How much of this is just "AI is bad at everything", but in the math case, it's easier for the lay person to tell.
It's all just passable garbled nonesense that the reader (goes to lengths) to interept based on their prior knowledge, which is not expressed in the syntax of what these systems output.
In the case of mathematics, we're far less willing to "BS away" the interpretive failures. But if we were equally demanding, likewise, all prose generated by these systems isnt AI "getting" anything either.
Pass a film reel thru' a shredder and an art student would still call it a film. Pass math thru' and a mathematician wont. This says more about our ability and inclination to make sense out of nonesense when in apparent communicative situations (since, when speaking to a person, this actually improves our mutual understanding).
So, how much of AI is just hacking people's cognitive failures: (1) people's willingness to attribute intention; (2) people's willingness to impart sense "at all costs" to apparent communication; and (3) "hopeium".
Have you ever used Github CoPilot? It does a lot of useful work, automating away rote typing in programming. Have you tried Dall-E or Stable Diffusion? They make good looking images. This comment seems completely unmoored from where the state of the art is right now.
Math follows a completely different approach with respect to how machine-learning AIs do their thing.
Reason derives its strength in having a few primitives and creating new assertions through the transformation of symbols by following precise rules (which is how algorithms work).
In ML-based AIs, everything is imprecise and probabilistic, and this kind of generation gets its strength from building recognizable from utterly imprecise inputs and training - quite the opposite of how logic and reason evolve. Now, "classic" AI was a powerful way to derive new knowledge, and automatic theorem proving is a strong discipline; but the recent breakthroughs in AI are not directly applicable to classic techniques.
Do you know what machine-learning AIs could be good for? Generating "insight" in problem solvers for guiding the theorem demonstrations through the proof search space, trying to find the best sub-spaces to explore. If there's a way to create human-like general AI, it will likely combine both kinds of generation - the rational methods of symbolic logic and the "irrational" statistical methods of ML.
I haven't used copilot because I'm not sure I'm allowed, but I'll try it on a personal project eventually.
I'm hoping it's not as bad as Dall-E and Stable Diffusion - I've tried to use those to generate some generic product looking stock photos for a demo and it's spectacularly bad. The only context I see it get praised is fantasy style art - and that is visually appealing nonsense by definition.
If the code generated by copilot has the same "looks convincing but is fundamentally flawed" quality then it sounds like an insidious bug generator.
sure, but co-pilot is mostly just copying code (see, for example, the issue with it producing quake source code).
If you think of AI as a dial from sample(data) to mean(data), then as the dial is turned towards the mean() you get more "generic" results, but also more garbled ones.
Copilot is more like a search engine, having turned the dial more towards sample().
The real invention of the NN is simply to provide that dial in a trainable way.
The only change to the "state of the art" is the size of the weights, and how long they take to train. This "advancement" is no more impressive than google indexing more webpages.
There has been no step-change advancement in AI in, perhaps, 50 years. All we see today is a product of hardware, in GPU/CPUs able to compress TBs of data into c. 300GB of weights. And likewise, the internet to provide it and SSDs to hold it.
The "magic" of AI is no more the magic of wikipida, here: copilot is good only because million+ programmers made github good.
I agree. It's possible to point out the clear limitations of current AI without being oblivious to the huge, indisputable advances that have occurred.
People thought it might take centuries for a computer to defeat a top human in Go. Then deep learning showed up and a few years later it's the opposite.
A lot of the things deep learning methods are doing now are things no one had any idea how long research would take to achieve, or if they were even possible.
Personally, I think we are currently hitting some walls that might take a while to climb before we get to AGI, but I am very impressed at the recent progress.
> How much of this is just "AI is bad at everything"
"AI Language Models" are not touted as some general AI that is smart at everything, like a clever person with multiple intellectual skills integrated into one.
AI language models are for modeling language, not for math problem solving, or anything else. People good at language aren't always good at math.
DeepL produces very good, correct translations for "Alice has five more balls than Bob, who has two balls after he gives four to Charlie. How many balls does Alice have?" into numerous languages, even though it doesn't offer a solution.
I have little doubt that an AI system could be trained to translate word problems like this into systems of equations, which could be dumped into a some decades-old CAS to obtain a solution, which the AI could map back into the verbal domain through the identities between the math variables like x and Alice's apples.
"Hey look, that human who is supposedly good at math can't produce a painting of the Grand Canyon in the style of Monet, even if given eight months to do it, and is easily defeated in chess."
> How much of this is just "AI is bad at everything", but in the math case, it's easier for the lay person to tell
Honestly, even as someone generally pretty dismissive of the AI hype, I'm not sure you can go that far. The whole reason we have specific mathematical notation is that human languages often are not super great at dealing with it, and English in particular is pretty abysmal for being both unambiguous and precise (and I'd be surprised if language models didn't end up suffering from biases analogous to how many image recognition AI models have been found to not deal well with a diverse set of human appearances). We don't teach math the same way we teach English, and we certainly don't expect people to be experts at teaching both, so why would we expect an AI model designed for language to be able to do math?
Because there is an algorithm for it. Convert the strings into floating point numbers, add them, convert them back to strings. It’s a leetcode medium question. It should be learnable.
The article talks about abstract math questions, but even arithmetic is hard for language models.
Language models aren't built for math. Their improvement/training cycles aren't sensitive to the exactness and rule-based nature of mathematical language, plus there are probably a lot of bad/misleading examples of math in the source data.
You'd have to be unrealistically pessimistic to call what GPT-3 and other huge language models produce "nonsense".
It's not that they were not built for math, but more like verification is hard. But it's hard for humans as well. A large generative model + a fast verifier could do wonders.
AlphaGo was built on that - the model can propose moves, but you can verify who won in the end. There are some code generation models that write their own tests as well, or use externally provided tests to verify their solutions. The DeepMind matrix multiplication algorithm was also "learning from verification" of generated solutions, because it's trivial to do that. In general verification remains an open problem.
I think if we replaced "AI" with "taking averages over subsets of historical examples", then there'd be no mystery for when "AI" will be good or bad at anything.
