Orthogonal finetuning (OFT) offers highly parameter-efficient adaptation while preventing catastrophic forgetting, but its high runtime and memory demands limit practical deployment. We identify the core computational bottleneck in OFT as its weight-centric implementation, which relies on costly matrix-matrix multiplications with cubic complexity. To overcome this, we propose OFTv2, an input-centric reformulation that instead uses matrix-vector multiplications (i.e., matrix-free computation), reducing the computational cost to quadratic. We further introduce the Cayley–Neumann parameterization, an efficient orthogonal parameterization that approximates the matrix inversion in the Cayley transform via a truncated Neumann series. These modifications allow OFTv2 to achieve up to 10x faster training and 3x lower GPU memory usage without compromising performance. In addition, we extend OFTv2 to support finetuning quantized foundation models and show that it outperforms the popular QLoRA in training stability, efficiency, and memory usage.

Adapting large language models (LLMs) to specific tasks remains challenging due to the extensive retraining required, prompting the need for efficient adapter techniques. Despite this, the concurrent serving of multiple adapters, each with unique matrix shapes, poses significant system-level challenges. To address these issues, we identify an opportunity in structurally sparse adapters, which, unlike low-rank adapters, maintain consistent matrix shapes while varying in sparsity patterns. Leveraging this characteristic, we introduce SpartanServe, a system designed for efficient concurrent serving of LLMs using multiple structurally sparse adapters. SpartanServe employs a unified matrix multiplication operation and a novel memory management technique to enable effective batching. Furthermore, the incorporation of Triton kernels enhances the acceleration of matrix multiplication in the serving process. Experimental results demonstrate that SpartanServe achieves 2.12× speedup over S-LoRA when serving 96 adapters using a single NVIDIA A100 GPU (40GB), showcasing its efficacy in concurrent LLM serving.