Revisiting Prefix-tuning: Statistical Benefits of Reparameterization among Prompts

Prompt-based techniques, such as prompt-tuning and prefix-tuning, have gained prominence for their efficiency in fine-tuning large pre-trained models. Despite their widespread adoption, the theoretical foundations of these methods remain limited. For instance, in prefix-tuning, we observe that a key factor in achieving performance parity with full fine-tuning lies in the reparameterization strategy. However, the theoretical principles underpinning the effectiveness of this approach have yet to be thoroughly examined. Our study demonstrates that reparameterization is not merely an engineering trick but is grounded in deep theoretical foundations. Specifically, we show that the reparameterization strategy implicitly encodes a shared structure between prefix key and value vectors. Building on recent insights into the connection between prefix-tuning and mixture of experts models, we further illustrate that this shared structure significantly improves sample efficiency in parameter estimation compared to non-shared alternatives. The effectiveness of prefix-tuning across diverse tasks is empirically confirmed to be enhanced by the shared structure, through extensive experiments in both visual and language domains. Additionally, we uncover similar structural benefits in prompt-tuning, offering new perspectives on its success. Our findings provide theoretical and empirical contributions, advancing the understanding of promptbased methods and their underlying mechanisms. * Equal Contribution † Qualcomm Vietnam Company Limited * ,j ′ ,p V * ,j ′ ) denotes a mixing measure, i.e., a weighted sum of Dirac measures δ, associated with unknown parameters At the same time, the values of the matrix A 0 j , the expert parameter η 0 j , and the bias parameter a 0 j are known for all 1 ≤ j ≤ N . Additionally, the matrices B ∈ R d×d and C ∈ R 1×d are given and they play the role of pre-trained projection matrices in the context of prefix-tuning in equation ( 6 ).