How it works: a probability distribution over sequences of consecutive tokens.
Why it works: these absolute madmen downloaded the internet.
Why it works: these absolute madmen downloaded the internet.
In the end, we are not really in the business of copying the brain but creating models that learn from data. If we arrive at a model that can solve the problem we are interested in through different means than a human would, e.g. first pre-train on half of the internet and then fine tune on your taks, we would be quite happy and it would not be seen as a dealbreaker. Of course, we would really like to have models that learn faster or have more skills, but it's amazing what's possible right now. What I find inspiring is how simple the fundamental building blocks are that our models are composed of, from gradient descent to matrix multiplication to Relus (just a max(x,0)). It's not magic, just research.
Transformers famously employ the Softmax activation inside the attention matrix. Very rare to see Softmax anywhere other than the final layer.
... reads like
A monad is just a monoid in the category of endofunctors.
> In category theory, a monad is a structure that is similar to a monoid in the category of endofunctors. A monoid is a mathematical object that consists of a set of elements, along with a binary operation that combines the elements in a specific way. For example, the set of integers, with the operation of addition, forms a monoid.
> In the category of endofunctors, a monad is a similar structure, but it is defined in terms of functions instead of elements. An endofunctor is a function that takes a mathematical object, called the "domain," and maps it to another mathematical object, called the "codomain." For example, the function that maps a set to its power set (the set of all subsets of the set) is an endofunctor.
> A monad in the category of endofunctors is a structure that consists of an endofunctor, along with two natural transformations that satisfy certain conditions. A natural transformation is a function that maps one endofunctor to another, in a way that is consistent with the structure of the domain and codomain of the endofunctors. The two natural transformations that are part of a monad are called the "unit" and the "multiplication" natural transformations.
> The unit natural transformation is a function that maps an object in the domain of the endofunctor to the endofunctor itself. The multiplication natural transformation is a function that maps the endofunctor to itself, in a way that is consistent with the structure of the domain and codomain of the endofunctor. The unit and multiplication natural transformations must satisfy certain conditions in order for the structure to be a monad.
> Overall, a monad in the category of endofunctors is a structure that is similar to a monoid in the category of sets. It consists of an endofunctor, along with two natural transformations that satisfy certain conditions. This structure is useful in category theory and related fields, because it allows us to abstract away from the specific details of the endofunctors and focus on the general properties of the structure.
pretty good explanation, actually
Like, I saw the other day it creates a C code that creates a Lisp code that creates a Pascal code. Is this based on an entirely previous creation?
The code examples are perfect case studies, they don't actually work. They aren't just slightly wrong, they're completely nonsensical.
Another example is "is <number> prime?", it can't answer things like that, and it will make up something that may or may not be accurate.
The model has no concept of what is true or false, it's essentially trying to predict what is the most likely token to come next.
It seems to know stuff because the knowledge comes from the dataset, hence techniques like zero-shot, few-shot and prompt-based learning.
This is not technically true. It can and does create things that are new. There are lots of new poems and jokes right here in this thread. I asked it, for example, to give me its top 10 reasons why Bigfoot knocks on camper trailers, and one of its answers was "because it likes to play with its food." I did a lot of searching to try to find this joke out there on the internet, and could not. I've also had it create Weird Al style songs for a variety of things, and it does great.
If these aren't new creations, I'm not sure what your threshold is for creating something new. In a sense I can see how you can say that it only "looks" new, but surely the essays generated by students worldwide mostly only "look" new, too...
A good idea when dismissing those machine learning models is to check whether a human would pass your standards. I miss the aspect when the dismissive "they only interpolate or memorise" arguments come. I am also quite bounded by my knowledge or what I have seen. Describe something I have never seen to me and ask me to draw it, I would fail in a quite hilarious way.
Hilariously, ChatGPT is also quite bad at arithmetic, like myself. I thought this is what machines are supposed to be good at!
Thats not so different from how humans do this. When we need to add or multiply we switch from freeform thought to executing the Maths programs that were uploaded into our brains at school.
A human might have a thought process that starts with the idea that people are food for Bigfoot, and then connects that to phrase of "playing with your food".
But GPT generates responses word by word. And it operates at a word (token) level, rather than thinking about the concepts abstractly. So it starts with "Because it likes to play" which is a predictable continuation that could end in many different ways. But it then delivers the punchline of "with its food".
Was it just a lucky coincidence that it found an ending to the sentence that paid off so well? Or is the model so sophisticated that it can suggest word "plays" because it can predict the punchline related to "food".
The best source would be the GPT-3 paper itself: https://paperswithcode.com/method/gpt-3
I know there were some deep learning papers on how to train a model to pass the PIQ portion without human-coded heuristics (because, you could easily write a program to solve such questions if you knew ahead of time the format of the questions). I don't remember the outcomes however.
Then each token’s embedding is roughly multiplied with a set of matrices called “attention head” that yield three lists: query, key, value, each of 128 numbers behaving somewhat like a fragment of an embedding. We then take the query lists for the past 2048 tokens, and multiply each with the key lists of each of those 2048 tokens: the result indicates how much a token influences another. Each token’s value list get multiplied by that, so that the output (which is a fragment of an embedding associated with that token, as a list of 128 numbers) is somewhat proportional to the value list of the tokens that influence it.
