In other words, only inference cost is holding it back from completely changing everything.
So if we have a shortcut to getting something like GPT4 to run locally on a small device, watch out.
I can propose an alternate view of things. Not that I'm going to argue that it is the only true statement in the world, but I think it is necessary for a thought to progress to have an alternative hypothesis.
So the proposition is: formal symbolisms can deal only with those problems that where already solved in imprecise human's languages.
To invent calculus and orbital mechanics you need first to talk for a several centuries (or thousands of years?) about what is position and velocity, you need to talk your way upto acceleration, and then you need to find a way to measure them and to define in a strict geometric terms. Ah, and infinity, it was a very counter-intuitive idea, Xenon invented some of his paradoxes specifically to point at counter-intuitiveness. When Newton came all these talks and debates did the most of work for him.
> the ability to understand the human tongue is insignificant compared to the power of math.
But the fun is: you cannot know if someone understands math if they do not understand human language too. You cannot teach math to those who cannot speak human language.
Math is a cream on top with a limited applicability. What math can say about love? I do not like to sound like Dumbledor, but really behind all we do there is an emotions motivating us. Math cannot deal with emotions, because it was built that way and because non-math talks about emotions hadn't bring a good model for emotions, which math could express in a formalized language.
> Dijkstra says
I wonder when he said it? Before AI concluded that expert-systems based on logic were acknowledged to be a failure or after that?
> To invent calculus and orbital mechanics you need first to talk for a several centuries (or thousands of years?) about what is position and velocity, you need to talk your way upto acceleration, and then you need to find a way to measure them and to define in a strict geometric terms. Ah, and infinity, it was a very counter-intuitive idea, Xenon invented some of his paradoxes specifically to point at counter-intuitiveness. When Newton came all these talks and debates did the most of work for him.
For the sake of argument, let's grant your story about what you need to invent calculus.
But once you invented calculus, you can then use it to solve all kinds of problems that you would never in a thousand years be able to handle with mere talk.
Not "all kinds of problems" but very specific kinds of problems which is possible to formalize into a math language. How would you go about inventing thermodynamics if you didn't know words "temperature" and "pressure"? You'd need to start for your senses that can tell you "this is a hot surface", or "this is a cold one", or "this one is colder than that", you need to decide that "coldness" is a "negative heat" (it is not the most obvious idea for an animal, because animals have as receptors for a cold, so receptors for a heat, you could feel hot and cold at the same time, if you managed to stimulate both kinds of receptors at the same time). Then you need to notice that some materials change volume when heated, then you need to come up with an idea to use measurements of a volume to measure a temperature, and only then you can try to invent pV=nRT, which becomes almost tautological at that point, because your operational definition of a temperature makes it equivalent to a volume.
After that you really can use calculus and make all sorts of quantitative statements about thermodynamic systems. But before all that "mere talk" was finished thermodynamics was not a kind of a problem calculus can deal with.
In fact that kind of 'finishing' is very important, because otherwise you can waste a lot of time talking without noticing that you are not going anywhere. See eg philosophy or theology or pre-scientific-revolution science (ie natural philosohpy and natural history).
I think you could conceive of abstraction from other forms, maybe something like platonic forms as a base instead of language (again probably not in humans, but in others)
However, this paper is evidence that the field is figuring out how to built what's actually needed, which is a good thing.
If you want to measure its ability to do mindlessly repetitive tasks without diverging from instructions, you should compare it to humans doing the same, not expect it to act like a calculator.
If you want to measure its ability to solve problems that involve many such steps that are simple to express but tedious to carry out, ask it to write and evaluate code to do it instead.
But whether or not it can "do maths" to your definition depends very much on what you want it to do, and how you define "do maths". To me it's irrelevant if it's doing the low-level calculations as long as it knows how to express them as code. If I wanted a calculator I'd use a calculator. And I don't consider a calculator able to "do math" just because it can precisely add numbers.