Would we expect a discrete melodic structure to be expressible as averages of prior music? No.
It doesn't surprise me that an AI model for language can't grok maths or music. I can't see how a language model can map to maths. Hell, I don't even know how to describe music in words. It's possible to articulate some maths in words, but that often involves using words with unexpected definitions.
That’s what a musician does. They make short loops and loop them.
This reads like someone who knows sheet music and theory but does not listen to music. It’s repetition of short phrases over and over.
I’m not really sure what people expect of general AI trained on human generated outputs. It can’t make up anything anything “net new” only compose based upon what we feed it.
I like to think AI is just showing us how simple minded we really are and how our habit of sharing vain fairy tales about history makes us believe we’re masters of the universe.
That solution has a compressed representation of half the internet.
NNs are "garabled nonesense" insofar as they try to generalise; insofar as they are search engines, they provide apparent sense by just repeating something in their database (= weights).
This might make sense as a response solely to the title of the article, but I have to admit I find it puzzling as a reaction to its content. Notwithstanding the title, the article mentions a model called Minerva that scored fully 50% on the MATH dataset of high-school/undergrad mathematical problems. For comparison, a human computer science PhD student scored 40%. [1]
For context, Minerva came out this July. When it was tested on a national math exam, it scored higher than that year's class of graduating high school seniors. [2] A mere eight months (!) earlier, OpenAI had announced [3] they'd trained a language model that solved math word problems almost as well as an average middle-schooler. So even if you believe — rightly or wrongly — that current capabilities aren't very impressive, it's worth remembering that your understanding of current capabilities might not be entirely accurate, even if it's only a few months out of date.
Incidentally, it may be worth looking at some examples of these models' outputs before deciding what they can or can't do. Here's Minerva solving some math problems, for example:
I'll admit I find it challenging to interpret these results as "passable garbled nonesense [sic]", though perhaps I'm not being demanding enough. At any rate, when these models go from beating 10-year olds at math to beating 18-year olds at math in the span of 8 months, one does start to wonder how much of the hype is really due to over-interpretation — and what the next 8 months have in store.
Current sequence models don't have the right structures to represent math. Even if they use floating point internally, they can't really float the point because the nonlinearity in the model has a certain scale.
A system that processes language can take advantage of the human desire for closure
The problem is that human language is approximate and correct math is not, so pattern matching on prose text is doomed. AI trained on exact math does a lot better. But that's not fully generic so fails the weird GPT goal of modeling all of human intelligence through prose. That's not how people solve math at all.
GPT's "Superficially plausible but wrong" math is actually pretty good match for non-expert bad-at-math average human behavior.
Mwell, the article claims, and points to work that also claims, that large language models can actually be made to perform arithmetic well. They need fine-tuning, verification, chain of thought prompting and majority voting to be combined but the linked Google blog says that Minerva hit 78.5% accuracy (on the GSM8K benchmark).
For me the problem is that we can look at the output and say if it's right or wrong, but we know what language models do, internally: they predict the next token in a sequence. And we know that this is no way to do arithmetic, in the long run, even though it might well work over finite domains.
Which is to say, I'm just as skeptical as you are, and probably even more, but I think it's useful to separate the claim from what has actually been demonstrated. Google claims its Minerva model is "solving maths problems" but what it's really doing is predicting solutions to problems like the ones it's been fine-tuned on, and those problems are problems stated at least partly in natural language, not "naked" arithmetic operations. In the latter, language models are still crap because they can't use the context of the natural language problem statement to help them predict the solution.
Btw, "chain of thought prompting" if I remember correctly is a process by which an experimenter prompts the language model with a sequence of intermediary problems. So it's not so much the model's chain of thought, as the experimenter's chain of thought and the experimenter is asking the model to help him or her complete their chain of thought. I have a fuzzy recollection of that though.
That's interesting, I hadn't made the connection between executive function and intelligence.
I went through a burnout in 2019 that felt like having a stroke. My brain finally reached such a level of negative reinforcement after years of failure that it wouldn't let me work anymore. I'd go to do very simple tasks, everything from brushing my teath to writing a TODO list, and it was like the part of my brain that performed those tasks wasn't there anymore. Or at least, it no longer obeyed if it perceived a potential reward involved. It was like my motivation got reversed. I had to relearn how to do everything, despite knowing that no reward might come for a very long time, which took at least 6 months before I began recovering. The closest answer I have is that my brain healed through faith.
I only bring it up because executive function may be associated with a subjective experience of meaning. If there's truly no point to anything, then it's hard to summon the motivation to string together a sequence of AI tasks into something more like AGI.
I guess that's another way of saying that nihilism could be the final hurdle for AGI to overcome. It's like the human philosophical question of why there's something instead of nothing. Or why angels would choose to be incarnate on Earth to experience a life of suffering when it's so much easier to remain dissociated.
that solves word problems using the methods of the old AI. The point is that is is efficient and effective to use real math operators and not expect to fit numbers through the mysterious bottleneck of neural encoding.
> language models just need to translate problems into code of some kind that can be run to get the answer
A huge "just"! Isn't this the magic step? Translating ambiguous symbols to meaning and combining them in meaningful ways is a big deal which, apparently, these AI models cannot do. They can just parrot things.
I'm not so sure about that. Of course computers can do arithmetic operations, but this is not the same as solving math problems, proving theorems, etc.
Even mathematical objects are approximated up to an approximation error in a computer (like a differentiable manifold or a real number).
That's because they're not modelling anything. The shocking thing about current AI models is that just sort of repeating and copying from memory what you've heard and seen gets you 97% of the way to imitating a person.* They still need to generate actual models somewhere to create consistency; so many generated images with one eye completely different from the other, or three arms, or fingers that grow into their cellphones.
If you solve this, you've probably solved almost anything in the simulation field. I have no confidence that the solution will even be complicated. Information consumed needs to be used to add to some sort of model, and that model always needs to be used as part of input. The complicated part would be to make that base model able to modify itself reasonably based on input, to tolerate constant inconsistency, and to constantly refine itself towards consistency i.e. ruminate.
