11–20 of 235 posts
Earlier quoted context omitted.
It's recently been shown that even though the numbers are represented with different tokens, the network learns to form an internal representation that understands the progression from one token to the next.
The idea that each number has to be inside ones Brain or Neural Network or Token is plainly wrong. Network has to grasp the "abstract" number, but it clearly did not grasp that concept.
Thank you for this. Technically it's not GPT-3, but GPT-NeoX-20B, although they are based on a similar architecture. The poor performance is most likely due to not having a large database of math problems to draw from. Github, for example, is part of the dataset that is used to train both GPT-3 and GPT-Neo variants, which is partly why they can generate meaningful code (sometimes). I wonder how a model finetuned for…
Poor performance is more likely due to how transformer neural networks view numbers. It memorises them like words instead of modeling their numerical structure. Thus even if it’s seen the number 3456 and 3458, it knows nothing of 3457. Totally different embedding. It’s like a kid memorising a multiplication table instead of learning the more general principle of multiplication (related: this illusion is why big model…
Deep Symbolic Regression for Recurrent Sequences https://arxiv.org/abs/2201.04600
If you look at embedding visualization it is very clear that the model learns order of numbers.
(Interactive demo: http://recur-env.eba-rm3fchmn.us-east-2.elasticbeanstalk.com... )
There is also:
Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets https://arxiv.org/abs/2201.02177
Again, looking at visualizations the model very clearly grasps the structure of the function it models.
Earlier quoted context omitted.
The idea that each number has to be inside ones Brain or Neural Network or Token is plainly wrong. Network has to grasp the "abstract" number, but it clearly did not grasp that concept.
How would you test if it grasped the concept?
This paper shows fairly conclusively that the network 'groks' modular addition.
Earlier quoted context omitted.
The idea that each number has to be inside ones Brain or Neural Network or Token is plainly wrong. Network has to grasp the "abstract" number, but it clearly did not grasp that concept.
How would you test if it grasped the concept?
This just shows that this model did not learn anything. Humans do not see billions of examples to add numbers. We see just few and can apply learned notation and procedures to infinity with 100% precision. GPT-3 learned mathematical intuition. Humans can hardly learn multiplication table over months and repetitions of same examples, and that table hardly matters at all. GPT-3 is just plainly wrong objective they tryi…
Sure, with pen and paper we can follow specific algorithms manually to very slowly get a precise result. If we wanted a computer to merely follow instructions, then I suspect that there are better ways...
Arithmetic seems like an example where it would help to learn from the real world, not just from text. I learnt to add up by watching my teacher manipulate plastic Lego-style blocks. Put 3 blocks with 2 blocks, and you have 1, 2, 3, 4, 5.
Earlier quoted context omitted.
How would you test if it grasped the concept?
Being able to extrapolate to numbers that were not in the training set, perhaps? At least that'd be a basic part of the requirement.
Deep Symbolic Regression for Recurrent Sequences https://arxiv.org/abs/2201.04600
(Interactive demo: http://recur-env.eba-rm3fchmn.us-east-2.elasticbeanstalk.com... )
Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets https://arxiv.org/abs/2201.02177
Both of these models can generalize to numbers it have not seen.
This just shows that this model did not learn anything. Humans do not see billions of examples to add numbers. We see just few and can apply learned notation and procedures to infinity with 100% precision. GPT-3 learned mathematical intuition. Humans can hardly learn multiplication table over months and repetitions of same examples, and that table hardly matters at all. GPT-3 is just plainly wrong objective they tryi…
But your conclusion here is entirely wrong: the model clearly is learning something. From eyeballing this, the model is right about 10% of the time. If it were spitting out random digits the accuracy would effectively be zero. So exactly what is it learning? Is it memorising exactly equations that it saw in training? Is it learning ngram patterns that occur frequently in arithmetic equations?
I'm not an expert on these things and I'd love to hear from someone who is.
Thank you for this. Technically it's not GPT-3, but GPT-NeoX-20B, although they are based on a similar architecture. The poor performance is most likely due to not having a large database of math problems to draw from. Github, for example, is part of the dataset that is used to train both GPT-3 and GPT-Neo variants, which is partly why they can generate meaningful code (sometimes). I wonder how a model finetuned for…
Poor performance is more likely due to how transformer neural networks view numbers. It memorises them like words instead of modeling their numerical structure. Thus even if it’s seen the number 3456 and 3458, it knows nothing of 3457. Totally different embedding. It’s like a kid memorising a multiplication table instead of learning the more general principle of multiplication (related: this illusion is why big model…