Meanwhile I've had lengthy discussions with GPT about subjects like orbital mechanics and calculating atmospheric effects where it correctly used maths that I had to double-check not because I didn't trust GPT (though I also want't to verify for that reason) but because I didn't know the maths (not that it was anything particularly advanced, but I lost interest in maths during my CS degree and picked the minimum amount of maths I could get away with).
By my definition it can "do maths" just fine. I guess you don't consider my view of that "reasonable". I can live with that, as meanwhile, it will keep doing maths for me when I need it.
Of course this was also a case of moving the goalposts to set up a strawman - in the comment of yours I replied to, you claimed it couldn't reliably add two numbers.
I'm not moving goalposts, the original claim was that LLMs can "do math". Primary school arithmetic is math.
GPT-4 can't do math and that's okay, I don't understand why so many of you are so touchy and defensive about this. It's a limitation that exists, nothing more, nothing less.
If you train a model to do math (and optimize representation for that), it'll do math. GPT-4 just isn't, and, generally speaking, they aren't, because it's much more efficient to train them to "use a calculator". Same as with humans.
I find it really comical that this is what people complain about GPT over - there's zero benefit to get LLMs to get good at this over other tasks. To the extent we get it "for free" as a benefit of other learning, sure, but when we make kids practice this over and over again to drill doing it without getting sloppy, it has traditionally been out of some belief that it's important, but a computer will always have a "calculator" that is far more efficient than the LLM at its disposal and it's idiocy to care about whether it does that part well the tedious and hard way or knows how to describe the problem to a more efficient tool
I also find it comical that people use tasks where LLMs behaviour is if anything mot human-like, in its tendency to lose focus and start taking shortcuts (before GPT4 started writing Python instead, it'd for a while try really hard to not give you a step by step breakdown and instead clearly take shortcuts even you prompted it heavily to reason through it step by step), when presented with stupidly repetitive tasks as examples of how they're not good enough.
All human knowledge is "symbolic". that is, knowledge is a set of abstractions (concepts) along with relations between concepts. As an example, by "knowing" addition is to understand the "algorithm" or operations involved in adding two numbers. reasoning is the act of traversing concept chains.
LLMs dont yet operate at the symbolic level, and hence, it could be argued that they dont know anything. LLM is a modern sophist excelling at language but not at reasoning.
If you include a large amount of properly solved math in its training text, it gets MUCH better at that kind of math.
It has a very deep set of intelligences that are alien to us, that allow it to predict and ACT LIKE us, when it comes to generating the next word. You're only seeing the output of those intelligences through a very lossy channel.
As a side note, there are structures in human language that apparently encode much more information that you might think at first glance. The fact that Word2Vec had such mathematical properties, despite it's relative simplicity, astound me to this day. Throwing a bunch of sine/cosine values on top of that to represent position in a sentence to enable LLMs is also amazing in that it works.
- The result of 69*94 is 6466.
SDXL-ligtning/cascade can generate images in 200ms which is fast enough to fit in a web request, and paradoxically makes it even cheaper to generate.
And using groq at 500 t/s is wild compared to any of the other platforms.
I’m glad people are doing it though, and I’ll happily adapt to accessing inference at that speed.
I thought mmap'ing models to only keep the currently needed pieces in RAM was something that was figured out ~6 months ago? Performance wasn't terribly great iirc, but with how much faster 1.58B is, it should still be okay-ish.
For LLM, you are mostly dealing with b = W @ a where a and b are vectors, only W is the matrix. If a is sparse (i.e. have a few 0s), you don't need all the columns from W to do the matrix-vector multiplication. A cleverly arranged W can make sure during inference, only related columns loaded from flash. Further more, if you can apply "One Weird Trick" paper to this matrix-vector multiplication, you can shard W by rows, i.e. `b[i:i+n] = W[i:i+n,:] @ a[i:i+n] for i in range(N, N / b)` such that while the previous b[i:i+n] is still computing, you have visibility on which columns of the next matrix to be loaded already.