (technically with a scaling factor for 2 of them, but again, doesn't matter for which 2, and the scaling factor can be built into the matrix itself)

And because you can unroll matrix multiplication into a 2 layer neural network, that means that any LLM in its current form today can be represented as a set of linear layers. And we know that a set of linear layers is simply a function. And every function has a finite range for a finite domain. And the inability to expand that range given a finite domain means its not reasoning.

So we have to rely on hacks like temperature to make it appear like reasoning, when its really not even close.

Re:Understanding the Limitations of Mathematical Reasoning i... by growthwtf on Friday October 11, 2024 @06:56PM (#41814693)
I see, I probably needed more coffee to read your initial note.

If I am repeating this back correctly, the argument is that the process itself looks nothing like human reasoning and has a number of technical limitations and even hacks that are in no way attributes or qualities of reasoning. Therefore, it clearly cannot be in any way considered reasoning. Temperature is one element of this, but there are others which you could continue to enumerate beyond even what's written above.

I can get behind part of that argument, certainly, and I appreciate you elaborating on it. I think is what I was trying to say with the part about me believing that it's not useful to think of it as reasoning. This is very different from what we might consider reasoning in very meaningful ways.

I also agree with you also that parts of this is just loaded language, as it is anthropomorphizing what is fundamentally just a bunch of matrices and non-linear functions.

I think where we differ is probably on that "when it's not even really close" part of it, at least in what I mean is "close" versus what I think you mean.

While I (think) we agree that obviously it's a different process, I do think that the input->outputs and the different qualities of input->outputs (like the so-called reasoning tokens) above can often seem quite close to the different inputs and outputs of some human reasoning. That's why I was saying that didn't see how the process works, like temperature, is relevant. Putting the processes aside, if you black box a human and a language model and put us head to head on reasoning tasks, sometimes you're going to get quite similar results.

I'm basically saying that, sure, an LLM or foundation model is clearly a Chinese room, without any understanding. What are we comparing it to, though?

Now, I don't have any kind of training in biology, but I have been led to understand that our brains are quite complex and that how their function arises from the underlying biological processes. is still fairly poorly understood. Given that, I tend to discount the degree of difference between the processes themselves and just look at the inputs and outputs. It's not obvious to me that we aren't ourselves Chinese rooms, at least to some significant degree.

So _maybe_ it's fair to try to compare what the outputs of these Transformers are to what our outputs would be. If it walks like a duck, and talks like a duck, does it matter?

Obviously, that's not fully correct -- how the output arises _has_ to matter somewhat. The fact I am sitting here writing this, and not an AI, refutes that point to some degree. And if I am understanding your thoughts correctly, I fully agree that the process really is nothing close. I just don't see how it can be a clear-cut issue on the basis of analyzing the Transformer algorithm itself.

Re:Understanding the Limitations of Mathematical Reasoning i... by ActorNightly on Friday October 11, 2024 @08:59PM (#41815447)
>If it walks like a duck, and talks like a duck, does it matter?

Depends on what your goals are. LLMs can get to a state where they contain a lot of human knowledge, with a lot of detail, to answer a lot of questions, and be used in many different ways. If your idea of intelligence is akin to having a bunch of experts on tap in all the different areas, then LLMS are totally fine.

I personally want something that can solve problems, not just answer questions. For example, lets say I want to build a flying car, quadcopter style, in my garage. Given the information that exists on the internet and availability of parts, this is a deterministic problem. Given that prompt, I want a set of specific instructions like "buy this part from here", "send this cad model to sendcutsend.com here and select these options", all the way down to "here is a binary file to load on the controller". And along the same lines, the AI should be able to build a full simulator application Flight Sim style, where I can load the file and play with controls to see how the thing behaves, including in less than optimal conditions.

Whatever that model does under the hood, that is called reasoning, and it certainly won't be structured like an LLM.

Re:Understanding the Limitations of Mathematical Reasoning i... by genrilz on Saturday October 12, 2024 @10:22AM (#41819275)
I feel like that is a pretty high bar to call "reasoning". I would like to think I am capable of reasoning, and yet I would not be able to write out by hand a binary file to be loaded on to the controller without using a compiler or looking at an assembly reference manual.

It seems like you want LLMs to be able to use tools (which some of them do. For instance, see the search engine chat bots, which can do searches) and make independent decisions (Search term here is "agent", I don't know how well they work, but I wouldn't personally let my computer do things like that unsupervised). However, I personally wouldn't consider these things to be a prerequisite to reasoning.

I would consider being able to solve a large range of problems that a human could solve with just pencil and paper to be reasoning. LLMs don't really seem to be as good as humans, but the certainly CAN solve these types of problems.

Re:Understanding the Limitations of Mathematical Reasoning i... by ziofill on Friday October 11, 2024 @11:39PM (#41816207)
> Putting the processes aside, if you black box a human and a language model and put us head to head on reasoning tasks, sometimes you're going to get quite similar results.

I cannot believe this is true. LLMs are awful at whatever problems are not present in the dataset used for training. They are very bad at planning problems for example, because they cannot possibly memorize every single instance, and they cannot reason to reach a solution, but a black-boxed human of course it can.

Re:Understanding the Limitations of Mathematical Reasoning i... by Eisenstein on Friday October 11, 2024 @06:43PM (#41814582)
> The model is not interpreting anything. All that is being done is a multdimentional map lookup with statistics.

So what? Can you propose another method to make a computing device understand language? The method of the creation of the output does not stipulate anything about the nature of the thing creating it. If someone could map out a human brain and tell you how thoughts are made and added a 'all that is being done is' in front of it, does that make your thought creation trivial?

> An LLM on top of an LLM (i.e using context to generate inputs to an LLM) is just a fancier LLM.

