Orthogonal Finetuning Made Scalable

TL;DR

This paper introduces OFTv2, a scalable and efficient orthogonal finetuning method that significantly reduces computational costs and memory usage, enabling practical deployment of parameter-efficient model adaptation.

Contribution

OFTv2 reformulates orthogonal finetuning to use matrix-vector operations and introduces a new orthogonal parameterization, greatly improving efficiency and scalability.

Findings

OFTv2 achieves up to 10x faster training.

It reduces GPU memory usage by 3x.

Outperforms QLoRA in stability and efficiency.

Abstract

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.