A Bayesian Interpretation of Adaptive Low-Rank Adaptation

Motivated by the sensitivity-based importance score of the adaptive low-rank adaptation (AdaLoRA), we utilize more theoretically supported metrics, including the signal-to-noise ratio (SNR), along with the Improved Variational Online Newton (IVON) optimizer, for adaptive parameter budget allocation. The resulting Bayesian counterpart not only has matched or surpassed the performance of using the sensitivity-based importance metric but is also a faster alternative to AdaLoRA with Adam. Our theoretical analysis reveals a significant connection between the two metrics, providing a Bayesian perspective on the efficacy of sensitivity as an importance score. Furthermore, our findings suggest that the magnitude, rather than the variance, is the primary indicator of the importance of parameters.