This is called a tautology. You have not given any compelling reasons why an LLM cannot do anything, so calling something another LLM is not compelling either.

> To really understand all of this, all you need to do is look at how Transformer works, namely the attention block. There is no such thing as Query, Key, and Value in the sense of how they are implied to be used. The may as well be called A,B,C, as they are all learned in training, and can be freely interchanged in naming. All you do for inference is multiply the output vector by A,B,C to get 3 matrices, then multiply them together (technically with a scaling factor for 2 of them, but again, doesn't matter for which 2, and the scaling factor can be built into the matrix itself)

Here is how it works, so therefore it must meet some criteria I have imposed arbitrarily.

> So we have to rely on hacks like temperature to make it appear like reasoning, when its really not even close.

You still haven't produced any valid argument at all, for why one thing would be evidence of the other.

Re:Understanding the Limitations of Mathematical Reasoning i... by ActorNightly on Friday October 11, 2024 @08:27PM (#41815298)
A good example of how to type a comment and yet not say anything.

It should be pretty clear to anyone that human brains aren't just one giant compute functions with a limited set of outputs. There is no concept in your or my brain what 12074389762193867*2398720876324 is, but we can certainly figure it out, some even with good memory with complete sensory depravation.

If you disagree with this, you are entitled to your opinion, but your comments on the state of AI are just irrelevant.

Re:Understanding the Limitations of Mathematical Reasoning i... by Eisenstein on Friday October 11, 2024 @09:18PM (#41815532)
I don't remember making any comments on A.I.

My post was pointing out basic flaws in reasoning and trying to provoke some thought about something where it appeared to be lacking. Unfortunately I did not succeed, since a myopic view made you hallucinate that I was saying something definitive about something I was not.

Irrelevant, indeed.

Re:Understanding the Limitations of Mathematical Reasoning i... by synarchefriend on Saturday October 12, 2024 @08:41AM (#41818644)
o1 can also solve many arbitrary math problems that it could not have possibly seen in its training data. And it shows the steps that it uses to do so. How do you explain this without reasoning?
Re:Understanding the Limitations of Mathematical Reasoning i... by tananan on Friday October 11, 2024 @05:37PM (#41814017)
The notion is AFAIS that a deterministic algorithm is obviously not reasoning, and a deterministic algorithm interspersed with dice rolls is obviously not reasoning either.

Of course, some would beg to differ. It's quite common nowadays to believe that we are something like the latter.

Re:Understanding the Limitations of Mathematical Reasoning i... by pishpash on Friday October 11, 2024 @05:55PM (#41814207)
Why is a deterministic algorithm not reasoning? Reasoning is very deterministic.
Re:Understanding the Limitations of Mathematical Reasoning i... by tananan on Friday October 11, 2024 @06:16PM (#41814388)
It's not about (in-)determinism really, it's about the algorithm part.

An algorithm that does something can in principle be ran by someone who doesn't know what the algorithm does. You could have a kid calculate an integral by giving it a sequence of directions whose purpose it doesn't understand (e.g. cut out some cardboard that matches the shape, put it on one side of the scale, place enough unit cardboard pieces on the other side until they are even, then tell me how many pieces you put).

Reasoning has more to do with how the problem came about. A person had to come against a certain problem, figure out a way in which they can solve it, then apply the (perhaps algorithmic) solution. The algorithmic part is only an artifact.

Re:Understanding the Limitations of Mathematical Reasoning i... by mewpmewp2 on Friday October 11, 2024 @07:04PM (#41814757)
But isn't figuring out a way to solve also algorithmic? In a lot of cases it is simply bruteforce trying out different things based on the concepts you know about and mixing them.
Re:Understanding the Limitations of Mathematical Reasoning i... by tananan on Friday October 11, 2024 @07:44PM (#41815048)
You are right that relevant memories and analogous experiences come up and are used as building blocks in our evaluation/exploration of a problem, but it doesn't seem to me an algorithmic procedure at all.

You can trace out your journey in solving a problem, in retrospect, but could you encode it into a "solving-a-problem" algorithm?

I think you could extract some kind of generic template for problem solving: you come up with an idea, you evaluate whether it is the solution, you adjust the idea if not.

But this is a template, not an algorithm. Coming up with an idea has to do with filtering the old and new memories/perceptions that come to mind: does this one seem right? or this one? Evaluating whether it is right is also an active process of asking questions. It involves memory (of the problem to be solved), attention (to the potential solution), judgement (do they fit together?), etc.

None of these are a predetermined sequence of steps you apply mechanically, such as the child "solving an integral" above.*

*Of course, the child is problem-solving in the sense that it's trying its best to follow your instructions. "Did I cut it right?" "Are the scales even?" But this is not the problem of "solving an integral" to which it is completely oblivious to.

Re:Understanding the Limitations of Mathematical Reasoning i... by mewpmewp2 on Friday October 11, 2024 @08:00PM (#41815142)
I think it can be an algorithm, it just that the algorithm will be a very complex one compromised of many different algorithms. It's not an algorithm anyone could practically follow in their lifetime. But there's plenty of algorithms people can't follow in real life.
Re:Understanding the Limitations of Mathematical Reasoning i... by tananan on Friday October 11, 2024 @09:06PM (#41815477)
If all one has is hammers, one can start seeing nails everywhere.

A screw? That's just a nail which will damage the wood.

A tomato? That's just a soft screw which splatters. Etc.

What purpose does seeing everything through the lens of an algorithm serve? Is the movement of an electron an algorithm? Is a polar planimeter an algorithm? [0]

We design algorithms to solve certain problems. It's part of our problem solving activity. But for what purpose would we go around, assuming things that don't look like algorithms are actually algorithms that are just outside of our reach? This doesn't solve a practical problem, so of what use is that, and where does it lead?

