The scaling parameter, denoted as , is an important hyperparameter in Low-Rank Adaptation (LoRA). This parameter acts as a scalar multiplier for the LoRA update, typically represented as . It modulates the extent to which the adapted weights influence the original pre-trained weights , working in conjunction with the low-rank matrices and and the chosen rank to control the overall impact of the adaptation.
The modified forward pass, incorporating , represents the final output for an input as:
Here, represents the frozen pre-trained weights, and constitutes the low-rank update learned during fine-tuning. The parameter directly scales the contribution of this update.
However, it's important to note a common implementation convention, particularly prevalent in libraries like Hugging Face's PEFT (peft). In practice, the update is often dynamically scaled during training by . When this convention is used, the effective forward pass calculation looks like:
This scaling by aims to decouple the magnitude of the weight adjustments from the choice of rank . If the elements of matrix are initialized using a standard distribution (e.g., Gaussian) and is initialized to zero (a frequent strategy to ensure the initial state matches the pre-trained model), the variance of the product might scale with . Dividing by helps normalize this effect, allowing to function more consistently as a control for the overall strength of the adaptation, somewhat independent of .
Think of as controlling the "intensity" or magnitude of the fine-tuning adaptation applied over the base model's representations. It fine-tunes how much the learned task-specific adjustments () alter the output compared to the original frozen weights ().
Effectively, setting involves balancing the contribution from the general pre-trained knowledge encapsulated in and the specific task adaptations learned in . It is a critical hyperparameter that typically requires empirical tuning based on the specific task, dataset, model architecture, and the chosen rank .
There isn't a single, universally optimal value for . Its selection interacts with other hyperparameters, especially the rank and the learning rate used for training matrices and . Common approaches include:
The best approach often depends on empirical validation. If fine-tuning with LoRA appears too aggressive (e.g., validation loss increases rapidly) or too conservative (e.g., model performance plateaus below expectations), adjusting is a primary lever for control, complementary to tuning the rank and the optimizer's learning rate.
In summary, provides an important mechanism for scaling the LoRA adaptation. While often implemented with a scaling factor related to the rank (i.e., ), its core purpose is to modulate the strength of the low-rank update applied to the frozen base model weights. Careful consideration and tuning of are necessary steps for optimizing model performance when using LoRA.
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