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.
The ViT models are never really trained from scratch - they are always finetuned as they require large amounts of data to converge nicely. The pretraining just provides a nice initialization. Why would one expect two ViT's finetuned on two different things - image and text classification end up in the same subspace as they show? I think this is groundbreaking.
I don't really agree with the drift far from the parent model idea. I think they drift pretty far in terms of their norms. Even the small LoRA adapters drift pretty far from the base model.
Perhaps we need to revisit the concept and have a narrow abstract and a lay abstract, given how niche science has become.
And this critique is likely not aimed at academics so much as the systems and incentives of academia. This is partially on the parties managing grants (caring much more about impact and visibility than actually moving science forwards, which means everyone is scrounging for or lying about low hanging fruit). It is partially on those who set (or rather maintain) the culture at academic institutions of gathering clout by getting 'impactful' publications. And those who manage journals also share blame, by trying to defend their moat, very much hamming up "high impact", and aggressively rent-seeking.
In any case, my impression is that this is not immediately more useful than a LoRA (and is probably not intended to be), but is maybe an avenue for further research.