1. Replacing pass/fail accuracy with smoother alternatives (e.g token edit distance) could be a terrible proxy for skill, depending on the task.

2. Even by the authors' metrics, they _still_ find a few potentially emergent abilities.

3. Hindsight is 20-20. Yes, we can revisit the data and fiddle until we find transforms that erase emergence from aptitude plots. The fact is, folk used commonplace test accuracy measurements, and the results were unpredictable and surprising. That's the true notable phenomenon.

I think there's value in the paper. Just...don't take its conclusions too far.

- Test 1: First he can just draw squiggles on the math test

- Test 2: Then he can do arithmetic correctly

- Test 3: He fails on the last details on the algebraic calculation.

Now, event though he fails on all tests, any reasonable parent would see that he improving nicely, and would be able to work in his chosen field in a year or so.

Or alternatively, if we talk about AI, we can set the Test as a threshold, and we see the results are continuously trending upwards, and we can expect the curve to breach the threshold in the future.

That is; measuring improvement, instead of pass/fail, allows one to predict when we might be able to use the AI for something.

When you actually do these millions of tests, I don't think it really matters what the exact success metric is - an AI which is 'closer to correct, but still wrong' on one test will still get more tests correct overall on the dataset of millions of tests.

I'm not saying LLM will achieve AGI (I don't know if it will, or when it does we'll even know). But somehow people seem to be judging AI's intelligence with this simple procedural:

1. Find a task that AI can't do perfectly. 2. Gotcha! AI isn't intelligent.

It just makes me question humans' intelligence if anything.

> Human beings do arithmetic problems wrong all the time

Humans built cars and planes and massive ships before we had calculators, that requires a massive amount of calculations that are all perfect to be possible. Humans aren't bad at getting calculations right, they are just a bit slow. Today humans are bad since we don't practice it, not because we can't. LLMs can't do that today, can learn and can't is a massive difference.

Compare that to understanding arbitrary base64-encoded strings; that's much harder for humans to do without tools. Tokenization still isn't _the_ greatest fit for it, but it's a lot more tractable, and LLMs can do it no problem. Even understanding ASCII art is impressive, given they have no innate idea of what any letter looks like, and they "see" fragments of each letter on each line.

So I'm not sure if I agree or disagree with you here. I'd say LLMs in fact have very impressive capabilities to learn logical structures. Whether grammar is the problem isn't clear to me, but their internal representation format obviously and enormously influences how much harder seemingly trivial tasks become. Perhaps some efforts in hand-tuning vocabularies could improve performance in some tasks, perhaps something different altogether is necessary, but I don't think it's an impossible hurdle to overcome.

The tokens are just the input - the internal representation can be totally different (and that format isn't tokens).

The conversion to a helpful form is required anyway (also lets remember that computers don't work in base 10, and there isn't really a reason to believe that base 10 is inherently great for LLM's either)

    hundreds | tens | ones

        1        2      3
    +   2        1      5
    -----------------------
        3        3      8

unoDOOOOS(third) {}{}{} [512354]_ = three"ate

* replace {}{}{} with addition, {}{} is subtraction unless followed by three spaces in which case it's also addition * translate and correct any misspellings * [512354] look up in your tables * _ is 15 * dotted lines indicate repeated numbers

Technically they're doing the same thing. One we would assume is harder to learn the fundamental concepts from.

The issue is not the fact that the model "thinks or doesn't think in tokens". The model is forced at the final sampling/decoding step to convert it's latent back into tokens, one token at a time.

The models are fully capable of understanding the premise that they should "output a 5-7-5 syllable Haiku", but from the perspective of a model trying to count its own syllables, this is not possible, as its own vocabulary is tokenized in such a way that not only does the model not have direct phonetic information within the dataset, but it literally has no analogue for how humans count syllables (measuring mouth drops). Models can't reason about the number of characters or even tokens used in a reply too for the same exact reason too.

The person you're replying to broadly is right, and you are broadly wrong. The internal format does not matter when the final decoding step forces a return of tokenization. Please actually use these systems rather than pontificating about them online.

That'd depend on the design of the neural net and training objective.

It's certainly not something that comes naturally to an LLM which neither has numbers as inputs or outputs, nor is trained with an arithmetic objective.

Consider inputting "12345 * 10" into GPT-4. First thing it is going to do is tokenize the input, then embed these tokens, and these embedding vectors are then the starting point of what the transformer has to work with...

https://platform.openai.com/tokenizer

You can use OpenAI's tokenizer tool (above) to see how it represents the "12345 * 10" character sequence as tokens, and the answer is that it breaks it down into the token ID sequence [4513, 1774, 353, 220, 605]. The [4513, 1774] represents the character sequence "12345", and "605" represents the character sequence "10".

These token ID's will then be "embedded", which means mapping them to points in a very high dimensional space (e.g. 4096-D for LLaMA 7B), so each of those token ID's becomes a vector of 4096 1's and 0's, and these vectors are what the model itself actually sees as input.

So, for "12345 * 10", what the model sees during training is that whenever it sees V1 V2 V3 V4 it should predict V5, where V1-5 are those 4096-D input token embeddings. The model has no idea what any of these mean - they might represent "the cat sat on the mat" for all it knows. They are just a bunch of token representations, and the LLM is just trying to find patterns in the examples it is given to figure out what the preferred "next token" output is.

So, could you build (and train) a neural net to multiply, or add, two numbers together? Yes you could, if that is all you want to do. Is that what an LLM is? No, an LLM is a sequence predictor, not an NN designed and trained to do arithmetic, and all that is inside an LLM is a transformer (sequence-to-sequence predictor).