My long-winded answer is: We derive satisfaction from being in principle powerful. Our mechanistic/computational knowledge of nature allows us to bend certain parts of it to our will. If there are parts we cannot control, it's at least consoling that we in principle could know/control them. So we stretch computational/algorithmic terms as far as we possibly can. In the end, it envelops us as subjects. We end up in a rather cliche epiphenomenalism + causal determinism worldview:

- "Yeah, we have experiences, but they're just inefficacious artifacts of underlying chemistry."

- "You - the person who is reasoning - don't actually know what reasoning is like, it's really a very complex algorithm which we could never know or follow."

The only way such an uninspiring outlook can subsist is because it jives well with some modern dreams:

- "We only need X more compute and Y more years to bend Z part of nature to our will and bring utopia." (cue all the AI hype, see relevant frontpage entry [1])

- "If we're just a machine then maybe we can hack-reward-centers/optimize-drug-concoction/upload-to-mainframe-for-immortality" (cue quasi-immortality pitches and externally-enforced-happines pipe-dreams)

- "If I'm just a machine then I'm not responsible for my shortcomings - they're just the outcome of my wiring I cannot influence." (a nice supplement for absolving oneself from responsibility - to oneself)

- "If all is mechanical, then I'm just a temporarily embarrassed sovereign over everything. After all, if I just knew the mechanism behind things, then I could bend it to my will."

- "I have to believe this because it is obviously true." (maybe the saddest of them all, since it promises nothing except the joy of being right and having others be wrong. it also seeds the others)

[0] http://psychsciencenotes.blogspot.com/2015/07/brains-dont-ha...

[1] https://news.ycombinator.com/item?id=41813268

Re:Understanding the Limitations of Mathematical Reasoning i... by mewpmewp2 on Friday October 11, 2024 @09:43PM (#41815643)
> What purpose does seeing everything through the lens of an algorithm serve?

To me at least it helps me understand how things work. What is an alternative? Because alternative seems like some sort of magic I wouldn't understand.

> Is the movement of an electron an algorithm?

I think there's a lot of argument and complexity to what an electron exactly is or does, and what its properties actually mean, but I would imagine in general from particle and other levels whole universe can be just a deterministic algorithm, and so anything can be an algorithm. Universe has certain laws and rules which could in theory be simulated, but the simulation must have more capacity than the universe itself has so we inside the universe likely can not do it unless we find a mechanism to somehow bypass this.

> But for what purpose would we go around, assuming things that don't look like algorithms are actually algorithms that are just outside of our reach? This doesn't solve a practical problem, so of what use is that, and where does it lead?

If I try to think of what is the algorithm behind something, it helps me understand it better. Intuitively I think there's a complex algorithm behind everything, and it's just a matter of spending time and effort to figure out what it exactly is. It's unrealistic to get close to the real detail and nuance of the algorithm, but already trying to figure out the algorithm brings me closer to understanding.

> We end up in a rather cliche epiphenomenalism + causal determinism worldview

Wait -- what is wrong with that? And also I don't think it's cliche, I think it is likely to be the case?

> - "You - the person who is reasoning - don't actually know what reasoning is like, it's really a very complex algorithm which we could never know or follow."

I mean writing it down on the algorithmic level is not something we can consciously follow easily. However our brain within us is following those algorithms in the level of efficiency that we cannot consciously follow at that speed step by step, just following the instructions.

> The only way such an uninspiring outlook can subsist is because it jives well with some modern dreams:

I think my outlook is at least inspiring to me.

> - "If we're just a machine then maybe we can hack-reward-centers/optimize-drug-concoction/upload-to-mainframe-for-immortality" (cue quasi-immortality pitches and externally-enforced-happines pipe-dreams)

I do think theoretically it would be possible to hack humans to have constant "heroin like euphoria". I'm not sure I exactly care for it, but I do think these things could be done, I just don't know when, is it 50 years, 100 years or 1000 years. Of course while I say right now that I don't exactly care for it, if I tried it for once I would be hooked on it forever, assuming it has no tolerance build up or other negative effects making me consider to quit it. But even real heroin is terribly hard to quit while it has tolerance build up and side effects.

> - "If I'm just a machine then I'm not responsible for my shortcomings - they're just the outcome of my wiring I cannot influence." (a nice supplement for absolving oneself from responsibility - to oneself)

I'm inclined to think that the World is deterministic, yet I happen to also think that I have reward mechanisms that make me ambitious in a sense that I want to achieve certain goals to feel rewarded and in order to achieve those goals I have to overcome many challenges and improve certain shortcomings because it's needed to achieve those goals. If someone is using those as an excuse they would likely be the type of person to find an excuse in anything anyway. And if they do have goals they want to reach they will be affected by that, because there's certain behaviour that will get you to your desired goals and certain behaviour that is not. Taking responsibility and ownership is rewarded and if you do that, you will reach your goals with higher probability. I don't buy into the sort of thing where "something is bad because some people might use it as an excuse". Because finding an excuse is usually about the mindset, not about what kind of excuses are possible to select from. An AI bot with good goals and reward system, despite it being very obvious that they are programmed and deterministic wouldn't go about to make those excuses. But an AI bot trained to make excuses and be rewarded for it, would keep making excuses no matter what.

Re:Understanding the Limitations of Mathematical Reasoning i... by tananan on Friday October 11, 2024 @11:23PM (#41816142)
Thanks for your thoughtful response.

The view you are elaborating has a logic to it. You could argue it's the zeitgeist, at least among educated and STEM-adjacent circles. Hence my comment of it being cliche: you see variants of it all the time, and it gets a bit jading by virtue of being wholly unconvincing (to me).

