Chinchilla Scaling: A replication attempt
arxiv.org
arxiv.org
> To map the SVG coordinates to the model size and training FLOP values, we used the location of the labels or ticks on the respective axes. This allowed us to establish a correspondence between the SVG coordinates and the actual data values represented in the plot.
They ... reconstructed the data ... from a plot ... using ruler and eyes? Why not just emailed the original authors for the raw data? I can't help but feel like @yuvaltheterrible debunking papers.
I'm pretty sure I'm not the only one who's written themselves a mini tool to even extract data from a bitmap plot based on the axes. Involves some manual steps (cropping mainly), but is very convenient for the cases where people not even use vector graphics, but sometimes even just screenshots of plots... Do I like it? Hell no! It's why I've put quite some effort in doing it better for my PhD thesis.
I remember my first year in grad school I was trying to replicate a work by a very prestigious university. It definitely wasn't reproducible from text but I did my best. Couldn't get close to their claims so I email the lead author (another grad student). No response. Luckily my advisor knew their advisor. Got a meeting and then I got sent code. It was nothing like what they claimed in the paper so I have no idea what they gave me. Anyways, my paper never got published because I couldn't beat them. It is what it is.
(Yes, I'd much rather use LaTeX)
also, we didn't reconstruct the data using a ruler, you can automate that entire process so that it's much more reliable than that
It would be nice if you could post if the actual data matches your reconstruction—now that you have it in hand. Would help us not worry about the data provenance and focus on the result you found.
what they did was to take the mean of the loss values across datapoints instead of summing them and used L-BFGS-B with the default tolerance settings, so the optimizer terminated early, and we can reproduce their results with this same mistake
so our reconstruction appears to be good enough
Industry research labs, especially Google deepmind, are notoriously closed up about their “proprietary” data. I’ve hit this wall multiple times in my own work in AI.
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.
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.
> 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...
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.
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?
Very unusual choice to reconstruct the dataset by eyeballing the graph in the source paper (why not just ask for it…?) and it’s not really clear why the result is dressed up behind the salacious-seeming abstract.
we did ask for the data but got no response until we published on arxiv
what is supposed to be "salacious" about the abstract?
"We have found three potential issues with Hoffmann et al.’s estimates of the Chinchilla scaling law that rely on Approach 3: 1. Their estimated model fits the reconstructed data very poorly. These conclusions hold even when accounting for potential noise in data reconstruction and excluding outlier models. 2. The confidence are implausibly tight given the number of data points. Obtaining confidence intervals that tight would require many hundreds of thousands of observations, while they likely had only ∼400. 3. Their estimated model implies a scaling policy that is inconsistent with their other approach"
Data point most people are probably looking for: "We find a range consistent with the 20 tokens per parameter rule of thumb. Indeed, our point estimates imply that 25.6 tokens per parameters is optimal."
Meanwhile, people noticed that for deployed models, inference cost often outweighs the initial training costs. It's sometimes better to train a smaller, faster model longer on more data, because it has lower overall cost (including environmental impact) if you're expecting to run the model a few million or billion times (e.g., [1]). So training past the Chinchilla optimum point became a lot more common, particularly after Llama.
Doubling your parameter count past that ratio will yield a better model than doubling your data and is much easier and cheaper to do.
No one really knows the answer to this question.
>Arguably because there's a larger state space that can be used to remember more contexts, which helps with both generalization and case-specific processing.
What I'm trying to say is that both models in either scenario are very over-parameterized and under-trained.
You say the answer is extra space ? The smaller model has not used anywhere near the space it has. They both have extra space.
It's like arguing a bigger drum is better because of extra space when all the water you plan to store will not take even half of your smaller drum
This doesn't take inference into account either, obviously.
Instead, they just redid the analysis based on a figure in the paper and found that the old model with slightly different parameters gave a better fit to the data. This is a valuable contribution, but a bit over-stated by the paper title, and the confrontational, "gotcha" tone of the paper is unwarranted.
A better framing would have been something like "Chinchilla Scaling: Reanalyzed".