The universal weight subspace hypothesis

> So, they found an underlying commonality among the post-training structures in 50 LLaMA3-8B models, 177 GPT-2 models, and 8 Flan-T5 models; and, they demonstrated that the commonality could in every case be substituted for those in the original models with no loss of function; and noted that they seem to be the first to discover this.

Could someone clarify what this means in practice? If there is a 'commonality' why would substituting it do anything? Like if there's some subset of weights X found in all these models, how would substituting X with X be useful?

I see how this could be useful in principle (and obviously it's very interesting), but not clear on how it works in practice. Could you e.g. train new models with that weight subset initialized to this universal set? And how 'universal' is it? Just for like like models of certain sizes and architectures, or in some way more durable than that?

Well intuitively it makes sense that within each independent model, a small number of weights / parameters are very dominant, but it’s still super interesting that these can be swapped between all the models without loss of performance.

It isn’t obvious that these parameters are universal across all models.

Prior to this paper, no one knew that X existed. If this paper proves sound, then now we know that X exists at all.

No matter how large X is, one copy of X baked into the OS / into the silicon / into the GPU / into CUDA, is less than 50+177+8 copies of X baked into every single model. Would that permit future models to be shipped with #include as line 1? How much space would that save us? Could X.model be baked into chip silicon so that we can just take it for granted as we would the mathlib constant "PI"? Can we hardware-accelerate the X.model component of these models more than we can a generic model, if X proves to be a 'mathematical' constant?

Given a common X, theoretically, training for models could now start from X rather than from 0. The cost of developing X could be brutal; we've never known to measure it before. Thousands of dollars of GPU per complete training at minimum? Between Google, Meta, Apple, and ChatGPT, the world has probably spent a billion dollars recalculating X a million times. In theory, they probably would have spent another billion dollars over the next year calculating X from scratch. Perhaps now they won't have to?

We don't have a lot of "in practice" experience here yet, because this was first published 4 days ago, and so that's why I'm suggesting possible, plausible, ways this could help us in the future. Perhaps the authors are mistaken, or perhaps I'm mistaken, or perhaps we'll find that the human brain has X in it too. As someone who truly loathes today's "AI", and in an alternate timeline would have completed a dual-major CompSci/NeuralNet degree in ~2004, I'm extremely excited to have read this paper, and to consider what future discoveries and optimizations could result from it.

EDIT:

Imagine if you had to calculate 3.14159 from basic principles every single time you wanted to use pi in your program. Draw a circle to the buffer, measure it, divide it, increase the memory usage of your buffer and resolution of your circle if necessary to get a higher precision pi. Eventually you want pi to a billion digits, so every time your program starts, you calculate pi from scratch to a billion digits. Then, someday, someone realizes that we've all been independently calculating the exact same mathematical constant! Someone publishes Pi: An Encyclopedia (Volume 1 of ∞). It becomes inconceivably easier to render cones and spheres in computer graphics, suddenly! And then someone invents radians, because now that we can map 0..360° onto 0..τ, and no one predicted radians at all but it's incredibly obvious in hindsight.

We take for granted knowledge of things like Pi, but there was a time when we did not know it existed at all. And then for a long time it was 3. And then someone realized the underlying commonality of every circle and defined it plainly, and now we have Pi Day, and Tau Day, because not only do we know it exists, but we can argue about it. How cool is that! So if someone has discovered a new 'constant', then that's always a day of celebration in my book, because it means that we're about to see not only things we consider "possible, but difficult" to instead be "so easy that we celebrate their existence with a holiday", but also things that we could never have remotely dreamed of before we knew that X existed at all.

(In less tangible analogies, see also: postfix notation which was repeatedly invented for decades (by e.g. Dijkstra) as a programming advance, or the movie "Arrival" (2019) as a linguistic advance, or the BLIT Parrot (don't look!) as a biological advance. :)

It does seem to be working for novel tasks.

The analysis is on image classification, LLMs, Diffusion models, etc.