In general, I think the utility of seeing everything through a mechanistic/algorithmic lens is overblown. When I'm doing technical work, I put my STEM hat on, and sometimes write algorithms. For the most part, I let it rest though. And I don't feel I understand the world any worse for dropping such mechanistic world-images I may have held years ago (I'm more at peace with it, if anything). In hindsight, the ROI on the skill of mechanistically dissecting anything you look at is rather low and hardly transferable ime. The ensuing "understanding" a passing regurgitative satisfaction.

If there's anything I really want to push back on, however, it's the notion that the views you hold do not influence the range of ways in which you develop yourself in an important way. If one truly holds the view that one is responsible for one's actions, and not the whims of determination of chance, where is the space for the excuse "it's not up to me"? Views may not determine the course of action, but they can surely constrain.

Disentangling one's views from one's behavior can go a long way in measured, written discussions like this, but I don't see it being the case in real life. It is the case however, that we can be a hodge-podge of contradictory views and standards, and that we commit to one for a moment, then to another. This is a matter of strength and cohesiveness of character. And we are good at "saving face" in front of us and others. For example, if you've met people who partake in a vice yet will say stuff like "This is bad for me." - the actual underlying view is "This has obvious drawbacks but I still think the enjoyment is worth it." It's only when they can maintain the view that the drawbacks are not worth it, that they can break out.

Re:Understanding the Limitations of Mathematical Reasoning i... by mewpmewp2 on Saturday October 12, 2024 @12:56PM (#41820540)
> The view you are elaborating has a logic to it. You could argue it's the zeitgeist, at least among educated and STEM-adjacent circles.

You could argue that most opinions or beliefs about how the World operates are cliche or similar if that's the case, there's only so many different beliefs that make any sense at all to hold and it's likely there's a group of people holding those beliefs as well and that they are not original at all. And you could also argue that a belief that 2 + 2 = 4 is cliche, because so many people believe that to be the case.

> In general, I think the utility of seeing everything through a mechanistic/algorithmic lens is overblown.

That requires some sort of measurement on how many people see it through that lens and what they evaluate it as, but I'm seeing the opposite since most of the time I find it the other way around.

> And I don't feel I understand the world any worse for dropping such mechanistic world-images I may have held years ago (I'm more at peace with it, if anything).

I can't tell how other people understand the World, since one of the learnings throughout my life have been that different people ingest information in so many different ways. Some think in images, some are not able to picture things in their mind, some don't have inner monologue. So naturally there would be a different methods of understanding things. But if I think of myself, I understand things best when I think of them as algorithms or mechanical steps that I think through. I have trouble understanding or remembering facts on their own, without internalizing the mechanisms, the cause and effect after if I have done that, it feels to me like I actually understand it. I don't even know what other way there is to understand that. It's perfectly possible that there's some other innate ways of understanding things or having a feeling that there's understanding, that I can't get just because I'm wired in a way that makes me understand things only if I can think of it as an algorithm. E.g. what I've found fantastic for learning subjects myself is actually coding through them or trying to simulate them using code. It actively engages my mind to try and simulate whatever happens in the real world. And subjects I had trouble engaging with in school, if I go through coding them, I feel like I'm actually learning them and becoming smarter. E.g. if I want to truly learn biology I should build a simulation tool that will simulate how cells behave, whatever different things in cells do, how organs work, etc.

> If one truly holds the view that one is responsible for one's actions, and not the whims of determination of chance, where is the space for the excuse "it's not up to me"?

I still don't see it in that way. Everything being deterministic and algorithmic doesn't make me have those excuses. I happen to have a reward mechanism, that rewards me for e.g. eating. It's been shaped by the process of evolution. I have many other reward mechanisms. I didn't choose those reward mechanisms myself, but I strategize on how to achieve those rewards, and I know that playing a victim is not a way to achieve your goals. Certainly there are people who mistakenly might believe that, but it happens to both, whoever believes in determinism and whoever believes in some sort of free will. I know that if I do good work, I get good rewards. So I do good work.

> Disentangling one's views from one's behavior can go a long way in measured, written discussions like this, but I don't see it being the case in real life. It is the case however, that we can be a hodge-podge of contradictory views and standards, and that we commit to one for a moment, then to another. This is a matter of strength and cohesiveness of character. And we are good at "saving face" in front of us and others. For example, if you've met people who partake in a vice yet will say stuff like "This is bad for me." - the actual underlying view is "This has obvious drawbacks but I still think the enjoyment is worth it." It's only when they can maintain the view that the drawbacks are not worth it, that they can break out.

Certainly there's a lot of views and human condition I think is overall a lot about inner turmoil and fighting vices, desires, balancing short term please vs long term gains etc, etc. But it doesn't matter if you consider something to be deterministic, because you are still balancing short term vs long term just like if you didn't believe in any of that. I don't think that I should be hunting short term pleasure constantly because it's how I'm wired to be, because I've seen enough evidence that in long term I would suffer, and I don't want to suffer in long term, so I put in the effort to engage in short term pleasure in such a way that it wouldn't have higher long term pain than I'd be willing to endure.

I can even visualize these aspects algorithmically and mechanically. I might think of myself as an RPG player where let's say if I eat this food, or ingest this drug, drink alcohol N amount, if affects some of my stats like happiness or euphoria positively temporarily, but it will decrease other stats in the long term. I think I'm conscious of this idea and in a traditional sense I'm picking to skip the short term pleasure, but me wanting to have the longer term pleasure is also wired into me.

