4 ms·

Can someone ELI5 this for a non-mathematician?

by niek_pas 10mo ago

poszlem 10mo ago
[flagged]
- embedding-shape 10mo ago
  Do you think maybe OP would have asked a language model for the answer if they felt like they wanted a language model to give an answer? Or in your mind parent doesn't know about LLMs, and this is your way of introducing them to this completely new concept?
  - NitpickLawyer 10mo ago
    Funny that the "human" answer above took 2 people to be "complete" (i.e. an initial answer, followed by a correction and expansion of concepts), while the LLM one had mostly the same explanation, but complete and in one answer.
    - embedding-shape 10mo ago
      Maybe most of us here don't seek just whatever answer to whatever question, but the human connection part of it is important too, that we're speaking with real humans that have real experience with real situations. Otherwise I'd just be sitting chatting with ChatGPT all day instead of wast...spending all day on HN.
      - pixl97 10mo ago
        If life is a jobs program, why don't we dig ditches with spoons?
      - NitpickLawyer 10mo ago
        Oh, I agree. What I found funny is the gut reaction of many other readers that downvoted the message (it's greyed out for me at time of writing this comment). Especially given that the user clearly mentioned that it was LLM generated, while also being cheeky with the "transformer" pun, on a ... transformer topic.
esafak 10mo ago
The model partially solves the problem but fails to learn the correct loop length: > An investigation of model errors (Section 5) reveals that, whereas large language models commonly “hallucinate” random solutions, our models fail in principled ways. In almost all cases, the models perform the correct calculations for the long Collatz step, but use the wrong loop lengths, by setting them to the longest loop lengths they have learned so far. The article is saying the model struggles to learn a particular integer function. https://en.wikipedia.org/wiki/Collatz_conjecture https://en.wikipedia.org/wiki/Collatz_conjecture
- spuz 10mo ago
  That's a bit of an uncharitable summary. In bases 8, 12, 16, 24 and 32 their model achieved 99.7% accuracy. They would never expect it to achieve 100% accuracy. It would be like if you trained a model to predict whether or not a given number is prime. A model that was 100% accurate would defy mathematical knowledge but a model that was 99.7% would certainly be impressive. In this case, they prove that the model works by categorising inputs into a number of binary classes which just happen to be very good predictors for this otherwise random seeming sequence. I don't know whether or not some of these binary classes are new to mathematics but either way, their technique does show that transformer models can be helpful in uncovering mathematical patterns even in functions that are not continuous.
  - jacquesm 10mo ago
    A pocket calculator that would give the right numbers 99.7% of the time would be fairly useless. The lack of determinism is a problem and there is nothing 'uncharitable' about that interpretation. It is definitely impressive, but it is fundamentally broken, because when you start making chains of things that are 99.7% correct you end up with garbage after very few iterations. That's precisely why digital computers won out over analog ones, the fact that they are deterministic.
    - fkarg 10mo ago
      yeah it's only correct in 99.7% of all cases, but what if it's also 10'000 times faster? There's a bunch of scenarios where that combination provides a lot of value
robot-wrangler 10mo ago
I'll take a shot at it. Using collatz as the specific target for investigating the underlying concepts here seems like a big red-herring that's going to generate lots of confused takes. (I guess it was done partly to have access to tons of precomputed training data and partly to generate buzz. The title also seems kind of poorly chosen and/or misleading) Really the paper is about mechanistic interpretation and a few results that are maybe surprising. First, the input representation details (base) matters a lot. This is perhaps very disappointing if you liked the idea of "let the models work out the details, they see through the surface features to the very core of things". Second, learning was burst'y with discrete steps, not smooth improvement. This may or may not be surprising or disappointing.. it depends how well you think you can predict the stepping.

Can someone ELI5 this for a non-mathematician?

poszlem 10mo ago

[flagged]

embedding-shape 10mo ago
Do you think maybe OP would have asked a language model for the answer if they felt like they wanted a language model to give an answer? Or in your mind parent doesn't know about LLMs, and this is your way of introducing them to this completely new concept?
- NitpickLawyer 10mo ago
  Funny that the "human" answer above took 2 people to be "complete" (i.e. an initial answer, followed by a correction and expansion of concepts), while the LLM one had mostly the same explanation, but complete and in one answer.
  - embedding-shape 10mo ago
    Maybe most of us here don't seek just whatever answer to whatever question, but the human connection part of it is important too, that we're speaking with real humans that have real experience with real situations. Otherwise I'd just be sitting chatting with ChatGPT all day instead of wast...spending all day on HN.
    - pixl97 10mo ago
      If life is a jobs program, why don't we dig ditches with spoons?
    - NitpickLawyer 10mo ago
      Oh, I agree. What I found funny is the gut reaction of many other readers that downvoted the message (it's greyed out for me at time of writing this comment). Especially given that the user clearly mentioned that it was LLM generated, while also being cheeky with the "transformer" pun, on a ... transformer topic.

esafak 10mo ago

The model partially solves the problem but fails to learn the correct loop length: > An investigation of model errors (Section 5) reveals that, whereas large language models commonly “hallucinate” random solutions, our models fail in principled ways. In almost all cases, the models perform the correct calculations for the long Collatz step, but use the wrong loop lengths, by setting them to the longest loop lengths they have learned so far. The article is saying the model struggles to learn a particular integer function. https://en.wikipedia.org/wiki/Collatz_conjecture https://en.wikipedia.org/wiki/Collatz_conjecture

spuz 10mo ago
That's a bit of an uncharitable summary. In bases 8, 12, 16, 24 and 32 their model achieved 99.7% accuracy. They would never expect it to achieve 100% accuracy. It would be like if you trained a model to predict whether or not a given number is prime. A model that was 100% accurate would defy mathematical knowledge but a model that was 99.7% would certainly be impressive. In this case, they prove that the model works by categorising inputs into a number of binary classes which just happen to be very good predictors for this otherwise random seeming sequence. I don't know whether or not some of these binary classes are new to mathematics but either way, their technique does show that transformer models can be helpful in uncovering mathematical patterns even in functions that are not continuous.
- jacquesm 10mo ago
  A pocket calculator that would give the right numbers 99.7% of the time would be fairly useless. The lack of determinism is a problem and there is nothing 'uncharitable' about that interpretation. It is definitely impressive, but it is fundamentally broken, because when you start making chains of things that are 99.7% correct you end up with garbage after very few iterations. That's precisely why digital computers won out over analog ones, the fact that they are deterministic.
  - fkarg 10mo ago
    yeah it's only correct in 99.7% of all cases, but what if it's also 10'000 times faster? There's a bunch of scenarios where that combination provides a lot of value

robot-wrangler 10mo ago

I'll take a shot at it. Using collatz as the specific target for investigating the underlying concepts here seems like a big red-herring that's going to generate lots of confused takes. (I guess it was done partly to have access to tons of precomputed training data and partly to generate buzz. The title also seems kind of poorly chosen and/or misleading) Really the paper is about mechanistic interpretation and a few results that are maybe surprising. First, the input representation details (base) matters a lot. This is perhaps very disappointing if you liked the idea of "let the models work out the details, they see through the surface features to the very core of things". Second, learning was burst'y with discrete steps, not smooth improvement. This may or may not be surprising or disappointing.. it depends how well you think you can predict the stepping.