Towards Symmetric Low-Rank Adapters

• URL: http://arxiv.org/abs/2504.03719v2
• Date: Tue, 15 Apr 2025 22:46:20 GMT
• Title: Towards Symmetric Low-Rank Adapters
• Authors: Tales Panoutsos, Rodrygo L. T. Santos, Flavio Figueiredo,
• Abstract summary: We introduce Symmetric Low-Rank Adapters, an optimized variant of LoRA with even fewer weights.<n>This method utilizes Low-Rank Symmetric Weight Matrices to learn downstream tasks more efficiently.
• Score: 3.3317825075368908
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we introduce Symmetric Low-Rank Adapters, an optimized variant of LoRA with even fewer weights. This method utilizes Low-Rank Symmetric Weight Matrices to learn downstream tasks more efficiently. Traditional LoRA accumulates fine-tuning weights with the original pre-trained weights via a Singular Value Decomposition (SVD) like approach, i.e., model weights are fine-tuned via updates of the form $BA$ (where $B \in \mathbb{R}^{n\times r}$, $A \in \mathbb{R}^{r\times n}$, and $r$ is the rank of the merged weight matrix). In contrast, our approach, named SymLoRA, represents fine-tuning weights as a Spectral Decomposition, i.e., $Q \, diag(\Lambda)\, Q^T$, where $Q \in \mathbb{R}^{n\times r}$ and $\Lambda \in \mathbb{R}^r$. SymLoRA requires approximately half of the finetuning weights. Here, we show that this approach has negligible losses in downstream efficacy.

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