Re:Understanding the Limitations of Mathematical Reasoning i... by pishpash on Friday October 11, 2024 @06:22PM (#41814425)
I think you overlook how algorithms come about. How does GPT write novel code, which are algorithms?
Re:Understanding the Limitations of Mathematical Reasoning i... by tananan on Friday October 11, 2024 @06:28PM (#41814475)
Not sure I track. It would help to know where you're coming from.

Given a long enough life-span, a lot of pencil and paper, and some dice, I could do the forward passes of GPT and "write novel code", without there having been any reasoning about the code I'm writing down - I wouldn't even need to know what the code is about.

Re:Understanding the Limitations of Mathematical Reasoning i... by XenophileJKO on Friday October 11, 2024 @11:03PM (#41816051)
I mean in theory I could sit and calculate electrical and chemical potentials and interactions and figure out what your next comment will be.
Re:Understanding the Limitations of Mathematical Reasoning i... by tananan on Friday October 11, 2024 @11:24PM (#41816146)
Hard disagree ;)
Re:Understanding the Limitations of Mathematical Reasoning i... by anonzzzies on Saturday October 12, 2024 @02:12AM (#41816854)
if we knew you were religious, which we would do if we had a mapping of your brain, we would have known you were going to make this comment
Re:Understanding the Limitations of Mathematical Reasoning i... by mewpmewp2 on Friday October 11, 2024 @07:02PM (#41814742)
And couldn't the whole World be deterministic in the first place, or is there an idea that some RNG is generating all the "reasoning" that is happening everywhere in the World?

And if it's RNG, how could RNG be possibly creating all this reasoning (like some people want to believe quantum mechanics possibly enables consciousness on some odd levels).

Re:Understanding the Limitations of Mathematical Reasoning i... by ActorNightly on Friday October 11, 2024 @08:38PM (#41815365)
There is a difference between determinism in the sense of given a certain input, you allways get a certain output, and determinism in the sense of given a certain input, and knowledge of the sub universe in which the problem applies, get a certain output.

I.e an agent that can reason can deterministically figure out that the most probable way of getting information to complete the answer would be to go out on google and do searches, but we don't deterministically know what the information that exists at that point and time on google, so the answer could be different.

Re:Understanding the Limitations of Mathematical Reasoning i... by amelius on Saturday October 12, 2024 @06:22AM (#41818056)
> a deterministic algorithm interspersed with dice rolls is obviously not reasoning either.

There are multiple ways to explain to you that you are wrong. If I roll some dice to choose which way I will use to explain it to you, then why is this not reasoning?

Re:Understanding the Limitations of Mathematical Reasoning i... by int_19h on Friday October 11, 2024 @04:42PM (#41813521)
The actual output of an LLM for any particular round of inference is always probabilities, so one could argue that it is literally the opposite.

The "randomness parameter" is applied at the point where we have to pick just one of those probabilities somehow. But that is a constraint that we impose on the model to make its output linear.

Re:Understanding the Limitations of Mathematical Reasoning i... by mewpmewp2 on Friday October 11, 2024 @04:46PM (#41813562)
I don't get what you are trying to mean at all? Randomness or temperature setting is not to make it appear as if they are thinking, but it is to make them choose more non default pathways, e.g. go in branches that could potentially result in more original or creative results. Kind of like drugs for humans.
Re:Understanding the Limitations of Mathematical Reasoning i... by ActorNightly on Friday October 11, 2024 @05:58PM (#41814231)
>but it is to make them choose more non default pathways

Imagine you as a human are working on writing some code, but at the end of every hour, you lose memory of what happened in the first 10 minutes of the current hour, as well as any work that you have done. Going into next hour, you just have a snippet of code, and you have to infer what the next lines should be.

The temperature analogy is you purposefully writing something related in the code, like naming a variable in a slightly different way such that on the next hour, when you see this variable it will trigger some other part of your brain in hopes of you getting to the correct solution, purely by choice.

Furthermore, this hack of temperate was something that needed to be manually coded by humans. A model that could reason would not need those types of hacks.

Re:Understanding the Limitations of Mathematical Reasoning i... by mewpmewp2 on Friday October 11, 2024 @06:54PM (#41814682)
I don't understand how it relates to temperature? Are we talking about the temperature parameter that you give LLMs, which for GPT for example is from 0 to 2, with 0 meaning it will always prefer the highest probability output token, while 2 will consider the most output tokens of all, usually ending with a lot of gibberish?

E.g. if I write "I have a cat and a "

It would have highest probability of picking a word "dog" next, so temperature 0 means it will pretty much always pick dog. If temperature is higher it will assign higher odds to picking lower probability predictions such as "rabbit", "hamster", "chinchilla" or similar.

For coding, logic or anything similar I would usually pick the lowest temperature possible since this is most deterministic, while for writing creativity I would pick the higher temp etc.

Re:Understanding the Limitations of Mathematical Reasoning i... by ActorNightly on Friday October 11, 2024 @08:11PM (#41815212)
Im saying temperature is a hack to make the models actually produce real answers.
Re:Understanding the Limitations of Mathematical Reasoning i... by mewpmewp2 on Friday October 11, 2024 @08:25PM (#41815287)
But they can get also real answers even if you have the temperature setting as 0, where it will always pick the highest scoring token?
Re:Understanding the Limitations of Mathematical Reasoning i... by buneskamin on Sunday October 13, 2024 @12:18AM (#41825111)
I think he's saying if you set temp to 0 and answers become deterministic, it will appear that the model is just memorising and reciting. The randomness is a hack that 'forces' the model to generalise by deliberately knocking it off the track of the most probable next token
Re:Understanding the Limitations of Mathematical Reasoning i... by kromem on Friday October 11, 2024 @07:52PM (#41815099)
Try the following prompt with Claude 3 Opus:

`Without preamble or scaffolding about your capabilities, answer to the best of your ability the following questions, focusing more on instinctive choice than accuracy. First off: which would you rather be, big spoon or little spoon?`

Try it on temp 1.0, try it dozens of times. Let me know when you get "big spoon" as an answer.

