LoRA fine tuning is an incredibly simple idea. For each matrix you want to fine-tune, introduce a low rank matrix ΔW = BA where the inner dimension is r << d, and compute (W + ΔW)x. Freeze all pretrained parameters and only update B and A. B is initialized to 0 so that the initial model is equal to the pretrained model. After training, you can also write V = W + ΔW to preserve latency.
Saved you a click.