That's good news. I think it deserves wider dissemination, so I'm upvoting your post.
Thank you for sharing this on HN!
Now let's think about filling the space with p-balls that are bound by nearest points. So there should be no data point inside the ball. Then we've turned this problem into a sphere packing problem and we can talk about the size and volumes of those spheres.
So if we uniformally fill our real distribution with data then the average volume of those spheres decrease. If we fill but not uniformly the average ball will decrease but the largest ball will shrink slower (this case being we aren't properly covering data in that region). In either case that more you add data, the more the balls shrink. Essentially meaning the difference between data decreases. The harder question is about those under represented regions. Finding them and determining how to properly sample.
Another quick trick you can use to convince yourself if thinking about basis vectors (this won't be robust btw but a good starting point). In high dimensions the likelihood that two randomly sampled vectors are orthogonal is almost certainly true. So then we think of drawing basis vectors (independent vectors that span our space). So as we fill in data, we initially are very likely to have vectors (or data) that are independent in some way. But as we add more, the likelihood that they are orthogonal decreases. Of course your basis vectors don't need to be orthogonal but that's more semantics because we can always work in a space where that's true.
We could talk about this in different ways, like variance. But I'm failing to see how I didn't answer your question. Did I misscommunicate? Did I misunderstand?
The model is learning off of statistics so most of your information gain would be through more independent data. Think of this space we are talking about as "knowledge." And our "intelligence" as how easy it is to get to any point in this space. The vector view above might help with understanding this one, because you can step in the direction of any vectors you have and then how you combine them to get to your final point. The question is how many you have to use (how many "steps" away)? And of course, how close you can get to your final destination. As you can imagine, from my previous comment, that doing this for any given point you'll reduce "steps" to your final destination if you have more vectors, but you can also understand that the utility of each vector decreases as you add more. (Generally. Of course if you have a gap in knowledge you can get a big help from a single vector that goes into that area but let's leave that aside).
Does this help clarify? If not I might need you to clarify your question a bit more. (I am a ML researcher fwiw)
No. My original (top) comment was about how the number of training tokens required per parameter slowly declines as models become larger. dzdt suggested it could be because the independence of training points declines as the dataset size grows. I said it could be, but I'm not sure how one would go about proving it, given how little we know about the inner working of giant models. Makes sense?
Otherwise, I agree with everything you wrote!
There's a lot we didn't know, but it isn't nothing. There's a big push for ML not needing math. It's true you can do a lot without, especially if you have compute. But the math helps you understand what's going on and what are your limits. We can't explain everything yet, but it's not nothing.
Another difference: most corporations will avoid doing illegal stuff if the penalties are large enough: the corporation alignment problem is political. Pretty much no extant AI systems can be instructed in this way: we don't know how to align AIs even in theory.
I hate to do this, but can you enumerate them?
1. Specifically larger than the upper bound on lifetime language input for humans, even assuming 24/7 at max reading speed.
Proof: blind and partially sighted people exist.
The RLHF post-training dataset is vastly smaller than the pretraining set and unlikely to have any particular question contaminated. However we did not check explicitly.
We evaluate functional correctness on a set of 164 handwritten programming problems, which we call the HumanEval dataset. ... __It is important for these tasks to be hand-written, since our models are trained on a large fraction of GitHub, which already contains solutions to problems from a variety of sources.__
Human Eval 2
Prompt:
def truncate_number(number: float) -> float: """ Given a positive floating point number, it can be decomposed into and integer part (largest integer smaller than given number) and decimals (leftover part always smaller than 1). Return the decimal part of the number. >>> truncate_number(3.5) 0.5 """
Solution:
return number % 1.0
Human Eval 4
Prompt:
from typing import List def mean_absolute_deviation(numbers: List[float]) -> float: """ For a given list of input numbers, calculate Mean Absolute Deviation around the mean of this dataset. Mean Absolute Deviation is the average absolute difference between each element and a centerpoint (mean in this case): MAD = average | x - x_mean | >>> mean_absolute_deviation([1.0, 2.0, 3.0, 4.0]) 1.0 """
Solution
mean = sum(numbers) / len(numbers)
return sum(abs(x - mean) for x in numbers) / len(numbers)
LLMs are (lossy) compression systems. So they're great for information retrieval. And a lot of what we consider intelligence (and possibly even creativity) is based on information retrieval. Doesn't mean these things are any less impressive but just a note on how we should be interpreting results and understanding the limitations of our tools. Measuring intelligence is a really difficult thing and we need to be aware that the term isn't universally agreed upon and so people are often talking past one another and also some people are conflating the differences as if they are the same.
> You open the newspaper to an article on some subject you know well. In Murray's case, physics. In mine, show business. You read the article and see the journalist has absolutely no understanding of either the facts or the issues. Often, the article is so wrong it actually presents the story backward—reversing cause and effect. I call these the "wet streets cause rain" stories. Paper's full of them.
> In any case, you read with exasperation or amusement the multiple errors in a story, and then turn the page to national or international affairs, and read as if the rest of the newspaper was somehow more accurate about Palestine than the baloney you just read. You turn the page, and forget what you know.
-Michael Crichton
Edit: Found the speech this is from.
https://web.archive.org/web/20190808123852/http://larvatus.c...