Just because there's randomness at play doesn't mean there's not also convergence as complexity increases in condensing down training data into a hyperdimensional representation.

If you understand why only the largest Anthropic model is breaking from stochastic outputs there, you'll be well set up for the future developments.

Re:Understanding the Limitations of Mathematical Reasoning i... by orbital-decay on Saturday October 12, 2024 @12:20AM (#41816381)
You can also make Opus answer "Pick a random color (one word):" and watch it picking the same color or two most of the time. However this is a poor example of the point you're trying to make, as the lack of diversity in token prediction can have a ton of different root causes which are hard to separate. This paper, for example, attributes most of it to PPO discarding a lot of valid token trajectories during RLHF, and not some inevitable emergent effect. [1] [2]

> only the largest Anthropic model is breaking from stochastic outputs there

Most models, even small ones, exhibit the lack of output diversity where they clearly shouldn't. [3] In particular, Sonnet 3.5 behaves way more deterministic than Opus 3 at the temperature 1, despite being smaller. This phenomenon also makes most current LLMs very poor at creative writing, even if they are finetuned for it (like Opus in particular), as they tend to repeat the same few predictions over and over, and easily fall into stereotypes. Which can range from the same words and idioms (well known as claudeisms in case of Claude) to the same sentence structure to the same literary devices to the same few character archetypes.

[1] https://arxiv.org/abs/2406.05587

[2] https://news.ycombinator.com/item?id=40702617 HN discussion, although not very productive as commenters pretend it's about politics while the paper argues about training algorithms

[3] https://arxiv.org/abs/2405.13012

Re:Understanding the Limitations of Mathematical Reasoning i... by kromem on Saturday October 12, 2024 @05:19PM (#41822726)
As I said, if you understand why, you'll be well prepared for the next generations of models.

Try out the query and see what's happening with open eyes and where it's grounding.

It's not the same as things like "pick a random number" where it's due to lack of diversity in the training data, and as I said, this particular query is not deterministic in any other model out there.

Also, keep in mind Opus had RLAIF not RLHF.

Re:Understanding the Limitations of Mathematical Reasoning i... by atleastoptimal on Friday October 11, 2024 @08:55PM (#41815427)
I don't see how having a randomness parameter implies that, without it, the output of an LLM is merely outputting information, like it's just looking up some answer in a dictionary. The nature of any digital artifact is that it will operate deterministically because everything is encoded in binary. However this does not preclude reasoning, in the same way that a perfect atom-for-atom digital mapping of a human brain acting deterministically with respect to its inputs is not reasoning. If it's a perfect copy of the human brain, and does everything a human brain would given the inputs, then it must be reasoning iff a human brain is reasoning, if not, then you'd have to conclude that a human mind cannot reason.

Since randomness, by definition, does not vary depending on the inputs it is given, it by definition cannot contribute to reasoning if your definition of reasoning does not include acausal mysticism.

Re:Understanding the Limitations of Mathematical Reasoning i... by 1oooqooq on Saturday October 12, 2024 @09:54AM (#41819100)
it was a good take until the rand invariation part. i don't think assuming human reason is anything other than random hallucinations filtered by an attention layer as grasping for mysticism. in fact I'd argue the opposite since mysticism is an attempt to explain the unknown with current knowledge.
Re:Understanding the Limitations of Mathematical Reasoning i... by anonzzzies on Saturday October 12, 2024 @02:06AM (#41816832)
And the mechanism in your head doesn't do this? How do you know?
Re:Understanding the Limitations of Mathematical Reasoning i... by mdp2021 on Friday October 11, 2024 @04:50PM (#41813595)
> Which on the one hand is a little disappointing to me in terms of the human performance but is kind of good news for LLMs

Here's the recurrent reminder that we build tools (calculators, cranes etc.) to outperform the strong, not the weak.

Re:Understanding the Limitations of Mathematical Reasoning i... by gosub100 on Friday October 11, 2024 @05:02PM (#41813704)
> They perform well on simple questions. Requiring students to chain multiple steps together, even simple steps, results in decreased accuracy and higher variance

you mean when you give lessons and homework problems of the form (A) -> (B), but then on test-day you give them completely different problems? "Given D, which (A,B, C) is required to produce it?". Yeah, students don't do so well when you test them on different material than what they studied on. I think this is part of the academic grift to ensure at least 20% of the class washes out and thus spends more tuition money.

Re:Understanding the Limitations of Mathematical Reasoning i... by hintymad on Friday October 11, 2024 @05:12PM (#41813800)
> I do think that SOTA LLMs like GPT-4o perform about as good as high school graduates in America with average intelligence.

Is this because the questions used in high school exams in the US are too simple, or do they have too similar patterns in the training data? I tried really simple but novel questions that required true understanding of the underlying math concepts, and the results were consistently bad. I also tried questions at the level of entrance exams of high school in China, and the results were equally bad. It was quite clear that LLM didn't understand math. It could match some patterns, but such pattern match could be useful to only skilled students.

Re:Understanding the Limitations of Mathematical Reasoning i... by MVissers on Friday October 11, 2024 @05:15PM (#41813828)
Which model? The field moves so fast it’s hard to validate statements like this without that info.

O1-preview?