To solve this you would need some sub networks that are pretrained to handle numbers and math and other domains, and then you start training the giant LLM it can find and connect those things. But we don't know how to do that well yet afaik, and I bet all the big players has already tested things like that. As you say adding capabilities to the same model is hard.

Humans are good at the former, but not the latter.

Speak for yourself. Even though I've always been strong at my conceptual understanding and problem solving in math, I always found it difficult to avoid arithmetic mistakes on pen and paper and could never understand why I was assessed on that. I could have done so much better in high-school math if I was allowed to use a programmable computer for the calculations.

And I think it's the same for LLMs, we should assess them on doing the arithmetic in a single pass, but rather on writing the code to perform the calculation, and responding based on that.

But I do acknowledge that there are probably some or many humans that maybe can't reach that level of reliability with arithmetics.

This is why prompting LLM's to show their steps works so well, it makes them work through the problem "in their head" more efficiently, rather than just spit out an answer.

However, you can give LLM's external access to tools. Ask GPT4 a particularly challenging math problem, and it will write a python script and run it to get a solution. That is an LLM's "pen and paper".

No, that is an LLM's calculator or programming, it doesn't actually do the steps when it does that. When I use pen and paper to solve a problem I do all steps on my own, when I use a calculator or a programming language the tool does a lot of the work.

That difference is massive, since when I use a calculator that doesn't help me learn numbers and how they interact and how algorithms works, while if I do the steps myself I do. So getting an LLM that can reliably execute algorithms like us humans can is probably a critical step towards making them as reliable and smart as humans.

I do agree though that if LLMs could keep a hidden voice they used to reason before writing they could do better, but that voice being shown to the end user shouldn't make the model dumber, you would just see more spam.

Maybe we should be giving the LLM's MS paint instead of python to work out problems? There is nothing unique or "human" about running through a long division problem, it is ultimately just an algorithm that is followed to arrive at a solution.

Yes, which is why we should try to make LLMs do them and that way open them up to learn much more complex understanding of algorithms and instructions that humans has yet to build a tool for.

> You need to do a lot of "steps" to write a program that solves your question. Debatably even more steps and more complexity than using pen and paper.

What does this have to do with anything? I am highlighting a core deficiency in how LLMs are able to reason, you saying that what they currently do is harder doesn't change the fact that they are bad at this sort of reasoning.

And no, making such a program doesn't require more steps or understanding. You Google for a solution and then paste in your values, that is much easier to teach a kid than to teach them math. I am sure I can teach almost any 7 year old kid to add two numbers by changing values in a python program in about an hour, much faster than they could learn math the normal way. Working with such templates is the easiest task for an LLM, what we want is to try to get the LLM to do things that is harder for it.

"I have a problem for you to solve. Muffins sell for $3/each. rick bakes 30 muffins a day. Tom bakes 2 muffins monday, 4 tuesday, 6 wednsdays, up to 14 on sunday. On days which tom and jerry combined bake more than 41 muffins, the price of the muffins drops to $2.50. How much total revenue do rick and tom take in during a full week, combined."

Please tell me how ChaptGPT4 writing a script to solve that is not logical reasoning, while a human pulling out pen and paper to do it is...

I changed the prompt a bit (made all the numbers 3-4 digits) and gpt-4 answered with this, it just made up numbers for the days that you didn't add numbers for so it failed before it even came to arithmetics. Here is what it said, after I said this about tom "Tom bakes 2911 muffins monday, 491 tuesday, 699 wednsdays, up to 149 on sunday.", it just assumed sundays number was for all other weekdays not given a human wouldn't do that, and it missed the "up to" statement. Maye the large numbers I gave threw it off, but if that is enough to throw it of just shows that it can't really reason.

So thanks for that, more evidence these models are bad at reasoning.

Here is the first part of what it responded with, it is wrong already here:

   First, let's calculate the number of muffins baked by Tom during the week:

   Monday: 2911
   Tuesday: 491
   Wednesday: 699
   Thursday: 149
   Friday: 149
   Saturday: 149
   Sunday: 149

   Let's determine the days when Tom and Rick combined bake more than 4199 muffins:

   Monday: 2911 (Tom) + 3571 (Rick) = 6482
   Tuesday: 491 (Tom) + 3571 (Rick) = 4062
   Wednesday: 699 (Tom) + 3571 (Rick) = 4270

   On Monday, Tuesday, and Wednesday, they bake more than 4199 muffins combined, so the price of the muffins drops to $2851.50 on those days.

Unless of course you didn't realize that tom has a pattern to his baking, at which point to irony becomes palpable.

And on top of that, I am willing to bet if you give me your prompt, I would be able to restructure it in such a way that GPT4 would be able to answer it correctly. More often than not, people are just really bad at properly asking it questions.

I used your exact quote and just changed the numbers, it is still a perfect information problem.

Or, ah right you mean you gave me an imperfect information problem since you assumed the reader would guess those values. Yeah, I read it as a perfect information problem where all values were given, and then you would give the income as a range of possible income values based on how many muffins were baked on Sunday. None of the LLMs I sent it to managed to solve it entirely, it is a pretty easy problem.

Reasonable way to parse your sentence is:

   Monday: 2, Tuesday: 4, Wednesday: 6, Sunday: 0-14, rest: doesn't work so 0

If you didn't say he baked on those days then he didn't bake on those days. The specification is clear. If I say "I will bake 2 muffins on Tuesday and 6 muffins on Sunday" the reasonable interpretation is that I wont bake anything the rest of the days. Why would you assume he baked anything at all those days?

Or if I say "Emily will work Mondays and Thursdays", do you just guess the rest of the days she will work? No, you assume she just works those days.

Is that a standard problem you wrote from memory? Not sure why you would assume there were muffins baked in the days you didn't list.