We compute 96 attention heads in parallel, so that we get 128×96 = 12288 numbers, which is the size of the embedding we had at the start. We then multiply each with weights, sum the result, pass it through a nonlinear function; we do it 49152 times. Then we do the same again with other weights, but only 12288 times, so that we obtain 12288 numbers, which is what we started with. This is the feedforward layer. Thanks to it, each fragment of a token’s embedding is modified by the other fragments of that token’s embedding.
Then we pass that output (a window of 2048 token embeddings, each of 12288 numbers) through another multi-attention head, then another feedforward layer, again. And again. And again. 96 times in total.
Then we convert the output to a set of 50257 numbers (one for each possible next token) that give the probability of that token being the next syllable.
The token embedding matrix, multi-head attention weights, etc. have been learned by computing the gradient of the cross-entropy (ie. roughly the average likelihood of guessing the next syllable) of the model’s output, with respect to each weight in the model, and nudging the weights towards lower entropy.
So really, it works because there is a part of the embedding space that knows that a song is lyrical, and that a part of the attention head knows that sponge and bob together represent a particular show, and that a part of the feedforward layer knows that this show is near “underwater” in the embedding space, and so on.
Who does? This is nothing but a "God of the Gaps" argument in reverse.
Do you know language models can use external toys, such as a calculator. They just need to write <calc>23+34=</calc> and they get the result "57" automatically added. The same, they can run <search>keyword</search> and get up to date snippets of information. They could write <work>def is_prime(x): ... print(is_prime(57))</work> and get the exact answer.
I think the correlation pattern in language is enough to do real work, especially when fortified with external resources. Intelligence is most likely a property of language, culture and tools, not of humans and neural networks.
Language models are unsuitable for anything where the output needs to be "correct" for some definition of "correct" (code, math, legal advice, medical advice).
This is a well-known limitation that doesn't make those systems any less impressive from a technical point of view.
Can we fix it?
Because earlier today it told me that George VI was currently king of England. And I asked it a simple arithmetic question, which it got subtly wrong. And it told my friend there were a handful of primes less than 1000.
Everyone’s talking about it being a Google replacement. What’s the idea? That we train it over time by telling it when things are wrong? Or is the reality that these types of language models will only be useful for generating creative output?
If you ask a chat interface a question and it says "this is true", that's very different from a search engine containing a list of results where one of them might be untrue.
For one thing, you can look at all the queries and take a majority vote etc. Second, you can look at the source to see if it's trustworthy.
Every integer is interesting. "[...] if there exists a non-empty set of uninteresting natural numbers, there would be a smallest uninteresting number – but the smallest uninteresting number is itself interesting because it is the smallest uninteresting number [...]" (https://en.wikipedia.org/wiki/Interesting_number_paradox)
One way of checking what makes a number interesting is seeing what sequences it is in in the OEIS[1]. Interesting properties (squares, primes, palindromes, friendly numbers, etc) all have the first hundred or so numbers with those properties in a list. So I downloaded the dataset of all sequences from OEIS, and iterated through all integers to find the first one that is not in any sequence in the OEIS.
So, I present the smallest uninteresting number: 20,067. Every number before it is in at least one of the sequences - for example, 20,066 is 'a partial sum for a coordination sequence for the "pcu-i" 3D uniform tiling'. It is the first number that has no interesting properties other than trivial ones (like being a multiple of 3). It is the first uninteresting number, but one could say that makes it meta-interesting rather than being interesting in and of itself.
Edit: and after doing all that work I saw that someone else has already done so and put it in the wikipedia article. Oh well, at least I learned about set processing in Python.
No, 4021 is not a prime number. A prime number is a whole number greater than 1 that is divisible only by 1 and itself. 4021 is divisible by 17, which is a number other than 1 and itself, so it is not considered to be a prime number.
I guess I only tried the first few single digit primes. Fair enough!
If you start a sentence with a few words, think about the probability for what the next word might be. Imagine a vector (list) with a probability for every single other word in the language, proper nouns included. This is a huge list, and the probabilities of almost everything are near zero. If you take the very highest probability word, you'll get a fairly predictable thing. But if you start taking things a little lower down the probability list, you start to get what amounts to "creativity" but is actually just applied statistics plus randomness. (The typical threshold to use for how high the probability of a selected word should be is called the "temperature" and is a tunable parameter in these models usually.) But when you consider the fact that it has a lot of knowledge about how the world works and those things get factored into the relative probabilities, you have true creativity. Creativity is, after all, just trying a lot of random thoughts and throwing out the ones that are too impractical.
Some models, such as LaMDA, will actually generate multiple random responses, and run each of those responses through another model to determine how suitable the response is based on other criteria such as how on-topic things are, and whether it violates certain rules.
> Is this based on an entirely previous creation?
Yes, it's based entirely on its knowledge of basically everything in the world. Basically just like us, except we have personal volition and experience to draw from, and the capability to direct our own experiments and observe the results.
Not only that, but the imprint is also amenable to gradient descent, possessing a spectrum from easy- and difficult-to-predict structures.