I think a huge difference (which I think was approached through theories of embodied cognition) is that people start with a model (or the ability to create a model) of themselves. We can apply that model to other things and use it both to change how we ourselves behave, and how we speculate about the invisible states of other things. It's not for nothing that we can (and must) anthropomorphize anything.
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* Which was huge towards the confirmation of my belief that this is all people do 97% of the time.
This is factually wrong, both in terms of quantity and quality.
Current AI models are not "just sort of repeating and copying from memory". This is just an incorrect characterization of how they work and how they perform.
AI skeptics often say things like this then backpedal with something like "Well they aren't really repeating what they heard, but their generative model is just a slightly more sophisticated version of repeating what they've heard." But this weaker claim is also true of humans. It's certainly the case that >97% percent of what humans say is "just repeating and copying" in the same sense.
> Current AI models are not "just sort of repeating and copying from memory". This is just an incorrect characterization of how they work and how they perform.
You say this, but don't explain how. Because this is exactly what they are doing.
> AI skeptics often say things like this
I'm not really an AI skeptic. I think that we're very close to AI being indistinguishable from people. There are clearly problems that need to be solved, but I think the hardest problem was accepting the fact that humans are largely just copying and realizing that would be enough to get you 97% of the way there, especially if you gave a machine far more to copy than a human could consume.
> then backpedal with something like "Well they aren't really repeating what they heard, but their generative model is just a slightly more sophisticated version of repeating what they've heard." But this weaker claim is also true of humans. It's certainly the case that >97% percent of what humans say is "just repeating and copying" in the same sense.
Maybe I'm not expressing myself clearly, but it seems that you're just repeating my comment with a sneer. Agreeing angrily?
> “I think there’s this notion that humans doing math have some rigid reasoning system—that there’s a sharp distinction between knowing something and not knowing something,” says Ethan Dyer, a machine-learning expert at Google. But humans give inconsistent answers, make errors, and fail to apply core concepts, too. The borders, at this frontier of machine learning, are blurred.
This part resonates with me. There was a time when I could calculate congruent modulo problems with exponents, but I couldn’t do it step by step, I could only “hallucinate” in a fuzzy way to arrive at the solution, somehow like recalling the solution from memory.
When we have to explain our reasoning we can’t think the same way. It’s like thinking with a debugger attached.
Language models can generate a Python function that does the math perfectly.
I bet you would get better results if you tweaked the prompt to say "Generate a Python program that solves X math problem" and then just ran the resulting Python script.
That could only generate constructivist [0] proofs, and there are many things done in modern maths which are not constructivist. Maybe a better approach would be to use Curry-Howard [1] correspondence to directly get proofs from generated programs
Exactly, we need computer-equipped neural nets. Models need to use traditional UIs (including programming languages) and then we can talk about how to stop them. :)
It’s wishful thinking that I myself have once fallen for. I don’t trust our society to transition to a world with powerful machine intelligence safely, so would prefer a world in which ML progresses at a glacier’s pace.
Are there any general purpose models that are good at learning math? I mainly know basic feed-forward neural nets, but I don't think they do well outside their training region. Math, of course, has an infinite training region.
From my (limited) experience with the advanced ML models, they can "do basic math", but they make amateur mistakes with basic things - which indicates they don't actually know addition, but they are good at looking at patterns in existing language.
I would assume that state-of-the-art ML models could "convert a word problem into an equation", then feed that equation into a 30 year-old graphing calculator to "do the math"
The fact that no one has done this is an indicator that "there are more important things to work on", and it is just a matter of time that someone connects the two together
This seems so much like humans that it makes me think lots of people are learning math with an ML-like approach instead of… whatever the heck people like engineers and mathematicians are doing.
I attempted to create a general purpose model for the exact version of the "what comes next problem." It enumerated primitive recursive functions, trying them out as it went. The limitation to primitive recursive functions was convenient because they always terminate. I didn't have to filter out the functions that ran for too long. (or do I?)
The enumeration inherently includes functions of several variables, so I wasn't restricted to examples such as 1->1, 2->4, 3->9, 4->16 etc.
I could try it out on examples such as (1,2)->3 (2,1)->3 (0,2)->2, etc. Perhaps with enough it would "learn to add" = find a primitive recursive function that did addition.
I got as far as finding the first problem. The enumeration technique that I used was effectively doing a tree recursion, like that function for computing Fibonacci numbers that bogs down because Fib(10) is computing Fib(5) lots of times. I had a lot of numbers that coded for the identity function, lots of numbers that coded for the first few functions, making the whole thing bog down, trying the same few functions over and over under different numerical disguises.
I thought that I could see my way to fixing this first problem. Have some way of recognizing numbers that give forms that give the same function. I guessed that I could approximate this by saying that if two functions give the same value on a variety of arguments they are probably the same. Then I parameterise this criterion and tune. That opens the way to creating a consolidated enumeration, analogous to fixing the tree recursive fibonacci function by memoization, except trickier.
But my health is poor and I ran out of energy.
Also, I have a guess for the second problem. What happens if I fix the first problem and my enumeration reaches decently complicated primitive recursive functions. While they will all terminate, some might run for far too long, causing the process to bog down. Rejecting them on the basis of limiting the run time might work well. We are happy to only learn reasonably effect functions for doing maths.
It is a fun idea and I encourage others to have a go.
There is "LODA", which uses genetic algorithms, that continuously mutates existing math programs until discovering something new. It uses OEIS as training data, around 350k known integer sequences, such as primes/fibonacci. Around 100k programs have been mined so far.
> “When multiplying really large numbers together … they’ll forget to carry somewhere and be off by one,” says Vineet Kosaraju, a machine learning expert at OpenAI. Other mistakes made by language models are less human, such as misinterpreting 10 as 1 and 0, not ten.
So the expert has never seen a seven year old struggling in adding two single digit numbers together? Did the expert learn 1 and 0 being 10 first and learn to speak second?
> The MATH group found just how challenging quantitative reasoning is for top-of-the-line language models, which scored less than 7 percent. (A human grad student scored 40 percent, while a math olympiad champ scored 90 percent.)
