# VeRA: Vector-based Random Matrix Adaptation [VeRA](https://huggingface.co/papers/2310.11454) is a parameter-efficient fine-tuning technique that is similar to LoRA but requires even fewer extra parameters while promising similar or even better performance. As such, it is particularly useful when the parameter budget is very limited, e.g. when scaling to very large models. The reduction of the count of trainable parameters is achieved by sharing the same low-rank matrices across all layers, and only training two additional vectors per layer. ## How VeRA works LoRA updates a frozen base model by learning two small, low-rank matrices for each adapted layer. The rank is the inner dimension of these matrices, and it controls how much capacity the adapter has. In LoRA, increasing `r` or adapting more layers increases the number of trainable parameters quickly because every adapted layer learns its own pair of low-rank matrices. VeRA keeps the same low-rank adaptation idea but changes which parameters are trained. Instead of learning separate low-rank matrices for every layer, VeRA uses one frozen, randomly initialized pair of low-rank matrices, `A` and `B`, that is shared across layers. Each adapted layer only learns two scaling vectors, `vera_lambda_d` and `vera_lambda_b`, which rescale the shared matrices to produce a layer-specific update. Since `vera_lambda_d` has size `r`, VeRA's trainable parameter count still increases with `r` and with the number of adapted layers. However, it grows much more slowly than LoRA's because the large `A` and `B` matrices are shared and frozen instead of learned separately for each layer. This is why VeRA can use fewer trainable parameters than LoRA. In the simplified parameter count from the paper, LoRA scales with `2 * L_tuned * d_model * r`, where `L_tuned` is the number of adapted layers, `d_model` is the model dimension, and `r` is the rank. VeRA scales with `L_tuned * (d_model + r)` because the large low-rank matrices are shared and frozen, while only the smaller per-layer vectors are trained. When saving the adapter parameters, it's possible to eschew storing the low rank matrices by setting `save_projection=False` on the `VeraConfig`. In that case, these matrices will be restored based on the fixed random seed from the `projection_prng_key` argument. This cuts down on the size of the checkpoint, but we cannot guarantee reproducibility on all devices and for all future versions of PyTorch. If you want to ensure reproducibility, set `save_projection=True` (which is the default). To handle different shapes of adapted layers, VeRA initializes shared A and B matrices with the largest required size for each dimension. During the forward pass, submatrices A and B for a given layer are sliced out from these shared matrices and used as described in the paper. For example, adapting two linear layers of shapes (100, 20) and (80, 50) will create A and B matrices of shapes (rank, 50) and (100, rank) respectively. Then, to adapt a layer of shape (100, 20), submatrices A and B of shapes (rank, 20) and (100, rank) will be extracted. VeRA currently has the following constraint: - Only `nn.Linear` layers are supported. The abstract from the paper is: > Low-rank adaptation (LoRA) is a popular method that reduces the number of trainable parameters when finetuning large language models, but still faces acute storage challenges when scaling to even larger models or deploying numerous per-user or per-task adapted models. In this work, we present Vector-based Random Matrix Adaptation (VeRA), which significantly reduces the number of trainable parameters compared to LoRA, yet maintains the same performance. It achieves this by using a single pair of low-rank matrices shared across all layers and learning small scaling vectors instead. We demonstrate its effectiveness on the GLUE and E2E benchmarks, image classification tasks, and show its application in instruction-tuning of 7B and 13B language models. ## When to use VeRA VeRA is a good choice when: - You want to minimize the number of trainable parameters while maintaining performance comparable to LoRA. - You need to store or deploy many task-specific adapters, where smaller adapter checkpoints reduce storage requirements. - You are fine-tuning very large language models under tight memory or parameter budgets. ## When not to use VeRA VeRA may not be the best choice when: - You require independent low-rank matrices for each adapted layer, providing greater flexibility in the learned adapter parameters. - Your model requires adapting module types other than `nn.Linear`, since VeRA currently supports only linear layers. - Your model contains adapted linear layers with widely different input and output dimensions. Because VeRA shares a single pair of projection matrices across all adapted layers, these matrices must be sized for the largest shape. Models with a large variation in layer shapes (for example, transformer up- and down-projection layers) can therefore require over-provisioning shared projection matrices, reducing some of VeRA's parameter-efficiency advantage. ## Benchmark overview