> Finding that 70% of attention heads and 20% of feed-forward networks can be excised with minimal effect on in-context learning suggests that large language models are undertrained.
So why do the larger models perform so much better…?
So why do the larger models perform so much better…?
More parameters makes it easier to find solutions with low-energy.
Suppose we have a product of two variables z = x * y. And now suppose that the 'correct' product is z=2, and we're learning x and y. A very good analytical solution is x=1, y=2 (or vice versa) allowing us to eliminate either x or y from our learning problem. The total energy of (x, y) in this case is 1*2 + 2*2 = 5.
However, another solution is x = y = sqrt(2), which has energy 2: this solution is much closer to the origin. The extra variable means that we have a /surface/ of solutions instead of a unique solution, so we can hone in on ones that are easier to get to using our optimizer.
As you add more variables, you can find lower and lower energy solutions.
Consider that we initialize neural networks 'near' zero, and then walk with gradient descent in some direction towards a solution. Then adding lots of extra variables - wiggle room - makes it much easier to find a solution within walking distance of the (noisy) origin.
Would be interesting to try some explicit regularization. But unfortunately you need a million bucks to an experiment on LLMs. :/
Not being facetious, I don't know the answer, but that's my best guess
assuming the models are identical except one is bigger then the bigger model is better because 70% of a bigger number is larger than 70% of a smaller number.
Now if you train a smaller model much longer than the bigger model (more tokens) then you are reducing the level of "under-trainedness" to some degree. at some point, you may have a smaller model that is better than that larger model.
70% of a bigger number may be larger than 70% of a smaller number but no guarantee 70% of a bigger number is larger than say 90% of a smaller number and so on.
Just like quantization!
So the question is, perhaps: Why are big models required for compute-efficient training?
But I also disagree with takeaway.