Is this that surprising? How would our ieee editor score on the same problem set?
The situation is actually much worse for science, or any moving field. This models are by design and necessity historical. So that if, for example, the FDA issues a drug approval overnight, The model camp follow sudden changes in a “reasoned” why.
This is incorrect, and unclear why people think this.
The whole point of a good ML system is that it doesn't parrot training data. A good system can extrapolate novel answers from things it has seen. That is very far from "parroting".
Why instead of expecting a language to get math, don't we use the language model to generate code, run the code and use the result?
If a language model basically is the equivalent of a dumb human, how can we expect it to be better than us at math?Most humans use calculators even for simple equations.
I've been thinking about giving access to a search engine and a command line to a GPT-3 based AI, so that it can choose to run code it wrote or to expand its knowledge, I think that's a good way to expand its capabilities, even if that's probably how we're going to get skynet in the end.
More generally, they struggle to get thing right. They’re great at grammatical confabulation, but when you need a correct answer, or a correct drug recommendation, ask an expert.
It is a great sign that we are building AI in the right direction. Before building artificial human intelligence, it makes sense to get to the intelligence level of a mosquito or fly, then go to more intelligent animals in later iterations.
As most of the human knowledge is encoded in videos, getting better at understanding / generating videos will clearly get us closer to make computers understand the world.
I genuinely wonder if we will find there are some inherent tradeoffs to knowledge and understanding such that if we ever have machines that can “think like humans” they would in practice run into human-like cognition limits: ie such machines would be “bad at math” in the same way humans are “bat at math” compared to conventional computers.
Indeed. I posit that as we get closer and closer to simulating how the human brain works in the pursuit of artificial intelligence, we're going to start seeing more and more of the same "bugs" that humans have (logical fallacies, susceptibility to illusions, mental illness, etc.)
You think your job sucks now, just wait until you're dealing with the general AI over on the UX team that's trying to get your ass fired because it's fostering a 3 year old grudge over that time you said Chappie was stupid.
At first, I thought it was surprising that a language model with a restricted vocabulary (e.g. banning the letter "E") acts significantly more "mentally ill", and then I thought about how I would come across if forced to use that constraint all the time, and I realized that maybe I'd appear mentally ill too!
That's an interesting thought. However it's not cognitive limits that make humans bad at math, it's just a "hardware" issue: a human with a piece of paper is much better at math.
Even if neural networks were fundamentally incompatible with conventional computation, I don't see why you couldn't augment a neural network with a conventional ALU to do the numerical computations. This is exactly what humans do with pencil and paper - it's just a bit too slow.
Either the language model would need to know what it's doing or the host program would have to know what the AI is doing. Both seem out of reach. The latter seems more doable since you could hack something up for simple scenarios, but you'd effectively have to match the capabilities of the neural network in a classical way to handle every case (which would render using a neural net moot).
Btw, here's an example of how even a very simple zero-shot/prompt-engineering attempt to introduce a bit of system 2 reasoning into a language model can improve results.
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.
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.
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.
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.
How much of this is just "AI is bad at everything", but in the math case, it's easier for the lay person to tell.
It's all just passable garbled nonesense that the reader (goes to lengths) to interept based on their prior knowledge, which is not expressed in the syntax of what these systems output.
In the case of mathematics, we're far less willing to "BS away" the interpretive failures. But if we were equally demanding, likewise, all prose generated by these systems isnt AI "getting" anything either.
Pass a film reel thru' a shredder and an art student would still call it a film. Pass math thru' and a mathematician wont. This says more about our ability and inclination to make sense out of nonesense when in apparent communicative situations (since, when speaking to a person, this actually improves our mutual understanding).
So, how much of AI is just hacking people's cognitive failures: (1) people's willingness to attribute intention; (2) people's willingness to impart sense "at all costs" to apparent communication; and (3) "hopeium".
Have you ever used Github CoPilot? It does a lot of useful work, automating away rote typing in programming. Have you tried Dall-E or Stable Diffusion? They make good looking images. This comment seems completely unmoored from where the state of the art is right now.
Math follows a completely different approach with respect to how machine-learning AIs do their thing.
Reason derives its strength in having a few primitives and creating new assertions through the transformation of symbols by following precise rules (which is how algorithms work).
In ML-based AIs, everything is imprecise and probabilistic, and this kind of generation gets its strength from building recognizable from utterly imprecise inputs and training - quite the opposite of how logic and reason evolve. Now, "classic" AI was a powerful way to derive new knowledge, and automatic theorem proving is a strong discipline; but the recent breakthroughs in AI are not directly applicable to classic techniques.
Do you know what machine-learning AIs could be good for? Generating "insight" in problem solvers for guiding the theorem demonstrations through the proof search space, trying to find the best sub-spaces to explore. If there's a way to create human-like general AI, it will likely combine both kinds of generation - the rational methods of symbolic logic and the "irrational" statistical methods of ML.
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Dall-E produces good looking images within certain parameters.
When you are in its bounds it seems magical, once you go outside it seems like a weak joke.
And many of the reasons it is bad outside its sweet spot are fundamental to how it works not a flaw that can be iterated away.
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I haven't used copilot because I'm not sure I'm allowed, but I'll try it on a personal project eventually.
I'm hoping it's not as bad as Dall-E and Stable Diffusion - I've tried to use those to generate some generic product looking stock photos for a demo and it's spectacularly bad. The only context I see it get praised is fantasy style art - and that is visually appealing nonsense by definition.
If the code generated by copilot has the same "looks convincing but is fundamentally flawed" quality then it sounds like an insidious bug generator.
sure, but co-pilot is mostly just copying code (see, for example, the issue with it producing quake source code).
If you think of AI as a dial from sample(data) to mean(data), then as the dial is turned towards the mean() you get more "generic" results, but also more garbled ones.
Copilot is more like a search engine, having turned the dial more towards sample().
The real invention of the NN is simply to provide that dial in a trainable way.