For example, if I say Tom bakes up to 14 muffins on Sunday, then the reasonable interpretation is that Tom will bake 0-14 muffins on Sunday. Maybe you should write the prompt clearer if you mean something else? Because as written anyone would assume that he didn't bake the other day, and on sundays he baked up to 14 muffins.

Anyway, it failed even with your "up to" interpretation meaning the reader should fill in the values, it still made that math error. But it using your "up to" interpretation there is a huge red flag, since in a real environment nobody would give that kind of information as a riddle with hidden values, you would specify all the values for each day each person worked and the rest you assume the person just isn't working and baked 0 muffins. If the LLM starts to guess values for some patterns and words where it doesn't make sense then it is really unreliable.

Thankfully GPT4 has strong reasoning skills and knew exactly what I meant.

https://chat.openai.com/c/b0ed06f1-c0d3-46a6-b07c-289b328417...

I encourage you to see the chat yourself, and would love to here how it's not reasoning.

Edit: Fixed Link: https://chat.openai.com/share/991ca8af-f735-436f-bfc2-5df929...

you can click the [>_] at the end for the code generated.

Seem to have hit reply cut off

   Unable to load conversation b0ed06f1-c0d3-46a6-b07c-289b328417bb

I don't have a stake in this muffin game, but that's indeed how I interpreted the instructions when reading them.

Had it said "and so on up tp 14 on Sunday" I would assume he baked each day.

No, that's an LLM's Python playground.

An LLM's "pen and paper" is "think step by step" where it gets to see it's own output to keep track of what it is doing.

I'd expect that with appropriate prompting one could get a good model to one/few-shot learn how to do addition this way.

See below which I have just run on GPT4: https://chat.openai.com/share/3adb3aa2-8aec-474f-bdb0-4d761d...

That was how everyone did it back then, it really isn't that hard to do. Most people today never tried to do it so they think it is much harder than it actually is.

To add multi-digit numbers requires short term memory (are we on the units, or tens? was there a carry?), which LLMs don't have, so that's really the issue.

The normal workaround for lack of memory in LLMs is "think step-by-step" to use it's own output (which gets fed back in as an input) as memory, and I'd assume that with appropriate training data and prompting an LLM could learn to do it in this fashion - not just giving the answer, but by giving all the steps.

I suppose in theory LLMs could do limited precision math even without memory, if they did it in a single pass through their stack of transformer layers (96 for GPT-3) - use first few layers to add units and generate carry, next few layers to add tens, etc. I'm not sure how, or even if, one could train them to do it this way though - perhaps via a curriculum training agenda of first adding single digit numbers, then two-digit ones, etc ?

Is it?

LLMs fails to figure out that this is what it has to do, instead it looks like it has a ton of specialized rules to handle arithmetics that results in a lot of errors in the output and are extremely expensive to run.

Because an LLM is a neural network and neural networks contains neural networks. There is nothing stopping it from having an embedded neural network that learned how to do computations well, except an inability to identify such structures and patterns well enough to train for it.

IDK, there was an article posted here about yet another LLM that performed very badly on the math tests because they mistakenly left out all the math training data.

What impressed me was that it could learn any math at all from just 'reading' books or whatever. Though, perhaps, any correct answer could be attributed to pure luck, dunno.

A more serious byproduct of the tendency to talk about machines in anthropomorphic terms is the companion phenomenon of talking about people in mechanistic terminology. The critical reading of articles about computer-assisted learning —excuse me: CAL for the intimi— leaves you no option: in the eyes of their authors, the educational process is simply reduced to a caricature, something like the building up of conditional reflexes. For those educationists, Pavlov’s dog adequately captures the essence of Mankind —while I can assure you, from intimate observations, that it only captures a minute fraction of what is involved in being a dog.

https://www.cs.utexas.edu/users/EWD/transcriptions/EWD09xx/E...

1. Choose a few good blunt instruments we use to gatekeep students on the premise that it tests their "intelligence" (or wait, do we mean subject matter comprehension with this one?)

2. Apply a big ol' machine learning model to those tests

3. Woa it's smarter than a third grader! OMG it's smarter than a lawyer! You guys this must be ASI already!

Rhetoric and selective rigor can justify any perspective. Smart and stupid arguments can be made for any position. Water is wet

I also can't claim to know with certainty whether transformers are going to end up being AGI in some meaningful sense, but I will definitely say that we've created a lot of rubrics for assessing human intelligence that mostly exist for expediency, and a cursory glance at education should tell you there's a lot of Goodhart's Law going on with all of 'em. I know for a fact I can do a damn good job on your average multiple choice test on knowing some etymology and being good at logical elimination, and I can bullshit my way through an essay, both without taking the class, and I view this more as a flaw in the instrument than evidence that I'm a godlike superintelligence that can just know anything without studying it. Humans make a lot of tests that are soft to bullshitting with a little pattern-recognition thrown in

This is definitely not true in the real world. Approximate solutions are often good enough to answer a question.

And ChatGPT is definitely able to get improve its answer by iterating, it just depends on the toughness of the problem. If it's too difficult, no amount of iteration will get it much closer to the correct answer. If it's closer to its reasoning limits, then iterating will help.

Edit: was answering to gp, no idea how my post got here

> But if you stop them just there, an error persists

But humans doesn't stop there when they are making things that needs to be reliably correct. When errors aren't a big deal humans make a lot of errors, but when errors costs life humans become very reliable by taking more time and looking things over. They still sometimes makes mistakes that kills people, but very rarely.

I don't think everything has uncertainty and thresholds to it, especially, when it actually resides outside of a technical implementation.

