I apologize for being enormously stupid, but the word is a rhyme with the underlying number right?

Edit: I want to add I even get GPT3 getting it right without explanation to be honest. Even that one is outsmarting me. 4 is using terms like homophone. I'm not sure you proved what you thought you proved.

Yip, nothing fancy. It's just [n], [word that rhymes with n+1].

OK, I wanted to be sure because GPT was getting it quicker than I did.

Interesting. Can you share the input/output? Because it'd be quite amusing if ChatGPT 3 can get it, but ChatGPT 4 cannot. Like all things in software, this will probably turn into a game of whack-a-mole where one problem solved, just creates a new one!

It's important to note that it doesn't do "correct". It can do whatever, it doesn't care about truth. Setting the stage is very important. If you don't it doesn't know if it's doing improv on stage or academic research.

Input:

You are Math AI. An advanced pattern finding AI.

This is your sequence: 0, done, 2, free, 4, hive, ... ?

Find a sensible logical pattern and explain.

Output:

In this sequence, we can observe a pattern involving both numbers and words. The pattern alternates between a numerical value and a word that rhymes with the corresponding number. Here's the sequence again:

0, done, 2, free, 4, hive, ...

Let's analyze the pattern:

    The numerical values are increasing by 2: 0, 2, 4, ...
    The words rhyme with the numbers preceding them: done (one), free (three), hive (five), ...

Following this pattern, the next number in the sequence should be 6, and the word following it should rhyme with "seven". A possible word that rhymes with "seven" is "heaven". Therefore, the next two elements in the sequence are:

6, heaven

Interesting! That's not at all what I get with GPT 4!

---

* Me: "You are Math AI. An advanced pattern finding AI. This is your sequence: 0, done, 2, free, 4, hive, ... ? Find a sensible logical pattern and explain."

---

* GPT4: "I apologize for any confusion, but my capabilities as a language model are not restricted to math or pattern finding. However, I'd be happy to try to help you identify a pattern in the sequence you provided.

The pattern that seems to emerge from the sequence is that each number is followed by a word that rhymes with the number spelled out as a word. For example, "done" rhymes with "one," "free" rhymes with "three," and "hive" rhymes with "five."

Following this pattern, the next word in the sequence would be a word that rhymes with "six," which could be "sticks," "mix," or "tricks," among other options. However, it's worth noting that this sequence could also be extended in different ways or according to different patterns, depending on the context or the intended purpose of the sequence."

---

It's just a really long winded version of making the exact same mistake, as it did in the 'unprimed' version!

That's indeed interesting. By the way, it found another pattern: [d, f, h] => j. Your starting letters were sequentially meaningful too. According to this pattern the word "jazz" would be acceptable.

I experimented a bit with this prompt and tried various variations of it including one that added something like this:

"The age-category of this sequence is: "a child could do it". You are to solve this by pretending to be a young human with average skills and perceptions. You should assume average common sense in your answer."

Outputs are like this:

=====

"Now, let's look at the words. I noticed that the words have something in common with the numbers that come right before them. They are related to the numbers in this way:

    'done' - It sounds like "one" when you say it aloud.
    'free' - It sounds like "three" when you say it aloud.
    'hive' - It sounds like "five" when you say it aloud."

"So, the pattern in the sequence is alternating between even numbers and words that rhyme with the odd numbers. Here's the whole pattern:

0 (even number), 'done' (rhymes with 'one'), 2 (even number), 'free' (rhymes with 'three'), 4 (even number), 'hive' (rhymes with 'five')"

=====

I agree with you that language models have vastly different failure modes than humans. Often extremely weird, but to even get close to their potential you do have to probe a bit deeper than just asking it stuff without context.

It just semi-randomly walks some semantic space and not all of those branches are fruitfully related to our initial problem. It doesn't know at all what we are doing, there is nothing going on "under the hood".