The only change to the "state of the art" is the size of the weights, and how long they take to train. This "advancement" is no more impressive than google indexing more webpages.
There has been no step-change advancement in AI in, perhaps, 50 years. All we see today is a product of hardware, in GPU/CPUs able to compress TBs of data into c. 300GB of weights. And likewise, the internet to provide it and SSDs to hold it.
The "magic" of AI is no more the magic of wikipida, here: copilot is good only because million+ programmers made github good.
It's still little more than a fancy search.
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I agree. It's possible to point out the clear limitations of current AI without being oblivious to the huge, indisputable advances that have occurred.
People thought it might take centuries for a computer to defeat a top human in Go. Then deep learning showed up and a few years later it's the opposite.
A lot of the things deep learning methods are doing now are things no one had any idea how long research would take to achieve, or if they were even possible.
Personally, I think we are currently hitting some walls that might take a while to climb before we get to AGI, but I am very impressed at the recent progress.
> How much of this is just "AI is bad at everything"
"AI Language Models" are not touted as some general AI that is smart at everything, like a clever person with multiple intellectual skills integrated into one.
AI language models are for modeling language, not for math problem solving, or anything else. People good at language aren't always good at math.
DeepL produces very good, correct translations for "Alice has five more balls than Bob, who has two balls after he gives four to Charlie. How many balls does Alice have?" into numerous languages, even though it doesn't offer a solution.
I have little doubt that an AI system could be trained to translate word problems like this into systems of equations, which could be dumped into a some decades-old CAS to obtain a solution, which the AI could map back into the verbal domain through the identities between the math variables like x and Alice's apples.
"Hey look, that human who is supposedly good at math can't produce a painting of the Grand Canyon in the style of Monet, even if given eight months to do it, and is easily defeated in chess."
> How much of this is just "AI is bad at everything", but in the math case, it's easier for the lay person to tell
Honestly, even as someone generally pretty dismissive of the AI hype, I'm not sure you can go that far. The whole reason we have specific mathematical notation is that human languages often are not super great at dealing with it, and English in particular is pretty abysmal for being both unambiguous and precise (and I'd be surprised if language models didn't end up suffering from biases analogous to how many image recognition AI models have been found to not deal well with a diverse set of human appearances). We don't teach math the same way we teach English, and we certainly don't expect people to be experts at teaching both, so why would we expect an AI model designed for language to be able to do math?
Because there is an algorithm for it. Convert the strings into floating point numbers, add them, convert them back to strings. It’s a leetcode medium question. It should be learnable.
The article talks about abstract math questions, but even arithmetic is hard for language models.
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Language models aren't built for math. Their improvement/training cycles aren't sensitive to the exactness and rule-based nature of mathematical language, plus there are probably a lot of bad/misleading examples of math in the source data.
You'd have to be unrealistically pessimistic to call what GPT-3 and other huge language models produce "nonsense".
It's not that they were not built for math, but more like verification is hard. But it's hard for humans as well. A large generative model + a fast verifier could do wonders.
AlphaGo was built on that - the model can propose moves, but you can verify who won in the end. There are some code generation models that write their own tests as well, or use externally provided tests to verify their solutions. The DeepMind matrix multiplication algorithm was also "learning from verification" of generated solutions, because it's trivial to do that. In general verification remains an open problem.
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AI is bad at music also. Even the state of the art transformer models can't produce more than a few seconds of coherent melodic phrases.
I think if we replaced "AI" with "taking averages over subsets of historical examples", then there'd be no mystery for when "AI" will be good or bad at anything.
Would we expect a discrete melodic structure to be expressible as averages of prior music? No.
Have you heard the piano continuations of AudioLM?
https://google-research.github.io/seanet/audiolm/examples/
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Which is extra funny, because GOFAI models (e.g. David Cope's work) were doing a pretty OK job back in the 1990s!
It doesn't surprise me that an AI model for language can't grok maths or music. I can't see how a language model can map to maths. Hell, I don't even know how to describe music in words. It's possible to articulate some maths in words, but that often involves using words with unexpected definitions.
AI can be quite good at music,
but yes there is not yet at on-demand button rendering from a text prompt of bitstreams encoding composed performed and mastered music.
AI is bad at Audio. AI can do MIDI fine.
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That's wrong, and shows how ignorant you are of SOTA techniques for music generation. They are far ahead of that.
That’s what a musician does. They make short loops and loop them.
This reads like someone who knows sheet music and theory but does not listen to music. It’s repetition of short phrases over and over.
I’m not really sure what people expect of general AI trained on human generated outputs. It can’t make up anything anything “net new” only compose based upon what we feed it.
I like to think AI is just showing us how simple minded we really are and how our habit of sharing vain fairy tales about history makes us believe we’re masters of the universe.
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See the "joke explaining" examples on Page 36 of the paper: https://arxiv.org/abs/2204.02311 and tell me if it's just "passable garbled nonsense".
> 500 bn parameter model
That solution has a compressed representation of half the internet.
NNs are "garabled nonesense" insofar as they try to generalise; insofar as they are search engines, they provide apparent sense by just repeating something in their database (= weights).
Google, likewise, returns joke explanations.
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That's astonishing.
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This might make sense as a response solely to the title of the article, but I have to admit I find it puzzling as a reaction to its content. Notwithstanding the title, the article mentions a model called Minerva that scored fully 50% on the MATH dataset of high-school/undergrad mathematical problems. For comparison, a human computer science PhD student scored 40%. [1]
For context, Minerva came out this July. When it was tested on a national math exam, it scored higher than that year's class of graduating high school seniors. [2] A mere eight months (!) earlier, OpenAI had announced [3] they'd trained a language model that solved math word problems almost as well as an average middle-schooler. So even if you believe — rightly or wrongly — that current capabilities aren't very impressive, it's worth remembering that your understanding of current capabilities might not be entirely accurate, even if it's only a few months out of date.
