5 ms·

According to the LessWrong post, the smaller model trained on more data performs better on most of the tasks, but it’s worse on “college level math” questions.

According to the LessWrong post, the smaller model trained on more data performs better on most of the tasks, but it’s worse on “college level math” questions. I wonder why that is. Is it because the extra capacity of the larger model was used to basically memorize theorems? Or is it because the extra “brain power” let it model the math better? Oddly, one of the tasks that the smaller most outperformed the larger model on is “high school level math”! Very counterintuitive, and I am curious if there are any big takeaways lurking in that disparity.

deleted 5y ago
[deleted]
adamsmith143 5y ago
Probably right. Most people dump on these language models for this reason but it would be absurd for a HS student to have to re-derive the quadratic equation every time they worked on an Algebra problem so naturally you memorize it. Why should it be any different for a language model?
- eutectic 5y ago
  I never memorized the quadratic formula, and I did OK.
  - whimsicalism 5y ago
    Did you go to school in the US in the last 2-3 decades?
    - replygirl 5y ago
      Once you start calculus they let you use a real calculator
      - whimsicalism 5y ago
        That may be true, but in the US there are typically math courses before calculus.
        replygirl 5y ago
        But then we get a calculator.
        adamsmith143 5y ago
        Maybe we went to radically different schools but I certainly had to calculate by hand using the quadratic formula countless times where calculators were not allowed to be used. Anyway it distracts from the point so it's not relevant.
        whimsicalism 5y ago
        Even then, it is typically not a symbolic calculator so if your answer is a closed form function of variables, you're SOL with a TI-84.
    - eutectic 5y ago
      No, the UK. But completing the square only takes a minute.
      - whimsicalism 5y ago
        Try completing the square when the coefficients are variables :)
ShamelessC 5y ago
Gwern responded to a similar question in the comments section. (parent) > the fact that data and compute need to scale proportionally seems… like a big point in favor of NNs as memorizers/interpolators. (gwern) > Surely it's the opposite? The more bang you get out of each parameter, the less it looks like 'just' (whatever that means) memorization/interpolation. When you needed to increase parameters a lot, disproportionately, to cope with some more data, that does not speak well of abstractions or understanding. (If I can train a 1t model to get the same loss as what I thought was going to take a 100t model, why would I think that that 100t model must be memorizing/interpolating less?) Let's take your claim to its logical extreme: suppose we discovered tomorrow a scaling law that made parameters near-constant (log, let's say); would that not suggest that those parameters are super useful and it's doing an amazing job of learning the underlying algorithm and is not memorizing/interpolating?
- sillysaurusx 5y ago
  This isn’t addressing their question. And Gwern’s goal here is to (incorrectly) try to get rid of the idea that models are just memorizing and interpolating, when in fact memorization and interpolation is what we all do, including models. He’s just bothered by the idea that people think of models as less than magic. On the other hand, https://twitter.com/model_mechanic/status/1512976881183645698?s=21 https://twitter.com/model_mechanic/status/151297688118364569... is admittedly pretty magical, even if the basis of that magic is memorization and interpolation.
  - VirusNewbie 5y ago
    Why do you say they just memorize and interpret? I can teach GPT-2 new things, including new objects and their physical properties and it does a good job with that. That also means it has definitely not just regurgitated a matching sentence back to me.
    - replygirl 5y ago
      when i see a new object for the first time, i MEMORIZE what i INTERPRET as its identifying traits, and ask someone who has already MEMORIZED what that object is to INTERPRET a concept with which i can associate those traits. the next time i encounter an object with those traits i can then recall the associations, then compose those trait-level interpretations into an interpretation of an object. at a fundamental level that's all this is, compositions of associated memorizations and interpretations, which map to compositions of sentence parts the machine can regurgitate back to you
danuker 5y ago
It might just be by chance: the initial weights of one model could have been lucky in some areas, and unlucky in others. There's no way to tell other than training again, which is a costly proposition.
- eigenvalue 5y ago
  That seems pretty unlikely to me actually. As the models and training data get much bigger, I think the initial weights become less important (at least assuming your random weights have certain desirable statistical properties, which they do by construction usually).

deleted 5y ago

[deleted]

adamsmith143 5y ago

Probably right. Most people dump on these language models for this reason but it would be absurd for a HS student to have to re-derive the quadratic equation every time they worked on an Algebra problem so naturally you memorize it. Why should it be any different for a language model?

eutectic 5y ago
I never memorized the quadratic formula, and I did OK.
- whimsicalism 5y ago
  Did you go to school in the US in the last 2-3 decades?
  - replygirl 5y ago
    Once you start calculus they let you use a real calculator
    - whimsicalism 5y ago
      That may be true, but in the US there are typically math courses before calculus.
      - replygirl 5y ago
        But then we get a calculator.
        adamsmith143 5y ago
        Maybe we went to radically different schools but I certainly had to calculate by hand using the quadratic formula countless times where calculators were not allowed to be used. Anyway it distracts from the point so it's not relevant.
        whimsicalism 5y ago
        Even then, it is typically not a symbolic calculator so if your answer is a closed form function of variables, you're SOL with a TI-84.
  - eutectic 5y ago
    No, the UK. But completing the square only takes a minute.
    - whimsicalism 5y ago
      Try completing the square when the coefficients are variables :)

ShamelessC 5y ago

Gwern responded to a similar question in the comments section. (parent) > the fact that data and compute need to scale proportionally seems… like a big point in favor of NNs as memorizers/interpolators. (gwern) > Surely it's the opposite? The more bang you get out of each parameter, the less it looks like 'just' (whatever that means) memorization/interpolation. When you needed to increase parameters a lot, disproportionately, to cope with some more data, that does not speak well of abstractions or understanding. (If I can train a 1t model to get the same loss as what I thought was going to take a 100t model, why would I think that that 100t model must be memorizing/interpolating less?) Let's take your claim to its logical extreme: suppose we discovered tomorrow a scaling law that made parameters near-constant (log, let's say); would that not suggest that those parameters are super useful and it's doing an amazing job of learning the underlying algorithm and is not memorizing/interpolating?

sillysaurusx 5y ago
This isn’t addressing their question. And Gwern’s goal here is to (incorrectly) try to get rid of the idea that models are just memorizing and interpolating, when in fact memorization and interpolation is what we all do, including models. He’s just bothered by the idea that people think of models as less than magic. On the other hand, https://twitter.com/model_mechanic/status/1512976881183645698?s=21 https://twitter.com/model_mechanic/status/151297688118364569... is admittedly pretty magical, even if the basis of that magic is memorization and interpolation.
- VirusNewbie 5y ago
  Why do you say they just memorize and interpret? I can teach GPT-2 new things, including new objects and their physical properties and it does a good job with that. That also means it has definitely not just regurgitated a matching sentence back to me.
  - replygirl 5y ago
    when i see a new object for the first time, i MEMORIZE what i INTERPRET as its identifying traits, and ask someone who has already MEMORIZED what that object is to INTERPRET a concept with which i can associate those traits. the next time i encounter an object with those traits i can then recall the associations, then compose those trait-level interpretations into an interpretation of an object. at a fundamental level that's all this is, compositions of associated memorizations and interpretations, which map to compositions of sentence parts the machine can regurgitate back to you

danuker 5y ago

It might just be by chance: the initial weights of one model could have been lucky in some areas, and unlucky in others. There's no way to tell other than training again, which is a costly proposition.

eigenvalue 5y ago
That seems pretty unlikely to me actually. As the models and training data get much bigger, I think the initial weights become less important (at least assuming your random weights have certain desirable statistical properties, which they do by construction usually).