Somewhere between "it's always wrong" and "it's always right unless the bits got flipped by cosmic rays" we deem the accuracy to be good enough.

Any implementation (or write down etc.) of something can have errors, but the errors are in the implementation and do not give rise to uncertainty outside of the implementation. There is no uncertainty as to what the sum of two integers should be (within the usual mathematics).

Back-of-the-envelope / mental math often works like that, and it's something that humans regularly use, so clearly it has some use.

There may be some emergent features that represent phase changes that are truly difficult, even in retrospect, to predict, but I doubt these are common (does anyone even have a single convincing LLM example?).

I think the more normal case is that higher level capabilities are dependent on multiple lower level ones in ways that may be hard to predict. These smooth improvements in the constituent building blocks may often be there, but you'd have to know where to look (i.e. what the critical building blocks are).

In order to predict emergent capabilities you'd need to have identified ahead of time what the necessary building blocks are, and maybe done some simulation of what level each of those need would need to be at, to support the anticipated/hoped-for behavior.

Of course it's not just about scaling model size and/or data, but also about type and quality of data, where there may be abrupt changes between model versions. It's going to be very difficult ahead of time to analyze what new patterns/manipulations (i.e. building-block capabilities) the model will be able to learn from an updated training set, and therefore what emergent abilities can be built out of those new blocks.

I wonder how often the opposite happens, and model designers have been able to successfully identify that "in order to do X, we need capabilities A, B and C, and in order to get capabilities A, B and C, we need new datasets P & Q" ? In a hypothetical case like that they'd have been able to measure progress towards capability X.

As far as I know before transformers that just didn't happen at all since models couldn't contain that many separate skills without them interfering with each other. This whole thing with models having many high quality capabilities is still pretty new.

But yeah, I think we need something like that and all the best LLMs today probably already do it, but none have said what they do so that is just speculation.

Before LLMs (whether transformer-based or not) most NNs were built to perform single tasks - a single objective, so having multiple higher-level capabilities was essentially out of the question. Of course LLMs nominally only have a single objective too, predict next word, but really they are targeting language.

In the GOFAI era of rule-based symbolic AI there were also some systems/approaches that had multiple skills (e.g. expert systems like CYC, or cognitive architectures like SOAR), so maybe there are forgotten lessons there on decomposability of skills.

Isn’t that the case for most/all emergent behavior? If you change the scale and watch individual water molecules, you’d see them snapping into a crystal structure one by one instead of a sudden emergent block of ice.

[0] https://news.ycombinator.com/item?id=39812315

Different example: If you measure the number of cases of a given virus, it will either spread across the entire globe (R0 > 1, eg. COVID-19) or fail to spread widely (R0 looks binary. But if you were to measure R0 directly, you'd see a gradual increase, and could predict future variants/vaccine efficiencies/etc much more easily.

"Emergent" refers to eg. sigmoids, while "gradual" refers to eg. linear or logarithmic functions.

https://www.animations.physics.unsw.edu.au/jw/superheating.h....

I'm going to steal this for my epitaph, thanks

Mine would currently say:

Por tu culpa!

(this is all your fault)

But depending on the circumstances, I would be also fine with the one above. But very likely I would not care that much anymore ..

And that is even if there is a technical possibility to lower the temperature of every water molecule to -0.0001 simultaneously and demonstrate that it instantly freezes the entire volume in an instant. It'd be irrelevant since none of us live in that lab.

Water never arrives at 0 degrees all at once, so for practical purposes no. Even if it did, you cannot measure the temperature of every water molecule simultaneously to prove it.

Wow, is the title of the submission inaccurate or what!

A significant portion of the world was blindsided by the sudden emergence of "AI", but there were people that knew these things were coming.

This sounds kind of in line with what I gather Sam Altman's thinking is. They feel they can predict a model's reasoning abilities quite well based just on the size of the training compute and data.

Thank you!

What I've noticed is that my loss curves on small models for arithmetic will reach a steady state where they're still getting the answer wrong even if some digits are right. Yes you can keep training but the number of training epochs necessary seems to be inversely correlated exponentially with the model size

So a model with x parameters is going to take n^2 time as long as a model with 2x parameters

At a certain parameter count this basically means it is nigh impossible to get the right answer via training using gradient descent

The more parameters, the easier it is to drive to convergence, which is a real, important metric

At some point the estimated time for the ability to emerge spontaneously becomes greater than a human lifetime of even the lifetime of all humanity. So in the sense that increasing model size makes it tractable... I think it's fair to say that the ability emerges suddenly enough.

If you use a metric where improvement happens suddenly and unpredictably, you can't even estimate how much longer you need to train, because the ability might emerge spontaneously. But if the partial credit metric improves smoothly and predictably, you have a chance of extrapolating your training progress to see when you might hit your accuracy target, better than if you extrapolated accuracy directly.

And if you find that the estimated time is too long and you decide to train a bigger model, you can try to extrapolate across model sizes to estimate how big of a model you might need.

Eg. imagine a big corpus of arithmetic operations (say 2500 additions, 2500 subtractions, 2500 multiplications and 2500 divisions): you can test when a model passes computing all of those correctly, and it's probably obvious that you'll have a long list of "didn't pass" until you suddenly get it passing.

We absolutely do handle firm. Mathematics, logic, morality are all examples that have plenty of firm classifications, as is typical, everyday reasoning, eg. I would state that I am naasking in this thread and I am not TeMPOraL, and I would not state that I am 99.999% probably naasking but 0.001% possibly TeMPOraL.

> Which is why formal logic makes for a fine family of puzzle games, but fares extremely badly at describing reality and reasoning about reality.

The device you're reading this on would suggest quite strongly that this conclusion is wrong.