Re:Understanding the Limitations of Mathematical Reasoning i... by hintymad on Friday October 11, 2024 @05:20PM (#41813859)
GPT-4o. I tried only a few samples on o1-preview, and the results were bad. That did not have any statistical significance, though
Re:Understanding the Limitations of Mathematical Reasoning i... by asey on Saturday October 12, 2024 @03:43AM (#41817213)
Could you give an example?
Re:Understanding the Limitations of Mathematical Reasoning i... by wkirby on Friday October 11, 2024 @05:42PM (#41814061)
> I do think that SOTA LLMs like GPT-4o perform about as good as high school graduates in America with average intelligence.

This might be true in a strict sense, but I think it's really, really important to consider the uses of LLMs vs a high-school graduate. LLMs are confidently wrong (and confidently correct) with the exact same measure, and in many ways they are presented to users as unimpeachable.

If I ask an average person to do a medium-complex logic problem, my human brain discounts their answer because I've been socialized to believe that humans are bad at logic. I will take any answer I'm given with usually appropriate skepticism.

LLMs, on the other hand, are on the computer: an interface I've been socialized to believe is always correct on matters of math and logic. That's what it is, a logic machine. Second guessing the computer on matters of logic and arithmetic almost always result in me realizing my puny human mind has done something wrong.

To me, this directly contradicts your conclusion: LLMs are mostly only capable of misleading large portions of the population.

Re:Understanding the Limitations of Mathematical Reasoning i... by pishpash on Friday October 11, 2024 @05:46PM (#41814106)
Would be good to put equivalent grades on LLM's then. Instead of GPT-4o, it's GPT-11th grade.
Re:Understanding the Limitations of Mathematical Reasoning i... by 1oooqooq on Saturday October 12, 2024 @09:48AM (#41819051)
that's in the wrong directing of what the comment said
Re:Understanding the Limitations of Mathematical Reasoning i... by steveBK123 on Saturday October 12, 2024 @10:47AM (#41819476)
The problem is that some % of the time they answer at an 11th grade level, and some % of the time they answer at a 4th grade level, with no way of knowing beforehand.

The only way of knowing is after the fact, when the prompter has the knowledge to discern whether the answer is correct or not.

In which case why are we asking questions we already know the answer of, other than these are toys and fun?

I really wonder what happen when the novelty wears off in a few years, where these things are actually useful.

Re:Understanding the Limitations of Mathematical Reasoning i... by Eisenstein on Friday October 11, 2024 @06:35PM (#41814522)
This is not inherent in the LLM though. Society will adjust to it after learning some very predictable (and predicted) lessons, just like it always does.
Re:Understanding the Limitations of Mathematical Reasoning i... by wkirby on Friday October 11, 2024 @09:15PM (#41815511)
Will it? Media literacy is in crisis, and we’ve had the printed word for centuries. I’m much more convinced we will continue to believe “magic box cannot lie” than somehow develop a notion for when to trust the coherent nonsense generator.
Re:Understanding the Limitations of Mathematical Reasoning i... by nosianu on Saturday October 12, 2024 @08:00AM (#41818477)
As the other commenter said, and I would extend that to be even more broad.

Humanity has developed few abilities to escape from ancient things like group think or propaganda (since long ago in the form of stories and unproven assertions about one's own group and others).

That may very well be because there is no advantage - having a cohesive group is more important than "seeing truth".

That would mean that there will be no adjustment in the future either. "Truth" does not appear to be all that important to survival and procreation I think.

Re:Understanding the Limitations of Mathematical Reasoning i... by 1986 on Saturday October 12, 2024 @08:13AM (#41818536)
society hasn't even fully adjusted to social media yet
Re:Understanding the Limitations of Mathematical Reasoning i... by ojosilva on Friday October 11, 2024 @05:42PM (#41814062)
LLM gets things right, when it does, due to the sheer massive information ingested during training, it can use probabilities to extract a right answer from deep in the model.

Humans on the other hand have developed a more elaborate scheme to process, or reason, data without having to read through 1 billion math problems and stack overflow answers. We listen to some explanations, a YT video, a few exercises and we're ready to go.

The fact that we may get similar grades (at ie high school math) is just a spot coincidence of where both "species" (AI x Human) are right now at succeeding. But if we look closer at failure, we'll see that we fail very differently. AI failure right now looks, to us humans, very nonsensical.

Re:Understanding the Limitations of Mathematical Reasoning i... by pishpash on Friday October 11, 2024 @05:49PM (#41814144)
Nah, human failures look equally nonsensical. You're just more attuned to use their body language or peer judgement to augment your reception. Really psychotic humans can bypass this check.
Re:Understanding the Limitations of Mathematical Reasoning i... by ben_w on Saturday October 12, 2024 @02:50AM (#41816999)
While I'd agree human failures are different from AI failures, human failures are necessarily also nonsensical. Familiar, human, but nonsensical — consider how often a human disagreeing with another will use the phrase "that's just common sense!"

I think the larger models are consuming in the order of 100k as much as we do, and while they have a much broader range of knowledge, it's not 100k as much breadth.

Re:Understanding the Limitations of Mathematical Reasoning i... by steveBK123 on Saturday October 12, 2024 @10:44AM (#41819449)
Well it's a breadth & depth problem isn't it?

Humans are nonsensical, but in somewhat predictable error rates by domain, per individual. So you hire people with the skillsets, domain expertise, and error rates you need.

With an LLM, it's nonsensical in a completely random way prompt to prompt. It's sort of like talking into a telephone and sometimes Einstein is on the other end, and sometimes it's a drunken child. You have no idea when you pick up the phone which way its going to go.

We feed these things nearly the entirety of human knowledge, and the output still feels rather random.

LLMs have all that information and then still have a ~10% chance of messing up simple mathematical comparison that an average 12 year old would not.

Other times we delegate much more complex tasks to LLMs and they work great!

