Comment by gonehome | Hacker News Reader

Comment by gonehome | Hacker News Reader

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Check out GPT-3’s performance on arithmetic tasks in the original paper (https://arxiv.org/abs/2005.14165)

Pages: 21-23, 63

Which shows some generality, the best way to accurately predict an arithmetic answer is to deduce how the mathematical rules work. That paper shows some evidence of that and that’s just from a relatively dumb predict what comes next model.

They control for memorization and the errors are off by one which suggest doing arithmetic poorly (which is pretty nuts for a model designed only to predict the next character).

(pg. 23): ”To spot-check whether the model is simply memorizing specific arithmetic problems, we took the 3-digit arithmetic problems in our test set and searched for them in our training data in both the forms "<NUM1> + <NUM2> =" and "<NUM1> plus <NUM2>". Out of 2,000 addition problems we found only 17 matches (0.8%) and out of 2,000 subtraction problems we found only 2 matches (0.1%), suggesting that only a trivial fraction of the correct answers could have been memorized. In addition, inspection of incorrect answers reveals that the model often makes mistakes such as not carrying a “1”, suggesting it is actually attempting to perform the relevant computation rather than memorizing a table.”

It’s hard to predict timelines for this kind of thing, and people are notoriously bad at it. Few would have predicted the results we’re seeing today in 2010. What would you expect to see in the years leading up to AGI? Does what we’re seeing look like failure?

https://intelligence.org/2017/10/13/fire-alarm/

To me, this was by far the most interesting thing in the original paper, and I would like to find out more about it.

I think, however, we should be careful about anthropomorphizing. When the researchers wrote 'inspection of incorrect answers reveals that the model often makes mistakes such as not carrying a “1”', did they have evidence that this was being attempted, or are they thinking that if a person made this error, it could be explained by their not carrying a 1?

I also think a more thorough search of the training data is desirable, given that if GPT-3 had somehow figured out any sort of rule for arithmetic (even if erroneous) it would be a big deal, IMHO. To start with, what about 'NUM1 and NUM2 equals NUM3'? I would think any occurrence of NUM1, NUM2 and NUM3 (for both the right and wrong answers) in close proximity would warrant investigation.

Also, while I have no issue with the claim that 'the best way to accurately predict an arithmetic answer is to deduce how the mathematical rules work', it is not evidence that this actually happened: after all, the best way for a lion to catch a zebra would be an automatic rifle. We would at least want to consider whether this is within the capabilities of the methods used in GPT-3, before we make arguments for it probably being what happened.

> I think, however, we should be careful about anthropomorphizing. When the researchers wrote 'inspection of incorrect answers reveals that the model often makes mistakes such as not carrying a “1”', did they have evidence that this was being attempted, or are they thinking that if a person made this error, it could be explained by their not carrying a 1?

Occam's razor suggests that if you're getting errors like that it's because you're doing column-wise math but failing to combine the columns correctly. It's possible it's doing something weirder and harder, I guess.

I don't know what exactly you mean by "this was being attempted". Carrying the one? If I say it failed to carry ones, that's not a claim that it was specifically trying to carry ones.

Devil's advocate, it could be that it did the math correctly, then inserted the error because humans do that sometimes in the text it was trained on. That wouldn't be "failing" anything.

In that case it wouldn't get worse results than the data it trained on.

It can get worse results for example if the prompt is biased towards the worse part of the data.

I take your point - I had read into that quote the implication that there are other cases where something resembling carrying had been seen, but even just adding the properly-aligned digits modulo 10 would be impressive. I would, however, like to see more evidence that this seems to be happening more often than by chance, and is unlikely to be explicable in terms of the specific numbers in question appearing in close proximity in the training data, before I am willing to say that it is the most likely explanation.

Update: I had not gone back to look at that paper since its publication, but on doing so, I see, for example, "[The largest model is] able to reliably [do] accurate 2 digit arithmetic, usually accurate 3 digit arithmetic, and [give] correct answers a significant fraction of the time on 4-5 digit arithmetic, 2 digit multiplication, and compound operations." Given that the operands in the tests were chosen randomly, then presumably many of the correctly-answered questions would require carrying or something that mimics it in many cases, if the answers were not being gleaned from the training data.

This is a pretty small search space in comparison to the size of gpt-3. I would fully expect that the arithmetic table of 0-100 with numbers between 0-100 is present in sufficient density on the internet for this to be memorized by gpt-3.

None of the GPTs can do column-based math, because they can't see columns. Byte pair encoding doesn't preserve characters. "1", "3" and "13" are all different tokens. This is also why GPT can't rhyme.

Do you know how previously unseen numbers in the prompt are encoded, probably the same way? Then GPT3 can not do any math at all, unless the specific numbers were seen before?

The quote above referred to exact copies of the problems, not individual numbers. And the abysmal success rate on four and five digit numbers does suggest it has trouble on rarer numbers.

Occam's razor is a very very bad principle to bank on when reverse-engineering AI models because approaches which we consider "simple" (likely in a "natural" context) could be very different from what some high-dimensional statistical model trained on a large data corpus considers simple. Eg: If Occam's razor applied reasonably, then adversarial examples wouldn't be a thing.

Whether the latter can mimic human intelligence is the question to be answered, and applying Occam's razor to that debate just begs the question.

I don't have any special insight into the problem, but I'd say whatever form real AGI takes it won't be a language model. Even without AGI these models are massively useful though - a version of GPT-3 that incorporates a knowledge graph similar to TOME would upend a lot of industries.

https://arxiv.org/abs/2110.06176

Shouldn't a very complicated perceptron be capable of addition if the problem is extracted from an image? Isn't that what the individual neurons do?

forgetting to carry a 1 makes a lot of sense knowing GPT-3 is just a giant predict before-after model. Seeing 2000 problems it probably gets a good sense of how numbers add/subtract together, but there's not enough specificity to work out the specific carrying rule.

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