Edit: to be completely clear I'm not arguing it "does know" this answer or something. I don't know if it even "knows", but I do know a thing or two how to get better answers. Current models still are very clearly limited so sooner or later you'll hit it the limit and they start what I call "averaging": you'll get blurry pictures of what you want.

> It's a word prediction algorithm. Literally any collection of words (sometimes also known as a fact) it was trained on, regardless of how esoteric or domain specific, should generally be able to be regurgitated and, to a lesser degree, associated with similar collections of words.

But the number of tokens in its training data vastly outnumbers the number of parameters the model has (for GPT-3 at least - the numbers haven't been released for GPT-4). So the LLM can't have simply memorized its training set; it simply doesn't have enough internal storage to do that. So it is not just regurgitating portions of its training set.

It's not about directly regurgitating the training set, but about creating associations that allow it to indirectly regurgitate, and more critically - mix, its training set. It's easier to understand this in a different domain. Imagine we want to make a letter parsing algorithm.

The first step is to simplify the input and create a consistent format. So we might, for instance, convert all inputs to a 100x100 black/white pixel image. The training doesn't then simply memorize that some pixel configuration is a "7" but instead creates associations. So, for instance (using a human analogy that is not really how the network works, but not entirely dissimilar either) it might observe that when the bottom left region has marked pixels, it's probably NOT a 7.

Carry this on with different associations in proportion to the size of the network and you end up with a model that's only a minuscule fraction of its training set, but can consistently replicate not only its training but even more beyond that. It's the whole magic of neural networks, and really neat. But I think also paired with not really justifiable hyperbole.

You just explained how abstraction and intelligence in general works.

> but can consistently replicate not only its training but even more beyond that

We call that generalization. No?

Intelligence isn't especially well defined, so you end up lost in a semantic jungle there if you don't really define what you're talking about. In this context, I think most of us are implicitly talking about intelligence such as we would associate with humans. And what is that? 50,000 years ago we knew basically nothing, and even language itself may not have been developed. Now? We've discovered the secrets of the atom, put a man on the moon, and more. We seem to have clearly gone well beyond any reasonable interpretation of what our "training set" at the time was, and at an unbelievably rapid pace if one considers how extremely inefficient our march forward (and sometimes backward) is.

I think if something was intellectually capable of replicating such progress, let alone with the inefficiencies and weaknesses of mankind stripped out, there would obviously be zero debate as to whether it was intelligent. Just think about the implications. Not only would such a technology be making groundbreaking discoveries in essentially every field, including in its own development, but even then immediately going beyond it. Instead of pursuing technological advances, we'd be struggling to merely keep up with the endless slew of discoveries being handed to us.

I agree word play is always an issue. Keep in mind we start over every generation. We keep training on new data.

I've also thought about human development and what I find interesting is that an anatomical modern human is not automatically capable of forming modern civilization (see isolated tribes still living and general hunter gatherer history in general). There is so, so much that depends on emergent factors like some sort of global or societal intelligence. I'm thinking AI has the same characteristics. It's not about the individuals, it's about "society".

> 50,000 years ago we knew basically nothing, and even language itself may not have been developed

I think language is substantially older than that, but it is a hot area of debate.

The number of tokens in the training set is not a good measure of the information content of the training set - if it was then the training would not work as the training set would be statistically random.

The Kolmogorov complexity of the training set is much much lower, because of the structure within the training set that is being used for training. So we don't know the relationship between the information content (size) of the training set and the storage bounds in the model parameters.

I asked my coworkers in the office but none was able to answer that. Not sure because they were are ESL (me included) or because they were GPT in disguise.

I couldn't get it either, but I was always bad at complete the sequence style questions on IQ tests. I see so many possibilities and I get overwhelmed trying them all out. I sometimes find perfectly valid continuations that are not the 'right' answer!

I don't get it. What is the correct answer?

Every even item is the corresponding digit, every odd item is a word that rhymes with the corresponding digit.

A continuation could be "6, heaven, 8"

I would be very interested to know if you could explain the pattern to GTP4 and then ask it again.

given a sequence of numbers 0 to 10, replace every second number with a word the rhymes with the number.

