Comment by CommieBobDole
4 years ago
Also Excel is terrible at encoding MP3s.
It's a language model; why would we expect it do math or try to somehow shoehorn math into the model? Do the language centers of our brain do math?
If something approximating AGI is going to happen, it's going to be a lot of models tied together with an executive function to recognize and send things to the area that's good at working with them.
> It's a language model; why would we expect it do math or try to somehow shoehorn math into the model?
Language models can do math, or anyway arithmetic. That's because language models are trained to predict the next token in a sequence and an arithmetic operation can be represented as a sequence of tokens.
For example, see Figure 3.10 on page 22, here:
https://arxiv.org/abs/2005.14165
The only problem is that language models are crap at arithmetic because they can only predict the next token in a sequence. That's enough to guess at the answer of an arithmetic problem some of the time but not enough to solve any arithmetic problem all of the time.
More generally, the answer to your question is in the same Figure 3.10 I've referenced above. OpenAI (and others) have claimed that their large language models can do arithmetic. So then people tested the claim and found it to be a bag of old cobblers.
Hence the article above. Nobody's trying to "shoehorn" anything anywhere. It's just something that language models can do, albeit badly.
Right, but what you're describing is 'not being able to do math'. Like, if I've memorized a multiplication table and can give you any result that's on the table but can't multiply anything that wasn't on the table, I can't do multiplication.
It depends on how you see it. I agree with you, generally, but in the limit, if you memorised all possible instances of multiplication, then yes, you could certainly be said to know multiplication.
I've not just come up with that off the top of my head, either. In PAC-Learning (what we have in terms of theory, in machine learning) a "concept" (e.g. multiplication) is a set of instances and a learning system is said to learn a concept if it can correctly label each of a set of testing instances by membership to the target concept with arbitrary probability of error. Trivially, a learner that has memorised every instance of a target concept can be said to have learned the concept. All this is playing fast and loose with PAC-Learning terminology for the sake of simplification.
The problem of course is that some concepts have infinite sets of instances, and that is the case with arithmetic. On the other hand, it's maybe a little disingenuous to require a machine learning system to be able to represent infinite arithmetic since there is no physical computer that can do that, either.
Anyway that's how the debate goes on these things. I'm on the side that says that if you want to claim your system can do arithmetic, you have to demonstrate that it has something that we can all agree is a recognisable representation of the rules of arithmetic, as we understand them. For instance, the axioms of Peano arithmetic. Which though is a bit unfair for deep learning systems that can't "show their work" in this way.
What are some (non-nefarious) applications of generative language models that produce language which isn't constrained by some sort of rationality or directed by some sort of high-level goal?
The point isn't the math. The point is that, in math and similar disciplines, it's harder to get away with producing mostly undirected gibberish that happens to have some imputed meaning. The point is "use language to do something where it's easy to verify correctness and generating infinite amounts of synthetic data is trivial"
If a language model can't even do high school algebra, then I have a lot less confidence that it will ever be useful for customer service applications or any other number of potential applications outside of propaganda, advertising, and spam.
Well, because we want rational language models. Something with a sense of truth.
Math is not irrelevant—and I’m sure it’s a solvable problem with language models.
But if it's rational and has a sense of truth, then it's AGI. Which I don't think is impossible or even unattainable within a reasonable amount of time, but we're .001% of the way there, not 50% or 75%.
These models are fascinating, but the problem 'a lot of the things this model generates lack any semantic meaning' is inherent and likely insurmountable without connecting the model to other, far more complex models that haven't been built yet.
We are at the level where our models can consistently generate blocks of text with full sentences in them that make grammatical sense. Which is pretty cool.
But the next step is being able to consistently generate full sentences that make grammatical sense and usefully convey information. And while the current models do that a lot of the time, they don't do that all of the time because they don't and can't know the difference without essentially being a different thing. Because to do that consistently, we need an "understanding what things mean" model. Which is many orders of magnitude larger and more difficult than a text generator.
Language models aren’t even terrible at math. The Minerva paper provides a devastating counterexample. It will soon be replaced by more powerful linguistic-mathematical systems. Within the next twelve months we may well see 100% performance on all major benchmarks.