[PheonixPharts]

> Now, is it 10k examples? No, but I think it was on the order of hundreds, if not thousands.

I have kids so I'm presuming I'm allowed to have an opinion here.

This is ignoring the fact that babies are not just learning labels, they're learning the whole of language, motion planning, sensory processing, etc.

Once they have the basics down concept acquisition time shrinks rapidly and kids can easily learn their new favorite animal in as little as a single example.

Compare this to LLMs which can one-shot certain tasks, but only if they have essentially already memorized enough information to know about that task. It gives the illusion that these models are learning like children do, when in reality they are not even entirely capable of learning novel concepts.

Beyond just learning a new animal, humans are able to learn entirely new systems of reasoning in surprisingly few examples (though it does take quite a bit of time to process them). How many homework questions did your entire calc 1 class have? I'm guessing less than 100 and (hopefully) you successfully learned differential calculus.

[educasean]

> kids can easily learn their new favorite animal in as little as a single example

Until they encounter a similar animal and get confused, at which point you understand the implicit heuristic they were relying on. (Eg. They confused a dairy cow as a zebra, which means their heuristic was a black-and-white quadrupedal)

Doesn't this seem remarkably close to how LLMs behave with one-shot or few-shot learning? I think there are a lot more similarities here than you give it credit for.

Also, I grew up in South Korea where early math education is highly prioritized (for better or for worse). I remember having to solve 2 dozen arithmetic problems every week after school with a private tutor. Yes, it was torture and I was miserable, but it did expose me to thousands more arithmetic questions than my American peers. All that misery paid off when I moved to the U.S. at the age of 12 and realized that my math level was 3-4 years above my peers. So yes, I think human intelligence accuracy also does improve with more training data.

[interloxia]

Not many zebras where I live but lots of little dogs. Small dogs were clearly cats for a long time no matter what I said. The training can take a while.

[pea]

My favourite part of this is when they apply their new words to things that technically make sense, but don't. My daughter proudly pointed at a king wearing a crown as "sharp king" after learning about knives, saws, etc.

[dimask]

> How many homework questions did your entire calc 1 class have? I'm guessing less than 100 and (hopefully) you successfully learned differential calculus.

Not just that: people learn mathematics mainly by _thinking over and solving problems_, not by memorising solutions to problems. During my mathematics education I had to practice solving a lot of problems dissimilar what I had seen before. Even in the theory part, a lot of it was actually about filling in details in proofs and arguments, and reformulating challenging steps (by words or drawings). My notes on top of a mathematical textbook are much more than the text itself.

People think that knowledge lies in the texts themselves; it does not, it lies in what these texts relate to and the processes that they are part of, a lot of which are out in the real world and in our interactions. The original article is spot on that there is no AGI pathway in the current research direction. But there are huge incentives for ignoring this.

[naasking]

> Not just that: people learn mathematics mainly by _thinking over and solving problems_, not by memorising solutions to problems.

I think it's more accurate to say that they learn math by memorizing a sequence of steps that result in a correct solution, typically by following along with some examples. Hopefully they also remember why each step contributes to the answer as this aids recall and generalization.

The practice of solving problems that you describe is to ingrain/memorize those steps so you don't forget how to apply the procedure correctly. This is just standard training. Understanding the motivation of each step helps with that memorization, and also allows you to apply that step in novel problems.

> The original article is spot on that there is no AGI pathway in the current research direction.

I think you're wrong. The research on grokking shows that LLMs transition from memorization to generalized circuits for problem solving if trained enough, and parametric memory generalizes their operation to many more tasks.

They have now been able to achieve near perfect accuracy on comparison tasks, where GPT-4 is barely in the double digit success rate.

Composition tasks are still challenging, but parametric memory is a big step in the right direction for that too. Accurate comparitive and compositional reasoning sound tantalizingly close to AGI.

[imtringued]

Every time I see people online reduce the human thinking process to just production of a perceptible output, I start questioning myself, whether somehow I am the only human on this planet capable of thinking and everyone else is just pretending. That can't be right. It doesn't add up.

The answer is that both humans and the model are capable of reasoning, but the model is more restricted in the reasoning that it can perform since it must conform to the dataset. This means the model is not allowed to invest tokens that do not immediately represent an answer but have to be derived on the way to the answer. Since these thinking tokens are not part of the dataset, the reasoning that the LLM can perform is constrained to the parts of the model that are not subject to the straight jacket of training loss. Therefore most of the reasoning occurs in-between the first and last layers and ends with the last layer, at which point the produced token must cross the training loss barrier. Tokens that invest into the future but are not in the dataset get rejected and thereby limit the ability of the LLM to reason.

