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The universal weight subspace hypothesis

arxiv.org

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Re: The universal weight subspace hypothesis

#91

Post by bob1029 »

EvanAnderson wrote: post #12
VikingCoder wrote: post #5

I find myself wanting genetic algorithms to be applied to try to develop and improve these structures... But I always want Genetic Algorithms to show up in any discussion about neural networks...

I have a real soft spot for the genetic algorithm as a result of reading Levy's "Artificial Life" when I was a kid. The analogy to biological life is more approachable to my poor math education than neural networks. I can grok crossover and mutation pretty easily. Backpropagation is too much for my little brain to handle.

My entire motivation for using GAs is to get away from back propagation. When you aren't constrained by linearity and chain rule of calculus, you can approach problems very differently.

For example, evolving program tapes is not something you can back propagate. Having a symbolic, procedural representation of something as effective as ChatGPT currently is would be a holy grail in many contexts.

Re: The universal weight subspace hypothesis

#93

Post by augment_me »

daemonologist wrote: post #86
modeless wrote: post #58

This seems confusingly phrased. When they say things like "500 Vision Transformers", what they mean is 500 finetunes of the same base model, downloaded from the huggingface accounts of anonymous randos. These spaces are only "universal" to a single pretrained base model AFAICT. Is it really that surprising that finetunes would be extremely similar to each other? Especially LoRAs? I visited one of the models they refe…

I agree - the results on the finetunes are not very surprising. The trained-from-scratch ResNets (Figure 2 and Section 3.2.1) are definitely more interesting, though somewhat limited in scope. 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.

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.

Re: The universal weight subspace hypothesis

#94

Post by augment_me »

mlpro wrote: post #77
modeless wrote: post #58

This seems confusingly phrased. When they say things like "500 Vision Transformers", what they mean is 500 finetunes of the same base model, downloaded from the huggingface accounts of anonymous randos. These spaces are only "universal" to a single pretrained base model AFAICT. Is it really that surprising that finetunes would be extremely similar to each other? Especially LoRAs? I visited one of the models they refe…

Why would they be similar if they are trained on very different data? Also, trained from scratch models are also analyzed, imo.

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.

Re: The universal weight subspace hypothesis

#95

Post by augment_me »

I think the paper in general completely oversells the idea of "universality".

For CNNs, the 'Universal Subspace' is simply the strong inductive bias (locality) forcing filters into standard signal processing shapes (Laplacian/Gabor) regardless of the data. Since CNNs are just a constrained subset of operations, this convergence is not that surprising.

For Transformers, which lack these local constraints, the authors had to rely on fine-tuning (shared initialization) to find a subspace. This confirms that 'Universality' here is really just a mix of CNN geometric constraints and the stability of pre-training, rather than a discovered intrinsic property of learning.

Re: The universal weight subspace hypothesis

#96

Post by scotty79 »

moelf wrote: post #64
scotty79 wrote: post #47

Earlier quoted context omitted.

> Wouldn't this also mean that there's an inherent limit to that sort of model? If all need just 16 dimensions if we ever make one that needs 17 we know we are making progress instead of running in circles.

you can always make a new vector that's orthogonal to all the ones currently used and see if the inclusion improves performance on your tasks

> see if the inclusion improves performance on your tasks

Apparently it doesn't at least not in our models with our training applied to our tasks.

So if we expand one of those 3 things and notice that 17-th vector makes a difference then we are having progress.

Re: The universal weight subspace hypothesis

#98

Post by farhanhubble »

westoncb wrote: post #68
farhanhubble wrote: post #41

Earlier quoted context omitted.

It might we worth it to use that subset to initialize the weights of future models but more importantly you could save a huge number of computational cycles by using the lower dimensional weights at the time of inference.

Ah interesting, I missed that possibility. Digging a little more though my understanding is that what's universal is a shared basis in weight space, and particular models of same architecture can express their specific weights via coefficients in a lower-dimensional subspace using that universal basis (so we get weight compression, simplified param search). But it also sounds like to what extent there will be gains d…

My understanding differs and I might be wrong. Here's what I inferred:

Let's say you finetune a Mistral-7B. Now, there are hundreds of other fine-tuned Mistral-7B's, which means it's easy to find the universal subspace U of the weights of all these models combined. You can then decompose the weights of your specific model using U and a coefficient matrix C specific to your model. Then you can convert any operation of the type `out=Wh` to `out=U(C*x)` Both U and C are much smaller dimension that W and so the number of matrix operations as well as the memory required is drastically lower.

Re: The universal weight subspace hypothesis

#99

Post by rhaps0dy »

augment_me wrote: post #93
daemonologist wrote: post #86

Earlier quoted context omitted.

I agree - the results on the finetunes are not very surprising. The trained-from-scratch ResNets (Figure 2 and Section 3.2.1) are definitely more interesting, though somewhat limited in scope. 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.

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…

Thank you for saving me a skim
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