The correct phrase should be "sudden/unexpected emergence". Otherwise the phrase "gradual emergence" would be an oxymoron.

Again, I understand this might not align with what you think "emergence" means in the English language, in the same way in which "metal" in physics has a completely different meaning from "metal" in chemistry, "metal" in astrophysics, and "metal" in the English language.

https://en.wiktionary.org/wiki/emergent#English

> (philosophy, sciences) Having properties as a whole that are more complex than the properties contributed by each of the components individually.

If they've said that it requires a sudden jump then they're trying to redefine the word to mean something it doesn't. But I haven't heard anyone else use that definition.

The emergent properties of AI are like "how can it write and entire Python program when we've only ever asked it to predict single words". It doesn't require any sudden jumps.

I work in AI and ML but my academic background is in the philosophy of mind. When people talk about "emergence" w/r/t AI I assume they're speculating about how consciousness might be an emergent property of a neural network, in the same way some people speculate that our minds are emergent properties of our brains. I think that speculation is foolish, but that is beside the point. It has nothing to do with a sudden jump in abilities, per se.

Each subfield defines rigourous terms and some may be overloaded.

It is impossible to have any universal definition of words that are universal, exact definitions have to be domain specific.

In this context, its charitable to note that some polysemy is at work within the domain (because the application of terms is so new) and so its useful to have these kind of distinction-making conversations.

Many confusions arise when people have different senses of a term but insist there is no polysemy and they're all talking about the same thing.

LLMs are plausibility engines. The fundamental hypothesis on trial here is that increasing plausibility corresponds to increasing correctness. This is easily rejected for the human-sourced content that trains them, implying an upper bound on any dependent phenomenon. It follows that simply scaling LLMs will not produce AGI.

This is one way to look at LLMs. But it doesn't automatically impose an upper bound on their capabilities.

Humans are reproductive organisms. This is also true. At a glance, it would seem that humans could not evolve to be intelligent. They are only selected on their reproductive abilities. But obviously the categorization, while true, doesn't impose an upper bound on human abilities.

LLMs are evolved to be as efficient as possible at retaining knowledge.

A simple strategy for retaining knowledge is memorization. Neural networks definitely can do that.

A different strategy for retaining knowledge is using algorithms. Neural networks can evolve to retain knowledge using algorithms too. For instance, it has been shown that a small neural network evolved FFT-like structures to perform addition. It started out with memorization, which was far from perfect, but later in the training it switched to an algorithm using FFT for addition which produced perfect results.

I think the better LLMs retain knowledge through sophisticated compression. It involves building a world model and ways to relate the input text to that model.

I see it as the building blocks of a reasoning machine. It is incomplete and buggy, and the current architectures might hit a ceiling soon, but nonetheless it is a completely different thing than pure memorization.

Note that OpenAI admits that pre-training (pattern finding and matching) is where the abilities on professional tests comes from.

Even proofs in presburger arithmetic have an upper bound on the second level of the polynomial hierarchy, which is way beyond the computational power of any LLM

https://arxiv.org/abs/2207.00729

>The model’s capabilities on exams appear to stem primarily from the pre-training process and are not significantly affected by RLHF. On multiple choice questions, both the base GPT-4 model and the RLHF model perform equally well on average across the exams we tested

https://arxiv.org/abs/2303.08774

To practically scale, parallelism is required, and the ability to find algorithms within the L or TC0 complexity classes is limited.

Remember that individual ANNs as used in transformers are just binary linear classifiers. Which you can do a lot with, but probably limited to P assuming we don't find out L or TC0 are larger than we think now.

Presburger arithmetic, or first order logic with (+,=), or (*,=) is the strongest FoL that is both complete and consistent. move up to Peano arithmetic and you start to hit the limits from Gödel, Church, and Turing.

There will be instances that an LLM can learn with CoT, zero shot etc...

But most of those will be due to luck or parallel patterns in the training set.

LLMs simplicity bias is great for plausible answers to our of distribution questions, but puts limits on what can be learned as far as 'algorithms' go.

They will work for 'there exists' problems far better than for any 'for all' or 'for most' problems unless they have learnable patterns in the training set.

The whole scientific system specifically being designed to suppress plausible-sounding-but-incorrect claims says otherwise.

But that we have came up with a scientific system is proof that humans actually can tell the difference, we might be bad at it but we still manage to do it. Humans that can't tell the difference are very unreliable and usually shunned in engineering and other STEM fields.

Furthermore, sometimes mistakes are made when assessing correctness, even in mathematical proofs. A correctness judgement thus still has a degree of plausibility associated with it.

I'm thus not sure if the distinction being made here isn't just one of degree.

I think humans has two levels here, "that sounds plausible" and "I can't imagine how this could be wrong so I am willing to risk my life on it". The second can still be wrong, but usually it isn't. For example when you walk on a bridge, you assume the bridge is there and confidently put down your foot even though you would die if that part of the bridge happened to be an hallucination.

So science is a set of statements and experiments that sums up to facts that humans can't imagine are wrong. Sometimes they are still a bit wrong, but then only slightly like newtons equations or theories that aren't backed up by experiments. But in general science is full of facts that humans stake their life on every day.

LLMs doesn't seem to have that certainty layer, something so certain that the LLM would stake its life on it. I'd for sure never stake my life on anything an LLM says as it is today, but I happily do it for humans every time I take the elevator etc.

The scientific method is just a way to make humans use that reliable part of their brain instead of the plausible part, even in situations that aren't life or death. I don't think it is possible to come up with something like the scientific method without having a built-in sense of what facts are.

