This would seem to predict that trained neural networks can be massively compressed
The LTH gives us a way to do this! It’s just so computationally expensive (iterative neuron pruning and evaluation) as to be useless.
with the fraction you can compress away rising with scale. This doesn’t seem to be the case.
It actually is! See here, which kind of gets at the question by finding that effective dimensionality of CIFAR NNs decreases with scale, and here, which directly identifies that “larger models have better generalization bounds and are more compressible than smaller models.”
The LTH gives us a way to do this! It’s just so computationally expensive (iterative neuron pruning and evaluation) as to be useless.
I don’t think the LTH applies to large language models. Or, to be more quantitative, I don’t think you can prune of the weights in a well trained LLM without significantly degrading performance. I think when papers say they found models to be highly prunable, it’s usually a case of 1) They tested on models that are undertrained or badly trained and so don’t use most of their capacity or 2) They have low standards for what counts as “degrading performance”.
It actually is! See here, which kind of gets at the question by finding that effective dimensionality of CIFAR NNs decreases with scale, and here, which directly identifies that “larger models have better generalization bounds and are more compressible than smaller models.”
I haven’t read these particular papers, but my first reaction is skepticism. The first paper seems like a prime candidate for failure mode 1. In addition, on a skim, I am pretty skeptical of their effective dimensionality calculations. Text says
Lanczos Calculations We use GPU enabled Lanczos as implemented in Gardner et al. (2018) to compute the eigenvalues approximately, running 100 steps to compute approximately 100 of the top eigenvalues. We note that our estimates of the effective dimensionality are somewhat biased from not including all of the small eigenvalues. However, these small eigenvalues will contribute negligibly and Lanczos will converge to the true eigenvalues if we ran k steps where k is the rank of the Hessian.
Which seems insane to me. Top 100 eigenvalues for nets with between 1e5 and 1.6e6 parameters trained on CIFAR-100??? If that’s not impacting their effective dimensionality calculation it’s got to have a crazy high cutoff, surely you are not getting good performance on CIFAR-100 with 100 Hessian eigenmodes, what the hell. This seems like it’s basically throwing away the signal effective dimensionality is supposed to measure.
Second paper I haven’t understood yet.
EDIT: I have now read the second paper a little more. They seemingly don’t even try to compress regular LLMs. They compress models trained with their weird SubLoRA technique which seem to score much worse loss than regular models on text prediction. Like, these look barely better than random in table 2. And the generated text from them in Appendix F looks like word salad. So this paper seems pretty irrelevant to the question at hand.
Basically, neural network priors are pretty good if they’re trained well, and they mostly don’t waste capacity. If you’ve got a nice general algorithm that the net can learn using only of its parameters, it’ll do that. But it’s not going to stop there and leave the other unused. It’s going to learn the next useful general algorithm, and then the next one and the next one, because you can basically always get better at predicting text on the internet. If nothing else, free parameters can always be used to memorise more stuff.
The LTH gives us a way to do this! It’s just so computationally expensive (iterative neuron pruning and evaluation) as to be useless.
It actually is! See here, which kind of gets at the question by finding that effective dimensionality of CIFAR NNs decreases with scale, and here, which directly identifies that “larger models have better generalization bounds and are more compressible than smaller models.”
I don’t think the LTH applies to large language models. Or, to be more quantitative, I don’t think you can prune
I haven’t read these particular papers, but my first reaction is skepticism. The first paper seems like a prime candidate for failure mode 1. In addition, on a skim, I am pretty skeptical of their effective dimensionality calculations. Text says
Which seems insane to me. Top 100 eigenvalues for nets with between 1e5 and 1.6e6 parameters trained on CIFAR-100??? If that’s not impacting their effective dimensionality calculation it’s got to have a crazy high cutoff, surely you are not getting good performance on CIFAR-100 with 100 Hessian eigenmodes, what the hell. This seems like it’s basically throwing away the signal effective dimensionality is supposed to measure.
Second paper I haven’t understood yet.
EDIT: I have now read the second paper a little more. They seemingly don’t even try to compress regular LLMs. They compress models trained with their weird SubLoRA technique which seem to score much worse loss than regular models on text prediction. Like, these look barely better than random in table 2. And the generated text from them in Appendix F looks like word salad. So this paper seems pretty irrelevant to the question at hand.
Basically, neural network priors are pretty good if they’re trained well, and they mostly don’t waste capacity. If you’ve got a nice general algorithm that the net can learn using only