Incidentally, it may be worth looking at some examples of these models' outputs before deciding what they can or can't do. Here's Minerva solving some math problems, for example:
https://dl.airtable.com/.attachmentThumbnails/32f10fc59039c7...
https://dl.airtable.com/.attachmentThumbnails/f6f86e0edd14d1...
https://dl.airtable.com/.attachmentThumbnails/d9bc743dca1015...
https://dl.airtable.com/.attachmentThumbnails/51562ef70c2b14...
https://dl.airtable.com/.attachmentThumbnails/c081906cc4d23b...
I'll admit I find it challenging to interpret these results as "passable garbled nonesense [sic]", though perhaps I'm not being demanding enough. At any rate, when these models go from beating 10-year olds at math to beating 18-year olds at math in the span of 8 months, one does start to wonder how much of the hype is really due to over-interpretation — and what the next 8 months have in store.
========================
[1] https://arxiv.org/pdf/1709.04326.pdf (For comparison, a 3-time Mathematics Olympiad gold-medalist scored 90%.)
[2] This was Poland's National Math Exam. Minvera scored 65%; the 2021 national average was 57%. See https://www.aitracker.org/ and Section 3 of the Minerva paper at https://arxiv.org/pdf/2206.14858.pdf
[3] https://openai.com/blog/grade-school-math/
Ashby strikes again.
Current sequence models don't have the right structures to represent math. Even if they use floating point internally, they can't really float the point because the nonlinearity in the model has a certain scale.
A system that processes language can take advantage of the human desire for closure
https://www.eurogamer.net/blood-in-the-gutter
to fool people into thinking it is more capable than it really is. Math isn't like that.
Floating point isn't relevant here.
The problem is that human language is approximate and correct math is not, so pattern matching on prose text is doomed. AI trained on exact math does a lot better. But that's not fully generic so fails the weird GPT goal of modeling all of human intelligence through prose. That's not how people solve math at all.
GPT's "Superficially plausible but wrong" math is actually pretty good match for non-expert bad-at-math average human behavior.
> GPT's "Superficially plausible but wrong" math is actually pretty good match for non-expert bad-at-math average human behavior.
Relevant blog post: https://www.greaterwrong.com/posts/YhgjmCxcQXixStWMC/artific... "The best experts in the field estimate it will be at least a hundred years before calculators can add as well as a human twelve-year-old."
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Mwell, the article claims, and points to work that also claims, that large language models can actually be made to perform arithmetic well. They need fine-tuning, verification, chain of thought prompting and majority voting to be combined but the linked Google blog says that Minerva hit 78.5% accuracy (on the GSM8K benchmark).
For me the problem is that we can look at the output and say if it's right or wrong, but we know what language models do, internally: they predict the next token in a sequence. And we know that this is no way to do arithmetic, in the long run, even though it might well work over finite domains.
Which is to say, I'm just as skeptical as you are, and probably even more, but I think it's useful to separate the claim from what has actually been demonstrated. Google claims its Minerva model is "solving maths problems" but what it's really doing is predicting solutions to problems like the ones it's been fine-tuned on, and those problems are problems stated at least partly in natural language, not "naked" arithmetic operations. In the latter, language models are still crap because they can't use the context of the natural language problem statement to help them predict the solution.
Btw, "chain of thought prompting" if I remember correctly is a process by which an experimenter prompts the language model with a sequence of intermediary problems. So it's not so much the model's chain of thought, as the experimenter's chain of thought and the experimenter is asking the model to help him or her complete their chain of thought. I have a fuzzy recollection of that though.
computers already do math. language models just need to translate problems into code of some kind that can be run to get the answer.
executive function/planning is probably the biggest problem at this point for ai.
That's interesting, I hadn't made the connection between executive function and intelligence.
I went through a burnout in 2019 that felt like having a stroke. My brain finally reached such a level of negative reinforcement after years of failure that it wouldn't let me work anymore. I'd go to do very simple tasks, everything from brushing my teath to writing a TODO list, and it was like the part of my brain that performed those tasks wasn't there anymore. Or at least, it no longer obeyed if it perceived a potential reward involved. It was like my motivation got reversed. I had to relearn how to do everything, despite knowing that no reward might come for a very long time, which took at least 6 months before I began recovering. The closest answer I have is that my brain healed through faith.
I only bring it up because executive function may be associated with a subjective experience of meaning. If there's truly no point to anything, then it's hard to summon the motivation to string together a sequence of AI tasks into something more like AGI.
I guess that's another way of saying that nihilism could be the final hurdle for AGI to overcome. It's like the human philosophical question of why there's something instead of nothing. Or why angels would choose to be incarnate on Earth to experience a life of suffering when it's so much easier to remain dissociated.
The point I'm trying to make is LLMs don't need to do everything just be the glue to other systems.
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That's not a bad approach, necessarily.
There is a fairly simple program in
https://www.amazon.com/Paradigms-Artificial-Intelligence-Pro...
that solves word problems using the methods of the old AI. The point is that is is efficient and effective to use real math operators and not expect to fit numbers through the mysterious bottleneck of neural encoding.
> language models just need to translate problems into code of some kind that can be run to get the answer
A huge "just"! Isn't this the magic step? Translating ambiguous symbols to meaning and combining them in meaningful ways is a big deal which, apparently, these AI models cannot do. They can just parrot things.
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I'm not so sure about that. Of course computers can do arithmetic operations, but this is not the same as solving math problems, proving theorems, etc. Even mathematical objects are approximated up to an approximation error in a computer (like a differentiable manifold or a real number).
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That's because they're not modelling anything. The shocking thing about current AI models is that just sort of repeating and copying from memory what you've heard and seen gets you 97% of the way to imitating a person.* They still need to generate actual models somewhere to create consistency; so many generated images with one eye completely different from the other, or three arms, or fingers that grow into their cellphones.
If you solve this, you've probably solved almost anything in the simulation field. I have no confidence that the solution will even be complicated. Information consumed needs to be used to add to some sort of model, and that model always needs to be used as part of input. The complicated part would be to make that base model able to modify itself reasonably based on input, to tolerate constant inconsistency, and to constantly refine itself towards consistency i.e. ruminate.