[TeMPOraL]

> People think that knowledge lies in the texts themselves; it does not, it lies in what these texts relate to and the processes that they are part of, a lot of which are out in the real world and in our interactions

And almost all of it is just more text, or described in more text.

You're very much right about this. And that's exactly why LLMs work as well as they do - they're trained on enough text of all kinds and topics, that they get to pick up on all kinds of patterns and relationships, big and small. The meaning of any word isn't embedded in the letters that make it, but in what other words and experiences are associated with it - and it so happens that it's exactly what language models are mapping.

[whyever]

I think there is a component of memorizing solutions. For example, for mathematical proofs there is a set of standard "tricks" that you should have memorized.

[aamar]

> How many homework questions did your entire calc 1 class have? I'm guessing less than 100…

I’m quite surprised at this guess and intrigued by your school’s methodology. I would have estimated >30 problems average across 20 weeks for myself.

My kids are still in pre-algebra, but they get way more drilling still, well over 1000 problems per semester once Zern, IReady, etc. are factored in. I believe it’s too much, but it does seem like the typical approach here in California.

[com2kid]

I preferred doing large problem sets in math class because that is the only way I felt like I could gain an innate understanding of the math.

For example after doing several hundred logarithms, I was eventually able to do logs to 2 decimal places in my head. (Sadly I cannot do that anymore!) I imagine if I had just done a dozen or so problems I would not have gained that ability.

[com2kid]

> This is ignoring the fact that babies are not just learning labels, they're learning the whole of language, motion planning, sensory processing, etc.

Sure, but they learn a lot of labels.

> How many homework questions did your entire calc 1 class have? I'm guessing less than 100

At least 20 to 30 a week, for about 10 weeks of class. Some weeks were more, and I remember plenty of days where we had 20 problems assigned a day.

Indeed, I am a huge fan of "the best way to learn math is to do hundreds upon hundreds of problems", because IMHO some concepts just require massive amounts of repetition.

[p1esk]

illusion that these models are learning like children do, when in reality they are not even entirely capable of learning novel concepts

Now imagine how much would your kid learn if the only input he ever received was a sequence of words?

[_flux]

Are you saying it's not fair for LLMs, because of the way they are taught is different?

The difference is that we don't know better methods for them, but we do know of better methods for people.

[_carbyau_]

Two other points - I've also forgotten a bunch, but also know I could "relearn" it faster than the first time around.

To continue your example, I know I've learned calculus and was lauded at the time. Now I could only give you the vagaries, nothing practical. However I know if I was pressed, I could learn it again in short order.

[TeMPOraL]

> This is ignoring the fact that babies are not just learning labels, they're learning the whole of language, motion planning, sensory processing, etc.

Yes. All that learning is feeding off one another. They're learning how reality works. Every bit of new information informs everything else. It's something that LLMs demonstrate too, so it shouldn't be a surprising observation.

> Once they have the basics down concept acquisition time shrinks rapidly

Sort of, kind of.

> and kids can easily learn their new favorite animal in as little as a single example.

Under 5 they don't. Can't speak what happens later, as my oldest kid just had their 5th birthday. But below 5, all I've seen is kids being quick to remember a name, but taking quite a bit longer to actually distinguish between a new animal and similarly looking ones they already know. It takes a while to update the classifier :).

(And no, they aren't going to one-shot recognize an animal in a zoo that they saw first time on a picture hours earlier; it's a case I've seen brought up, and I maintain that even most adults will fail spectacularly at this test.)

> Compare this to LLMs which can one-shot certain tasks, but only if they have essentially already memorized enough information to know about that task. It gives the illusion that these models are learning like children do, when in reality they are not even entirely capable of learning novel concepts.

Correct, in the sense that the models don't update their weights while you use them. But that just means you have to compare them with ability of humans to one-shot tasks on the spot, "thinking on their feet", which for most tasks makes even adults look bad compared to GPT-4.

> How many homework questions did your entire calc 1 class have? I'm guessing less than 100 and (hopefully) you successfully learned differential calculus.

I don't believe someone could learn calc in 100 exercises or less. Per concept like "addition of small numbers", or "long division", or "basic derivatives", or "trivial integrals", yes. Note that in-class exercises count too; learning doesn't happen primarily by homework (mostly because few have enough time in a day to do it).

[shkkmo]

> But that just means you have to compare them with ability of humans to one-shot tasks on the spot, "thinking on their feet", which for most tasks makes even adults look bad compared to GPT-4.

This simply is not true as stated in the article. ARC-AGI is a one-shot task test that humans reliably do much, much better on than any AI model.

> I don't believe someone could learn calc in 100 exercises or less.

I learned the basics of integration in a foreign language I barely understood by watching a couple of diagrams get drawn out and seeing far less than 100 examples or exercises.