There is no such thing in 'higher intelligence' beyond protoception. Pretty much every mammal has the same built in sense that you do, and yet none of them are carting around human intelligence. More so, when human children are left feral and not raised around other humans we typically consider them mentally disabled. Again, they learn the protoception stuff just fine, but all the stuff that "puts us above" the mammals is missing, it is not inane. Your counting, reading, and tools use are all learned behaviors after birth and form a continuous chain of learned behaviors taught by people (and more recently books and computers).

There is a reason that after development of the scientific method that most human endeavors experienced an exponential growth curve. It's because we don't recognise facts from fiction at a much higher rate than other animals, it's that we teach each other fact from fiction better than other animals.

Having a sense of what are facts and what are assumptions doesn't mean you are smart, but not having it means you are pretty dumb. LLMs doesn't have that.

Natural language is more powerful than programming languages since it lets us communicate assumptions, guesses, uncertainty etc, to other intelligent beings. So a good LLM needs to be able to consider certainty level of statements and act accordingly, todays LLMs doesn't do that so generate dumber responses than a human would since they lack a sanity checker.

AI is on a path to outperform humans at a large number of tasks and jobs that previously would have been described as requiring intelligence.

the implication sounds good, but is easily rejected with a counter example: a good student can surpass his master. A mediorcre student with multiple masters can surpass all of them (tangent: this is why the medival master-journeyman system was so efficient, I think).

Or to make the argument more abstract: Your implication seems to assume, that transferlearning does not exist.

I’ll repeat an assertion I’ve made in this forum before: that the benchmark for AGI will be when two AIs play one another at an incomprehensible game of their own devising.

However, there is a hidden corollary in my earlier statement. By implying an upper bound on the correctness of their answers, we can assess that LLMs will not themselves achieve sentience and form a civilisational threat. That actually increases their potential utility in many applications. Much as you wouldn’t, for safety’s sake, put a jet engine in a conventional car (occasional mad-scientist projects notwithstanding).

Edit distance seems like a strange way to test if the model understands arithmetic ([1], Figure 3). I think `1+3=3` would be equally as correct as `1+1=9`?

Why not consider how far off the model is `abs(actual-expected)`? I wonder if there is an inflection point with that metric.

https://arxiv.org/abs/2206.07682

We don't really know how LLMs do arithmetic. Maybe token edit distance would be interesting, but either way it doesn't really change the claim of the paper.

Unrelated: The link is incorrect, the one you're referring to is here: https://arxiv.org/pdf/2304.15004.pdf

Without using an algorithmic approach, it seems an LLM can only learn a bunch of partially correct heuristics, and attempt to generalize over examples.

I've played with this a bit in the past, and came to the conclusion that GPT-3 seems to have learnt to compare the size of numbers (whether accurately or via heuristics), and would get the approximate size of an answer right (depending on the task), even if not the actual value right. I seem to recall it also doing this for tasks like asking for a prime number greater than a particular value.

Imagine you could say 'calc' in your brain, and some separate subcomponent of your brain that is far more power efficient could return an answer almost instantly? You would not focus on understanding addition/subtraction, more you would focus on on when to use addition/subtraction/multiplication or whatever.

Not if math is your only goal, but there'd be value in making the models more powerful so that they could learn to do simple things like this (and not so simple things) by themselves. You can't have a tool for everything, and hopefully future AGI can itself do things that are more than just a mashup of existing tool capabilities.

You can spot-check with a survey of random samples. That’s also how we often test humans in their abilities.

What's interesting is that the quality of the answer when asking an LLM to explain arithmetics and asking it to perform arithmetics don’t seem to be necessarily correlated. I.e. an LLM might be able to perfectly explain arithmetics but completely fail at performing it.

In humans, we don’t expect this to be the case (although there are examples of the opposite case with idiots savants, or, to a lesser degree, with children who might be able to perform some task but not explain it).

This disconnect in LLMs is one of the most important differences to human intelligence, it would seem.

It isn't. It's stringing together likely tokens that approximate (often very effectively!) what its data corpus has done in the past. And, relatedly, the best way I've found GPT4 to solve a word problem is to tell it to write some Python code to spit out an answer; the actual computation part is an easier thing to figure out when it's just running code.

It gets the order wrong unless you tell it to “use Python”

https://chat.openai.com/share/4a673ea0-67d3-4256-b57d-dc1cf8...

https://chat.openai.com/share/5f558fc4-a0d0-494d-a3d7-ad78f5...

More: https://chat.openai.com/share/11c45192-6153-44b4-bb97-024e8d...

“The event at 3pm doesn’t fall within the 2.1-hour window around 5pm because this time window spans from 2:54 pm to 7:06 pm. The 3pm event occurred before the start of this window. Since 3pm is earlier than 2:54 pm, it’s outside the range we’re considering.”

Trillions of tokens!

https://chat.openai.com/share/32335834-9d12-421e-96b2-9aa6f1...

For the second example, I had to tell it to use Python

https://chat.openai.com/share/76e6cd67-ad49-4508-b05d-3d26a3...

On the other hand they'll spit out python code that'll get you the reversed text just fine.

It's also one of their greatest shortcomings when it comes to coding: They lack the ability to do any meaningful symbolical execution.

https://chat.openai.com/share/9faaae97-e20f-454e-b245-3e4c19...

https://twitter.com/AlexTamkin/status/1767248600919355670

Also that's not a reversal task because there was no input. It was free to make up anything that fits.