I think a huge difference (which I think was approached through theories of embodied cognition) is that people start with a model (or the ability to create a model) of themselves. We can apply that model to other things and use it both to change how we ourselves behave, and how we speculate about the invisible states of other things. It's not for nothing that we can (and must) anthropomorphize anything.
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* Which was huge towards the confirmation of my belief that this is all people do 97% of the time.
This is factually wrong, both in terms of quantity and quality.
Current AI models are not "just sort of repeating and copying from memory". This is just an incorrect characterization of how they work and how they perform.
AI skeptics often say things like this then backpedal with something like "Well they aren't really repeating what they heard, but their generative model is just a slightly more sophisticated version of repeating what they've heard." But this weaker claim is also true of humans. It's certainly the case that >97% percent of what humans say is "just repeating and copying" in the same sense.
> Current AI models are not "just sort of repeating and copying from memory". This is just an incorrect characterization of how they work and how they perform.
You say this, but don't explain how. Because this is exactly what they are doing.
> AI skeptics often say things like this
I'm not really an AI skeptic. I think that we're very close to AI being indistinguishable from people. There are clearly problems that need to be solved, but I think the hardest problem was accepting the fact that humans are largely just copying and realizing that would be enough to get you 97% of the way there, especially if you gave a machine far more to copy than a human could consume.
> then backpedal with something like "Well they aren't really repeating what they heard, but their generative model is just a slightly more sophisticated version of repeating what they've heard." But this weaker claim is also true of humans. It's certainly the case that >97% percent of what humans say is "just repeating and copying" in the same sense.
Maybe I'm not expressing myself clearly, but it seems that you're just repeating my comment with a sneer. Agreeing angrily?
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can you actually share what "current AI models" are then? Not trying to be rude, but you just said "na ah" and then refused to argument any position.
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There is a reasoning loop that LLMs are clearly missing.
"repeating and copying from memory what you've heard and seen gets you 97% of the way to imitating a person."
I'm in this hot take and I don't like it..
> “I think there’s this notion that humans doing math have some rigid reasoning system—that there’s a sharp distinction between knowing something and not knowing something,” says Ethan Dyer, a machine-learning expert at Google. But humans give inconsistent answers, make errors, and fail to apply core concepts, too. The borders, at this frontier of machine learning, are blurred.
This part resonates with me. There was a time when I could calculate congruent modulo problems with exponents, but I couldn’t do it step by step, I could only “hallucinate” in a fuzzy way to arrive at the solution, somehow like recalling the solution from memory.
When we have to explain our reasoning we can’t think the same way. It’s like thinking with a debugger attached.
Language models can generate a Python function that does the math perfectly.
I bet you would get better results if you tweaked the prompt to say "Generate a Python program that solves X math problem" and then just ran the resulting Python script.
It does not need to be AGI to be useful.
you can also tell the model that it doesnt know how to do math, and it respects that
https://twitter.com/goodside/status/1568448128495534081
This is pretty cool, although the "don't use outside the security sandbox" made me laugh: https://twitter.com/goodside/status/1568704302813700096/phot...
You mean "generate a Python function that calls a library that does math perfectly, right?
In the limit, it's going to design an AI to write some python to call a library that does the math perfectly.
Unlike 99.99% of human programmers, who can and often do implement everything in sympy/numpy from scratch ;-)
Exactly! Hey it gets the job done :)
Software is just a tall wedding cake of abstractions built on top of abstractions.
That could only generate constructivist [0] proofs, and there are many things done in modern maths which are not constructivist. Maybe a better approach would be to use Curry-Howard [1] correspondence to directly get proofs from generated programs
[0] https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_...
[1] https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspon...
Live demo of this you can run: https://twitter.com/sergeykarayev/status/1569377881440276481
That is also a very valid and interesting thing to do.
But it's also quite interesting to see how the model would do "by itself". All kinds of interesting lessons to be learned!
Yeah! It is interesting to try and figure out "what" the model is actually learning. It is a valid thread of scientific inquiry.
Exactly, we need computer-equipped neural nets. Models need to use traditional UIs (including programming languages) and then we can talk about how to stop them. :)
The title is contradicted by the contents of the article. Minerva’s 78% accuracy is a miraculous result considering the prior 7% SOTA.
And almost none of the commenters seem to have read the article, so everyone is saying how predictable this was. Quite bizarre.
It’s wishful thinking that I myself have once fallen for. I don’t trust our society to transition to a world with powerful machine intelligence safely, so would prefer a world in which ML progresses at a glacier’s pace.
Are there any general purpose models that are good at learning math? I mainly know basic feed-forward neural nets, but I don't think they do well outside their training region. Math, of course, has an infinite training region.
From my (limited) experience with the advanced ML models, they can "do basic math", but they make amateur mistakes with basic things - which indicates they don't actually know addition, but they are good at looking at patterns in existing language.
I would assume that state-of-the-art ML models could "convert a word problem into an equation", then feed that equation into a 30 year-old graphing calculator to "do the math"
The fact that no one has done this is an indicator that "there are more important things to work on", and it is just a matter of time that someone connects the two together
This seems so much like humans that it makes me think lots of people are learning math with an ML-like approach instead of… whatever the heck people like engineers and mathematicians are doing.
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> "convert a word problem into an equation"
Isn't this a huge step? It's not a minor detail remaining to be solved, but possibly the largest step!
What you describe is exactly what state of the art has done. They even lied and said it was "solving math problems" by calling numpy methods.
I attempted to create a general purpose model for the exact version of the "what comes next problem." It enumerated primitive recursive functions, trying them out as it went. The limitation to primitive recursive functions was convenient because they always terminate. I didn't have to filter out the functions that ran for too long. (or do I?)
The enumeration inherently includes functions of several variables, so I wasn't restricted to examples such as 1->1, 2->4, 3->9, 4->16 etc.
I could try it out on examples such as (1,2)->3 (2,1)->3 (0,2)->2, etc. Perhaps with enough it would "learn to add" = find a primitive recursive function that did addition.
