A Bayesian Interpretation of Adaptive Low-Rank Adaptation

TL;DR

This paper introduces a Bayesian approach to adaptive low-rank adaptation, leveraging theoretically supported metrics like SNR and the IVON optimizer, resulting in improved performance and efficiency over existing methods.

Contribution

It provides a Bayesian interpretation of importance scores in adaptive low-rank adaptation and demonstrates that magnitude is a key indicator of parameter importance.

Findings

Bayesian method matches or surpasses sensitivity-based importance metrics.

The proposed approach is faster than AdaLoRA with Adam.

Magnitude is identified as the primary importance indicator.

Abstract

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.