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Comment by ravi-delia | Hacker News Reader

I believe the dominant thinking is that GPT-3 has trouble with math because it doesn't see individual digits. It obviously has no trouble working on words, which are much more discreet than numbers. I wouldn't be surprised if it had trouble carrying a long equation though. When writing it can reconsider the whole context with each new word, externalizing that memory, but with most computations it would have to carry out the whole thing in one go. That's a lot of dedicated parameters for a single subtask.

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Even the tokenization is wonky. Imagine if you had no concept of math characters and instead has a lookup table of common-ngrams (BPE encoding). For example, the binary addition function “a+b” may be tokenized as a unary “3+b” because “3+b” occurs commonly. That tokenization is vastly different from “3.00000001+b”. GPT has to invert this tokenization artifact with finite training data.

Yeah, I think that's the most accepted explanation. Everything after my first sentence was total speculation, the tokenization is usually cited as the issue.

> with most computations it would have to carry out the whole thing in one go

Is there a way to allow models to say "let me think about this some more"? With language models like GPT-3 you emit one token per inference iteration, with its previous output fed back in as input/state. Can models opt out of providing a token, but still update state? That would allow it to break up the computation into discrete steps.

I think it would work, but backprop would be computed in a different way every time. I'm not an expert, so there may be sneaky ways around it, but I'm pretty sure you'd lose out on a long history of little efficiency improvements when you could just make it more recurrent instead.

I believe GPT-3 has a transformer-based architecture. So it doesn't recursively ingest it's own output in each iteration. I believe attention-based transformer models have enough complexity to be able to learn what you are talking about on their own.

Thank you for pointing out the difference. I went and reread about transformers; previously I thought they were a kind of RNN. (I am not an ML engineer.)

GPT-3's transformers only recur some finite amount. Attention does a lot compared to a bog standard RNN, and probably if the numbers were tokenized it would be enough for most reasonable computations, but eventually you definitely would hit a cap. That's probably a good thing, of course. The network and training are Turing complete together, but it would suck if the network itself could fail to terminate.

That would be neat. You could give it backspace and "let me think more" tokens that would signal the inference program to run it again on the prompt plus its own output. That way it could generate "thoughts thoughts thoughts [THINKMORE] thoughts thoughts thoughts [THINKMORE] [BACKSPACE]X 8 (The real output would go here""

It would of course have to be penalized in some way for [THINKMORE]ing to avoid infinite processing time. It would have to learn to reason at what point diminishing returns would kick in from continuing to [THINKMORE] VS recording its best answer. The penilization function would have to take into account remaining tokens that would fit in the transformer prompt.

Here it is: https://arxiv.org/abs/1611.06188

RNN outputs "confidence" bit which can guide computation to perform more steps to obtain more confidence in the result. Essentially, RNN asks "let me think about that some more".

But, separate ablation study found that if you just drop confidence bit altogether and allow RNN to compute some more every time (e.g., always perform 4 computations on single input for 1 output), you get same or better results without extra complexity of training.

There is also Microsoft Research's paper I can't find right now about the variable computation for image classification where there is a "confidence" bit at some of the final layers - if lower layer is cinfident enough, it's output will be used for classification, otherwise the output of that layer will be passed into more transformation of upper layers.

> But, separate ablation study found that if you just drop confidence bit altogether and allow RNN to compute some more every time (e.g., always perform 4 computations on single input for 1 output), you get same or better results without extra complexity of training.

Do they saw what happens if you do both? Perhaps the “benefit from a higher computation/per cycle” phenomena and the “benefit from signalling relative computation resource allocation” one are different.

I guess I’ll have to try and read the paper, but I’m new to the literature and am clueless about the current state of research.

Hardcoding a tokenization tweak that keeps individual digits separate would be a trivial change to the preprocessing that would not affect the rest of the model training process.

Can it do math on "prose numbers", eg. "two thousand three hundred and four"?

Not super well in the GPT-2 based models I have access to. It falls into different error modes though, diving into prose rather than even making an attempt. Makes sense in retrospect!

And that's where you see the man behind the curtain.

Next year: GPT-NG offloads it's answers to Amazon Mechanical Turk, and we've come full circle.

Yeah for sure. With energy prices soaring, Moore's law being morally over for since 2010, wages being so completely destroyed by the hatred Democrats have for them, and the sneaky little misconceptions and errors the golem's makers did not fight hard enough to let in, AI will be supplanted by plain I.

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