I don't think its that surprising actually. And I think the paper in general completely oversells the idea.

The ResNet results hold from scratch because strict local constraints (e.g., 3x3 convolutions) force the emergence of fundamental signal-processing features (Gabor/Laplacian filters) regardless of the dataset. The architecture itself enforces the subspace.

The Transformer/ViT results rely on fine-tunes because of permutation symmetry. If you trained two ViTs from scratch, "Attention Head 4" in Model A might be functionally identical to "Head 7" in Model B, but mathematically orthogonal.

Because the authors' method (SVD) lacks a neuron-alignment step, scratch-trained ViTs would not look aligned. They had to use pre-trained models to ensure the weights shared a coordinate system. Effectively, I think that they proved that CNNs converge due to it's arch, but for Transformers, they mostly just confirmed that fine-tuning doesn't drift far from the parent model.

Agreed. What's surprising here to me isn't that the fine tunes are compressible, it's the degree to which they're compressible. It seems like very little useful new information is being added by the fine-tune.

They're using SVD to throw away almost all of the "new information" and apparently getting solid results anyhow. Which of course raises interesting questions if replicable. The code doesn't seem to have been released yet though.

They are trained on exactly the same data in the same order with the same optimizer because they are literally the same base model. With a little fine tuning added on top.

I see now that they did one experiment with trained from scratch models. They trained five Resnet-50s on five disjoint datasets of natural images, most quite small. And IIUC they were able to, without further training, combine them into one "universal" model that can be adapted to have only somewhat worse performance on any one of the five datasets (actually one of them is pretty bad) using only ~35 adaptation parameters. Which is kind of cool I guess but I also don't find it that surprising?

I don't expect that you'd get the same finding at large scale in LLMs trained from scratch on disjoint and dissimilar data with different optimizers etc. I would find that surprising. But it would be very expensive to do that experiment so I understand why they weren't able to.

The trained from scratch models are similar because CNN's are local and impose a strong inductive bias. If you train a CNN for any task of recognizing things, you will find edge detection filters in the first layers for example. This can't happen for attention the same way because its a global association, so the paper failed to find this using SVD and just fine-tuned existing models instead.

I think there's two maybe subtle, but key concepts you're missing.

  1) "pertaining"
  2) architecture

2) the architecture and training methods matter. As a simple scenario to make things a bit easier to understand let's say we have two models with identical architectures and we'll use identical training methods (e.g. optimizer, learning rate, all that jazz) but learn on different data. Also to help so you can even reproduce this on your own let's train one on MNIST (numbers) and the other in FashionMNIST (clothing).

Do you expect these models to have similar latent spaces? You should! This is because despite the data being very different visually there are tons of implicit information that's shared (this is a big reason we do tuning in the first place!). One of the most obvious things you'll see is subnetworks that do edge detection (there's a famous paper showing this with convolutions but transformers do this too, just in a bit different way). The more similar the data (orders shouldn't matter too much with modern training methods but it definitely influences things) the more similar this will be too. So if we trained on LAION we should expect it to do really well on ImageNet because even if there aren't identical images (there are some) there are the same classes (even if labels are different)[0].

If you think a bit here you'll actually realize that some of this will happen even if you change architectures because some principles are the same. Where the architecture similarity and training similarity really help is that they bias features being learned at the same rate and in the same place. But this idea is also why you can distill between different architectures, not just by passing the final output but even using intermediate information.

To help, remember that these models converge. Accuracy jumps a lot in the beginning then slows. For example you might get 70% accuracy in a few epochs but need a few hundred to get to 90% (example numbers). So ask yourself "what's being learned first and why?" A lot will make more sense if you do this.

[0] I have a whole rant on the indirect of saying "zero shot" on ImageNet (or COCO) when trained in things like LAION or JFT. It's not zero shot because ImageNet is in distribution! We wouldn't say "we zero shotted the test set" smh