I got as far as finding the first problem. The enumeration technique that I used was effectively doing a tree recursion, like that function for computing Fibonacci numbers that bogs down because Fib(10) is computing Fib(5) lots of times. I had a lot of numbers that coded for the identity function, lots of numbers that coded for the first few functions, making the whole thing bog down, trying the same few functions over and over under different numerical disguises.
I thought that I could see my way to fixing this first problem. Have some way of recognizing numbers that give forms that give the same function. I guessed that I could approximate this by saying that if two functions give the same value on a variety of arguments they are probably the same. Then I parameterise this criterion and tune. That opens the way to creating a consolidated enumeration, analogous to fixing the tree recursive fibonacci function by memoization, except trickier.
But my health is poor and I ran out of energy.
Also, I have a guess for the second problem. What happens if I fix the first problem and my enumeration reaches decently complicated primitive recursive functions. While they will all terminate, some might run for far too long, causing the process to bog down. Rejecting them on the basis of limiting the run time might work well. We are happy to only learn reasonably effect functions for doing maths.
It is a fun idea and I encourage others to have a go.
There is "LODA", which uses genetic algorithms, that continuously mutates existing math programs until discovering something new. It uses OEIS as training data, around 350k known integer sequences, such as primes/fibonacci. Around 100k programs have been mined so far.
https://loda-lang.org/
I'm a contributer to LODA.
LODA runs on CPU. It doesn't use GPU. If you have spare computer, then please consider contributing with the mining. Your contribution helps.
https://boinc.loda-lang.org/loda/
Can't drive. Bad at math. AI's are becoming almost human.
Can they do passive aggressive dickhole manager? If so, we're doomed.
> “When multiplying really large numbers together … they’ll forget to carry somewhere and be off by one,” says Vineet Kosaraju, a machine learning expert at OpenAI. Other mistakes made by language models are less human, such as misinterpreting 10 as 1 and 0, not ten.
So the expert has never seen a seven year old struggling in adding two single digit numbers together? Did the expert learn 1 and 0 being 10 first and learn to speak second?
> The MATH group found just how challenging quantitative reasoning is for top-of-the-line language models, which scored less than 7 percent. (A human grad student scored 40 percent, while a math olympiad champ scored 90 percent.)
Is this that surprising? How would our ieee editor score on the same problem set?
The situation is actually much worse for science, or any moving field. This models are by design and necessity historical. So that if, for example, the FDA issues a drug approval overnight, The model camp follow sudden changes in a “reasoned” why.
Talking about this stuff would be so much easier if we stopped calling those software "AI".
It is a machine learning algorithm. It is an electronic Parrot.
thats it. And suddenly no one will wonder "OH MY WHY CANN IT NOT DO MATH< IT SMART?!?!"
> It is a machine learning algorithm.
True
> It is an electronic Parrot.
This is incorrect, and unclear why people think this.
The whole point of a good ML system is that it doesn't parrot training data. A good system can extrapolate novel answers from things it has seen. That is very far from "parroting".
Don't listen to these bots, they're all just parroting this same idea that models parrot.
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Why instead of expecting a language to get math, don't we use the language model to generate code, run the code and use the result?
If a language model basically is the equivalent of a dumb human, how can we expect it to be better than us at math?Most humans use calculators even for simple equations.
I've been thinking about giving access to a search engine and a command line to a GPT-3 based AI, so that it can choose to run code it wrote or to expand its knowledge, I think that's a good way to expand its capabilities, even if that's probably how we're going to get skynet in the end.
More generally, they struggle to get thing right. They’re great at grammatical confabulation, but when you need a correct answer, or a correct drug recommendation, ask an expert.
It is a great sign that we are building AI in the right direction. Before building artificial human intelligence, it makes sense to get to the intelligence level of a mosquito or fly, then go to more intelligent animals in later iterations.
As most of the human knowledge is encoded in videos, getting better at understanding / generating videos will clearly get us closer to make computers understand the world.
I genuinely wonder if we will find there are some inherent tradeoffs to knowledge and understanding such that if we ever have machines that can “think like humans” they would in practice run into human-like cognition limits: ie such machines would be “bad at math” in the same way humans are “bat at math” compared to conventional computers.
Indeed. I posit that as we get closer and closer to simulating how the human brain works in the pursuit of artificial intelligence, we're going to start seeing more and more of the same "bugs" that humans have (logical fallacies, susceptibility to illusions, mental illness, etc.)
You think your job sucks now, just wait until you're dealing with the general AI over on the UX team that's trying to get your ass fired because it's fostering a 3 year old grudge over that time you said Chappie was stupid.
At first, I thought it was surprising that a language model with a restricted vocabulary (e.g. banning the letter "E") acts significantly more "mentally ill", and then I thought about how I would come across if forced to use that constraint all the time, and I realized that maybe I'd appear mentally ill too!
You can play with LMs with constrained vocabularies here: https://huggingface.co/spaces/Hellisotherpeople/Gadsby
That's an interesting thought. However it's not cognitive limits that make humans bad at math, it's just a "hardware" issue: a human with a piece of paper is much better at math.
Even if neural networks were fundamentally incompatible with conventional computation, I don't see why you couldn't augment a neural network with a conventional ALU to do the numerical computations. This is exactly what humans do with pencil and paper - it's just a bit too slow.
Either the language model would need to know what it's doing or the host program would have to know what the AI is doing. Both seem out of reach. The latter seems more doable since you could hack something up for simple scenarios, but you'd effectively have to match the capabilities of the neural network in a classical way to handle every case (which would render using a neural net moot).
And no wonder, as they correspond much closer to a Kahneman system 1 than system 2, where we do most of our math.
Btw, here's an example of how even a very simple zero-shot/prompt-engineering attempt to introduce a bit of system 2 reasoning into a language model can improve results.
https://arxiv.org/abs/2201.11903
It seems like they know as much math as you would if you only listened to people talking about math your whole life
Don't feel too bad AI - most humans struggle to "get" math too!
The article is actually about how they are getting good at it :)
Maybe because it's not actual AI.
People struggle to get math, too.
I bet vision transformers understand math better because it’s somewhat artistic
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.
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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.