# Orthogonal Finetuning Made Scalable

arXiv: https://arxiv.org/abs/2506.19847 · HTML: https://mlsanity.com/paper/2506.19847/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 62 references that are in the map.
- First posted on arXiv 24 Jun 2025.

## Builds on (most cited first, 30 of 54)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Don't Give Me the Details, Just the Summary! Topic-Aware Convolutional Neural Networks for Extreme Summarization](https://mlsanity.com/paper/1808.08745/) (2018)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Teaching Machines to Read and Comprehend](https://mlsanity.com/paper/1506.03340/) (2015)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [AdaptFormer: Adapting Vision Transformers for Scalable Visual Recognition](https://mlsanity.com/paper/2205.13535/) (2022)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [Compacter: Efficient Low-Rank Hypercomplex Adapter Layers](https://mlsanity.com/paper/2106.04647/) (2021)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [Parameter-Efficient Transfer Learning with Diff Pruning](https://mlsanity.com/paper/2012.07463/) (2020)
- [Scaling & Shifting Your Features: A New Baseline for Efficient Model Tuning](https://mlsanity.com/paper/2210.08823/) (2022)
- [SPoT: Better Frozen Model Adaptation through Soft Prompt Transfer](https://mlsanity.com/paper/2110.07904/) (2021)
- [DyLoRA: Parameter Efficient Tuning of Pre-trained Models using Dynamic Search-Free Low-Rank Adaptation](https://mlsanity.com/paper/2210.07558/) (2022)
- [LST: Ladder Side-Tuning for Parameter and Memory Efficient Transfer Learning](https://mlsanity.com/paper/2206.06522/) (2022)
- [Training Neural Networks with Fixed Sparse Masks](https://mlsanity.com/paper/2111.09839/) (2021)
- [Controlling Text-to-Image Diffusion by Orthogonal Finetuning](https://mlsanity.com/paper/2306.07280/) (2023)

## Built on by (most cited first, 7 of 7)

- [POET-X: Memory-efficient LLM Training by Scaling Orthogonal Transformation](https://mlsanity.com/paper/2603.05500/) (2026)
- [Orthogonal Model Merging](https://mlsanity.com/paper/2602.05943/) (2026)
- [Orthogonal Concept Erasure for Diffusion Models](https://mlsanity.com/paper/2605.28902/) (2026)
- [CORA: Per-Slice Coherent Orthogonal Rotation for SVD-based Low-Rank Adaptation](https://mlsanity.com/paper/2607.02576/) (2026)
- [LOFT: Low-Rank Orthogonal Fine-Tuning via Task-Aware Support Selection](https://mlsanity.com/paper/2605.11872/) (2026)
- [Normalized Low-Rank Adaptation](https://mlsanity.com/paper/2608.31036/) (2026)
- [Multimodal Foundation Models Adaptation based on Domain-Aware Relaxed Orthogonal Subspace for Remote Sensing](https://mlsanity.com/paper/2609.13654/) (2026)

## Abstract (arXiv)

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.