ToPA: Block-wise Toeplitz Adaptation for Expressive and Efficient Fine-Tuning

Sicong Li, Qianqian Xu, Zhiyong Yang, Zitai Wang, Longtao Huang +2

Parameter-Efficient Fine-Tuning (PEFT) has emerged as a prevalent strategy for adapting large pre-trained models. Among PEFT techniques, reparameterization-based methods, particularly those that employ low-rank or sparsity structures, have attracted significant attention. However, these approaches often underperform full fine-tuning. Specifically, low-rank methods constrain the update rank, which is misaligned with the inherently high-rank nature of full fine-tuning. In contrast, sparsity-based techniques limit the flexibility of the parameter space and compromise connectivity across weights. To overcome these limitations, we explore the use of Toeplitz matrices, whose entries are constant along each diagonal, therefore providing a compact parameterization without imposing explicit rank or sparsity constraints. A straightforward approach is to update weights via a product of Toeplitz matrices. However, similar to RNNs, long multiplicative chains often lead to gradient instability. To address this issue, we propose \textbf{ToPA}, a more refined version of this idea that replaces standard Toeplitz matrices with block-wise Toeplitz, greatly increasing each factor's capacity and…