Can someone ELI5 "LoRA reduces the number of trainable parameters by learning pairs of rank-decompostion matrices while freezing the original weights"?
Original weights frozen = Rather than modify the original model, the training results are saved to a small file of only a few MB.
In practice this means you can fine tune a 30B parameter model on a consumer GPU in a couple of hours. Without LoRA you would need to run multiple expensive data center GPUs for days or weeks.
(1) https://en.wikipedia.org/wiki/Low-rank_approximation
Edited: By the way, it seems to me that there is an error in the wikipedia page because if the Low-rank approximation takes a larger rank then the bound of the error should decrease, and in this page the error increases.
It seems that the initial matrix of weights has a low rank approximation A and this implies that the difference E = W - A is small, also it seems that PCA fails when E is sparse because PCA is designed to be optimum when the error is gaussian.
Since the weights are derived from gradient descent, yeah we don't really know what the distributions would be.
A random projection empirically works quite well for very high dimensions, and is of course very cheap computationally.
Think of a point cloud of a piece of paper floating in the wind. It would be a 3xn list of points, but "really" it's a 2d piece of paper.
Just like I can rewrite the number 27 as 333 or 8+19 or (2^3)+(2^4)+3.. Given a single matrix one can find myriad ways to rewrite it as a sequence of matrices that have the same (or similar) numeric value, but with interesting or desirable properties. :D
My favorite example (which is used in signal processing) is to take your ugly matrix and rewrite it as a set of smaller matrices where most of the elements are zero, or a power of 2.
It turns out, computers can multiply by zeros and powers of two very fast
Why is fine-tuning done with separate alterations, rather than by mutating the original weights?
It's actually larger. If you just have two equally large matrices of the same dimension, one original, and one of "altercations"... then you can just add them together.
> Why is fine-tuning done with separate alterations, rather than by mutating the original weights?
Then you'd have to compute the gradients for the whole network, which is very expensive when the model has 7b, 65b, 165b parameters. The intent is to make that cheaper by only computing gradients for a low rank representation of the change in the weight matrix from training.
You have to do that with LoRA regardless, to compute the gradients for the lowest-level LoRA weights.
The goal of most parameter-efficient methods is to store one gold copy of the original model, and learn minor modifications/additions to the model. The easiest way to think about this is in some kind of deployment setting, where you have 1 capable model and you learn different sets of LoRA weights for different tasks and applications.
The original intent of parameter-efficient methods is to reduce the amount of storage space needed for models (do you really want to keep a whole additional copy of LLaMA for each different task?). A secondary benefit is that because you are fine-tuning a smaller number of parameters, the optimizer states (can take up to 2x the size of your model) are also heavily shrunk, which makes it more economical (memory-wise) to (parameter-efficient) fine-tune your model.
From the LoRa paper:
>When the pre-trained model is GPT-3 175B, the number of train- able parameters |Θ| can be as small as 0.01% of |Φ0|.
Consumer GPU, yes, but in practice LoRA doesn't actually reduce training time. What it mainly reduces is memory requirements. In fact LoRA training can often require more training steps than full fine-tuning and therefore be slower (you can imagine why this is the case: the optimization is trying to modify the mode's behavior a smaller number of parameters, and so has a harder job)
Here's an example of 20 seconds per epoch on a single consumer GPU: https://github.com/johnsmith0031/alpaca_lora_4bit/issues/7#i...
Can you qualify this? Is it still useful or not?
Is what still useful? A LoRA is about as good and useful as a full fine tune. If you have unlimited storage space to store them or unlimited compute to make them then I would still prefer full fine tunes. But the difference is marginal and generally not worth the storage space or increased compute costs for individuals.
The insight is that we don't need to modify a lot of parameters to get a generally competent model to do well on specific tasks. When you have a linear layer with a weight matrix of dimension d_in x d_out, the change you undergo during full finetuning is also a matrix of d_in x d_out, which can be huge. We represent the latter using two matrices of shape d_in x r and r x d_out. You save a lot of parameters when r is small. So when you use it, the input goes through two streams 1) the orignal frozen weight turning a vector of size d_in to d_out and 2) the low-rank weights turning a vector of size d_in to r and r to d_out. The two streams are then summed together. (There's a figure in the paper.)
This way of doing thing is nice for a few reasons. It's easy to parallelize. You can change r to control how many parameters to train. You can also merge the low-rank weights with the original one to avoid latency.
Note that we don't select a subset of the original parameters. We train extra ones.
I am assuming you can have n LoRA fine-tunings, say each specializing in one aspect of a coherent task, with n summers, running in parallel, and then combine them at the end? Or more generally, does LoRA enable a sort of modularizing around a core (un-merged) model?
And curious if you ever tried merging 2 or more fine-tunings and then testing the resultant single model (merge all) against the original tests to check retention?
https://arxiv.org/pdf/2202.13914.pdf
The gain isn't that significant. We don't understand what these low-rank updates represent, and they might not correspond to "skills" that humans have.
My background contains signal processing, "pre-deep learning ML", systems engineering, and firmware, and that sentence jumped out at me as crystal clear in my mind, despite not knowing what HuggingFace is or PyTorch.
Correct me if I'm wrong: These huge models involve lots of weights used in large matrices. The contribution of this work is to plug in some matrix factorization and learn a lower dimensional representation, instead of a large second matrix.
Fantastic!
Also makes me wonder what other performance improvements await through proper application of established and well known Mathematics. :D
[0] https://towardsdatascience.com/adding-custom-layers-on-top-o...
Add a task specific layer and only training that layer doesn't work well. In practice, people combine many of these things, e.g., LoRA + task-specific final layer.