I simply took the "interesting fact" and added this to the prompt: "Reverse the sentence. Here is the beginning: ".noitatipicerp laminim seviecer"

Here is the result I got:

".noitatipicerp laminim seviecer" (prompt) - "taht ecalp a sa treseted a fo noitinifed eht yb htraE no treseted tsegral eht sa ti seifilaqulc esnapxe tsa v s'acitr nA.serutarepmet gnizeerf sti etipseD.dnali ni sse l ne ve na d t so ac eht g n o l l a ff all wons ) mc 5 . 61( seh cni . 5 6 tuoba fo noitatipicerp launn a egareva htiw, noitatipicerp eltt i l y r e v s eveice r ti esuaceb treseted a sa deifissalc si acitr an t A. e cap s d n a l y ci sti ot eu d dekool revo net fo tneu qer itnA" .a n fe ts erita n o t se r tse degral s'd lro w e ht taht stcaf gnitanicsaf enO".

Manually reversed back into original order:

"One fascinating facts that th e w orl d's larged est r es t o n atire st ef n a. Anti req uent of ten over looked d ue to its ic y l a n d s pac e .A t na rtica is classified as a detesert because it r ecieve s v e r y l i ttle precipitation ,with average a nnual precipitation of about 6 5 . inc hes (16 . 5 cm ) snow lla ff a l l o n g the ca os t d an ev en l ess in iland.Despite its freezing temperatures.An rtica's v ast expanse cluqalifies it as the largest detesert on Earth by the definition of a detesert as a place that" - (prompt) "receives minimal precipitation."

I don't think so - because they seem to be able to repeat back any short sequence of characters without issue. If I pick anything from that text they struggled with, manually reverse it, and tell them to repeat the reversed word back to me, that works fine.

It's also not just an issue with reversing something character-by-character. You can ask them to reverse numbers or re-arrange words and they'll faceplant in the same way as soon as the input gets beyond a small threshold. Here surely there wouldn't be an issue with tokenization.

Of course if you would train a network on specifically the task of reversing text it would do quite well, but not because it's doing it using any straightforward algorithm. Nothing like what a human would be doing in that situation can be represented within their network - because they're directed graphs and there's no hidden state available to them.

The point is simply to demonstrate their inability to perform any novel task that requires even a tiny bit of what I dub "thought". By their very implementation they cannot.

My guess is the training data contains many short pairs of forward and backward sequences, but none after a certain threshold length (due to how quickly the number of possible sequences grows with length). This would imply there's no actual reversing going on, and the LLM is instead using the training data as a lookup table.

But I did look at the code during the session when I was creating the link. It’s just what you would expect - a dictionary of US Presidents and the year they were born and one line built in Python function to sort the list.

Second paragraph completely contradicts the title given.

> It is also important to consider the evaluation metrics used to measure emergent abilities. For instance, using exact string match as the evaluation metric for long-sequence targets may disguise compounding incremental improvements as emergence. Similar logic may apply for multi-step or arithmetic reasoning problems, where models are only scored on whether they get the final answer to a multi-step problem correct, without any credit given to partially correct solutions.

- Page 7, https://arxiv.org/pdf/2206.07682.pdf

They say that cross entropy loss in these cases goes down with model size incrementally, well before "emergent" capabilities appear. If so the model is improving (in a sense) even though these capabilities aren't observable below some critical size.

Would have loved to see the claim of emergence supported by an example as well. And more importantly, if the measure is boolean, completely wrong or completely right, then, well, I do expect to see a "sudden" jump in ability.

Though, the paper this article is about [2] mentions that among the "emergent" tasks they tested, 92% were measuring accuracy on either exact-string-match or multiple choice, so probably just bad metrics.

[1] https://arxiv.org/pdf/2206.07682.pdf

[2] https://arxiv.org/pdf/2304.15004.pdf

For example, it's useful to know your 1 trillion parameter self driving car model is actually 90 percent of the way there, but it's also useful to know that the threshold you need to meet to implement the technology will likely be met at some point when your parameter count increases.

And of course scientists try to understand complex processes and make them more predictible. That distinguishes science from magic. You said that like it's a bad thing

As for weak emergence[2] that is de facto.

As for strong emergence[3] well... do we have an example of the phenomena anywhere?

To be clear, ML people have a different definition which I do not think is entirely useful. Let's look at the wording used in [4]

  Scaling up language models has been shown to predictably improve performance and sample

  Emergence is when quantitative changes in a system result in qualitative changes in behavior.
  
  An ability is emergent if it is not present in smaller models but is present in larger models.

We've also after more research found smaller capable of performing things that large models can do. So the goal post moves and makes the condition of emergent abilities. [RTFA]

So how do we define emergent abilities? Everything static except for the number of parameters? Does this make sense? Changing the number of parameters is an abstracted way of changing the optimization technique or training method. Clearly these are also different by nature of different batch sizes and/or a LR scheduler. So it is hard to be consistent.

Not to mention that we are not great at predicting much of what networks can do in general. There's plenty of people working on the subject (though this is a small proportion of total ML researchers, even if we exclude those that are highly application focused). So are we gonna call something emergent if it is just something we don't know about? And who gets to be the one to decide? I've seen abilities called emergent that are clearly a result of training methods like KL Divergence but surprising to individuals who do not have a rigorous statistics and/or metric theory background.

It just all seems to be jumping the gun. It's a new field and a new science. I think it is okay if we're willing to admit that our understanding just isn't great yet. There's no need to embellish or over attribute. These models are without a doubt powerful and useful, but at the same time I feel we are happy to greatly exaggerate all aspects about them. And for the life of me, I can't figure out why critiques are interpreted as dismissive. You can call an LLM a stochastic parrot and still think it is a great achievement and useful tool. Moreso, criticism is essential. Criticism gives us direction in research. Hype gives us motivation. But the two have to be in balance. Motivation without direction is an undirected Monte Carlo search (can still work, but we can do better than a drunken man). Overly criticizing (turning into dismissing, such as calling LLMs useless) is just pulling wool over one's eyes. It is the equivalent of lights being turned off and deciding to sit down and give up. When the lights get turned off you should find how to turn them back on. And we have more clues than a pure random process. After all, aren't we trying to make these better? I know I am. It is why I got interested in researching these things in the first place. I just wish we could have moderate hype rather than this ridiculously excessive one (which I think operates in a feedback loop with excessive criticism as it drives polarization).