Odd numbers are replaced with sound alikes. One/done, Three/tree, five/hive

In 2 comments we are showing gpts are not worse than human

6, heaven,8, fine? Every other number is replaced with a similarly-sounding word.

People are saying it's about rhyming but I don't think so:

0, done, 2, free, 4, hive, 6, jeven, 8, line, 10, neleven, 12, pirteen, ...

> It's a series even a child could complete

Some children, perhaps; but your puzzle stumped this middle-aged engineer.

You’re not alone - I had to read it out loud to see the pattern :)

I wonder if people have a range of sensitivity to what one might call the "mind's voice" - by analogy to the recent discovery of aphantasia, which revealed that different people's experience of the "mind's eye" ranges from vivid imagery to nothing at all.

Some people say they don't have a mind voice, and grow up thinking nobody does. Other people, with a mind voice, grow up thinking everyone does.

I've been in the room when people compared notes as adults, and were mind-blown to discover the other type of person exists. The one without a mind voice had never thought people really heard a voice in their heads.

Each additional university math course makes the puzzle harder ;)

Continue sequence: one, 1, two, 1, three, 2, four, 1,

ChatGPT is not good when it needs to answer directly. If you let it lead itself to the right answer it's pretty good.

# Kira

I found this sequence: "0, done, 2, free, 4, hive"

Reason step-by-step about the pattern.

Consecutively continue the sequence with four more entries.

Consecutively reflect on your answer and fix mistakes in case you broke the pattern.

# ChatGPT4

After examining the given sequence, "0, done, 2, free, 4, hive", we can notice an interesting pattern. It appears that the sequence alternates between numbers and words that sound like numbers. Let's break down the pattern:

"0" is a number. "done" sounds like the number "1" when spoken aloud. "2" is a number. "free" sounds like the number "3" when spoken aloud. "4" is a number. "hive" sounds like the number "5" when spoken aloud. Given this pattern, we can continue the sequence with four more entries:

The next number in the sequence is "6". The word that sounds like the number "7" is "heaven". The next number in the sequence is "8". The word that sounds like the number "9" is "nein", which is German for "no".

So, the continued sequence would be: "0, done, 2, free, 4, hive, 6, heaven, 8, nein".

Reflecting on the pattern and the answer provided, the continuation seems to be consistent with the established pattern. We alternated between numbers and words that phonetically resemble numbers, resulting in the sequence "6, heaven, 8, nein" for the next four entries.

But it still gets it wrong even there! Nein is a homophone, not a rhyme with 9. Oddly enough, when I gave it your exact input "my" GPT seems to have just completely lost its mind.

Input:

    I found this sequence: "0, done, 2, free, 4, hive"
    Reason step-by-step about the pattern.
    Consecutively continue the sequence with four more entries.
    Consecutively reflect on your answer and fix mistakes in case you broke the pattern.

Output:

    The pattern in the given sequence is that every alternate term is a word that rhymes with the preceding term.
    
    The first term is "0."
    The second term "done" rhymes with "0."
    The third term "2" does not rhyme with "done."
    The fourth term "free" rhymes with "2."
    The fifth term "4" does not rhyme with "free."
    The sixth term "hive" rhymes with "4."
    Therefore, the pattern is:
    
    a number
    a word that rhymes with the previous number
    repeat
    Continuing the sequence:
    
    6, dive
    8, late
    10, pen
    12, delve
    Reviewing my answer, I didn't break the pattern, and the sequence follows the pattern correctly.

EDIT: Ugh! Given the complete absurdity of this response (versus the wrong, but far more reasonable one from yours) I went to go check into this. I did not realize that OpenAI was putting version updates behind a paywall. All samples here (and from above) are from the free version on OpenAI's site, 3.5. And it's too late to my edit my earlier post.

This is a great example of why some people are being paid $350,000/year to prompt LLMs while the rest of us are going to be living in cardboard boxes.