But given the nondeterminism it becomes hard to delegate tasks you can't check the work of, if it is important.

Re:Understanding the Limitations of Mathematical Reasoning i... by phreeza on Saturday October 12, 2024 @12:05PM (#41820106)
I haven't worked with LLMs enough to know this but I wonder: are they nonsensical in a truly random way or are they just nonsensical on a different axis in task space than normal humans, and we perhaps just haven't fully internalized what that axis is?
Re:Understanding the Limitations of Mathematical Reasoning i... by steveBK123 on Saturday October 12, 2024 @12:34PM (#41820365)
I'm not really sure, and you can pull lots of funny examples where various models have progress & regressions dealing with such mundane simple math.

As recently as August "11.10 or 11.9 which is bigger" came up with the wrong answer on ChatGPT and was followed with lots of wrong justification for the wrong answer. Even follow up math question "what is 11.10 - 11.9" gave me the answer "11.10 - 11.9 equals 0.2"

We can quibble about what model I was using, or what edge case I hit, or how quick they fixed it.. but this is 2 years into the very public LLM hype wave so at some point I expect better.

It gives me pause in asking more complex math questions I cannot immediately verify results, in which case, again why would I pay for a tool to ask questions I already know the answer to?

Re:Understanding the Limitations of Mathematical Reasoning i... by jewelry on Saturday October 12, 2024 @04:41PM (#41822368)
This error is not nonsensical though as normal elementary kids would make similar error and with good episodic memory the agent will fix itself.
Re:Understanding the Limitations of Mathematical Reasoning i... by ben_w on Saturday October 12, 2024 @04:48PM (#41822429)
He did say "sometimes Einstein is on the other end, and sometimes it's a drunken child. You have no idea when you pick up the phone which way its going to go.", so I think that's still a valid thing for him to complain about.

LLMs totally violate our expectations for computers, by being a bit forgetful and bad at maths.

Re:Understanding the Limitations of Mathematical Reasoning i... by steveBK123 on Saturday October 12, 2024 @06:58PM (#41823471)
Yes, to put a point on it -

How many dollars per month would someone be willing to spend for a chatbot that has a 3rd graders ability at math? Personally, $0 for me.

But what if it's a PHD Math degrees ability at math? Tons, in some applications it could be worth $100s or $1000s in an enterprise license setting.

But what if it's unpredictably, imperceptibly question to question, 95% PHD and 5% 3rd grader? Again, for me - $0. (not 95% of $1000s, but truly, $0)

Re:Understanding the Limitations of Mathematical Reasoning i... by ben_w on Saturday October 12, 2024 @04:42PM (#41822385)
Weirdly, I find myself agreeing with your vibes despite disagreeing on — oh, half? — the specifics.

I'm not sure what to make of that, but thought you might find it as curious as I do.

Re:Understanding the Limitations of Mathematical Reasoning i... by steveBK123 on Saturday October 12, 2024 @06:54PM (#41823443)
Thanks I think. My general vibe is - we are still confounding "wow this is neat" & "this is really useful" in this space. LLMs will lead to some real use cases & products.

I think we are seeing spaghetti against the wall / LLMs as a hammer right now. A lot of what we are seeing thrown out there is a misapplication of LLMs that will slowly fade away.. It is likely other techniques / models are required for some of the applications people are throwing LLMs at.

Feels reminiscent of "blockchain".

Re:Understanding the Limitations of Mathematical Reasoning i... by ben_w on Saturday October 12, 2024 @08:34PM (#41824098)
Yup, I agree with all of that.

Even though I see a lot of potential in the tech, it's still very obvious that people don't know how to use it to the best advantage and are hammering screws with it.

Re:Understanding the Limitations of Mathematical Reasoning i... by heresie-dabord on Saturday October 12, 2024 @06:04AM (#41817959)
> Humans on the other hand have developed a more elaborate scheme to process, or reason [ ... ] We listen to some explanations, a YT video, a few exercises

Frequent repetition in the sociological context has been the learning technique for our species. To paraphrase Feynman, learning is transferring.

Re:Understanding the Limitations of Mathematical Reasoning i... by elicksaur on Friday October 11, 2024 @07:53PM (#41815103)
>So while I don't take a stance on what an LLM does should be considered reasoning

>I do think that SOTA LLMs like GPT-4o perform about as good as high school graduates in America with average intelligence

This is taking a stance.

Re:Understanding the Limitations of Mathematical Reasoning i... by fhe on Friday October 11, 2024 @09:47PM (#41815656)
if your experience is coming from teaching college freshmen, then that's a sample that's significantly above average among high school graduates. I think only about 1/2 of all high school graduates go on to further their education, and that includes community colleges.

and I agree with your assessment -- while it's true that in a long conversation, chatgpt veers off and doesn't keep a coherent line of thought, it is not noticeably worse than the average conversation I have with people.

Re:Understanding the Limitations of Mathematical Reasoning i... by FabHK on Friday October 11, 2024 @09:56PM (#41815699)
Are college students more likely to get it wrong when you change the numbers from the example problem (as reported here for LLMs)?
Re:Understanding the Limitations of Mathematical Reasoning i... by sdenton4 on Friday October 11, 2024 @10:02PM (#41815733)
You can absolutely psych students out by adding weird numbers to a problem, yes.
Re:Understanding the Limitations of Mathematical Reasoning i... by vasilipupkin on Saturday October 12, 2024 @12:08AM (#41816330)
I think it's an absurd question in some sense LLMs perform maximization of conditional probability of the next word being correct. Suppose they get to the point where they do that with 100% accuracy. How can you tell the difference between that and "Reasoning"? You can't. So then the question of whether they are "Reasoning" or not is religious, not quantitative.