[0] Sabine Hossenfelder (I know HN loves her): https://www.youtube.com/watch?v=bJE6-VTdbjw

[1] Sean Carrol: https://www.youtube.com/watch?v=0_PdLja-eGQ

Yes, Sabine and Sean are both controversial characters but they are well known.

[2] Weak emergence is where some larger phenomena forms out of smaller phenomena and results in something that the smaller thing can't do. The result requires the interactions of parts of a system. Temperature is a common example because it is generally easier to discuss the aggregated value of all the particles' "jigglyness" rather than each individual particle. The resultant property can be derived from the individual components. Conway's game of life is another common example. But in game theory we'd call a coalition an emergent property since utility is higher in the collective than the sum of each individual. Clearly this is true for ANNs since they are composed of neurons and a single neuron cannot perform these tasks.

[3] Strong convergence is about behavior that CANNOT be derived from the individual constituents.

[4] https://arxiv.org/abs/2206.07682

The fact is, nobody expected that speaking natural language, let alone reasoning capabilities, would emerge at the scale of GPT-3.

Even the people that suspected that scaling would improve GPT-2 (i.e. OpenAI), were surprised by the results.

Clearly this is "strong convergence" according to your definition, behavior that cannot be derived or extrapolated from individual constituents (or smaller scale).

Tons of people expected it to "speak" natural language. I mean that's why we built it.

Jury is still out on reasoning.

I say this as a ML researcher btw

> Even the people that suspected that scaling would improve GPT-2 (i.e. OpenAI), were surprised by the results.

I'm sure some were, I'm sure some weren't. I mean as we've learned more about how it was trained and what it was trained on I think less people are being surprised. But fair to say that that's biased. But so is your version.

The problem is that __who__ is being surprised matters. A caveman would be surprised by a computer, because they have no reference. But we aren't. Perspective doesn't make the computer magic. Nor does it make it strong emergence. It just makes the caveman less knowledgeable. It's okay if we're the caveman.

> Clearly this is "strong convergence" according to your definition

LOL

> behavior that cannot be derived or extrapolated from individual constituents (or smaller scale).

Jury's still out. Don't count your chickens before they hatch. Currently this is an unanswerable question. Just because __WE__ can't derive it, doesn't mean it can't be derived. That's the difference in the definition.

It may very well be (I highly doubt it), but we have so little understanding of these networks that you can't make a strong claim in either way. But remember that strong emergence is a VERY bold claim, considering that we do not know of it anywhere in physics. This includes thermodynamics and quantum mechanics, mind you. But also remember that these fields too centuries to get to the point we're at now, and that still isn't a complete understanding (but it has accelerated for sure).

Strong claims require strong evidence.

Spend less time on twitter and more time reading papers and math books if you want to understand ML.

Depending on how you measure, they look instant or gradual

When you run AutoGPT, the outcome is not always predictable.

It does make sense to evaluate things like 3-digit-sum by “how close textually?” And “how close numerically?” and the phase change is an artifact of the actual question being “is fully correct?”

https://www.quantamagazine.org/how-quickly-do-large-language...

Emergent can be defined as the sudden appearance of novel behavior.

In reality, if you ask a good LLM to solve a math-related problem, it will write and run a Python program to return the answer. Sometimes this even works. Sometimes it returns garbage. And sometimes it realizes that its own answer isn't realistic and tries a different approach. Sometimes people claim this isn't a valid manifestation of intelligence.

Completely pointless study, unworthy of Wired or HN.

It was noticed that LLMs can do some arithmetic, but we are yet uncertain how much and how it happens exactly.

Which is stupid, because it's not. A pocket calculator can perform arithmetic, as can a Python program, or for that matter a Japanese cormorant, who counts the fish it helps you catch. None of those are considered capable of "reasoning" on their own.

Meanwhile, GPT4 will cheerfully write a program to carry out the required arithmetic operations (and then some.) A study that doesn't acknowledge that is worthless at best.

We don't want to see if the LLM can be used as a tool to do arithmetics, but whether it can learn complex data relationships like arithmetics. Arithmetics is a stepping stone, not a goal so that the model can solve it by invoking a calculator isn't relevant. The problems we want it to solve doesn't have tools like calculators so it doesn't help getting us there.

Agreed that generalized architectures will ultimately win out over hand-tweaked ones. But the patent wars that will eventually be fought over this stuff are where the real bitter lessons will come into play. At some point, we'll be forced back into the hand-optimization business because someone like OpenAI (or another Microsoft proxy) will have locked down a lot of powerful basic techniques.

So the key may be to find sets of operands that GPT4/Claude Opus are unable to solve, even with hints similar to what a teacher may give a student learning the topic. Until such a set is found, I'd say this capability continues to meet the "emergent" definition, as the only other explanation - that I can think of - is that the models "discovered" how to do arithmetic in a general way.

I mean..yeah. Maybe i've simply misunderstood but It seems like you're presenting this as an outlandish idea but something like this is what Neural Networks regularly end up doing especially in the limit (as loss trends down to zero).

https://cprimozic.net/blog/reverse-engineering-a-small-neura...

https://www.alignmentforum.org/posts/N6WM6hs7RQMKDhYjB/a-mec...

Nobody is going to find any such set because time and time again, neural networks show us complete memorization is actually more difficult than just learning the distribution (even if imperfectly).