The Scaling Law for LoRA Base on Mutual Information Upper Bound
This work addresses a focal issue in fine-tuning large models for researchers and practitioners, but it is incremental as it builds on existing LoRA methods by introducing a new metric.
The paper tackled the problem of understanding scaling laws in LoRA fine-tuning by proposing a new internal metric based on Mutual Information Upper Bound (MIUB) to measure dependency between pre-trained and new knowledge, showing it aligns more accurately and stably with scaling laws than external metrics like cross-entropy and perplexity in experiments on Llama3-8B and Phi3-3B models.
LoRA (Low-Rank Adaptation) is a widely used model fine-tuning method. In fine-tuning, the law among model performance, model parameters, and data complexity has been a focal issue in the field. Existing methods often leverage external metrics (such as cross-entropy or perplexity) to evaluate model performance. In the fine-tuning process for large models, two types of knowledge are typically involved: the frozen, general knowledge acquired by the model during pre-training and the new knowledge learned through the LoRA module from the current data. Generally, the less LoRA's learned knowledge relies on the large model, the more it captures the specific knowledge of new data, thereby enhancing its adaptability to new tasks. However, external metrics do not readily capture the dependency relationship between these two types of knowledge. Therefore, we designed an internal metric based on the Mutual Information Upper Bound (MIUB) theory to investigate the scaling law of large-model LoRA fine-tuning. In our experiments, we validated this approach on benchmark datasets, using the Llama3-8B and Phi3-3B models. The results show that the proposed MIUB metric aligns more accurately and stably with the scaling law of LoRA fine-tuning compared to cross-entropy and perplexity.