# Beyond Rotations: AuroOFT for Expressive Quantized Orthogonal Fine-Tuning

arXiv: https://arxiv.org/abs/2608.05253 · HTML: https://mlsanity.com/paper/2608.05253/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 15 references that are in the map.
- First posted on arXiv 5 Aug 2026.

## Builds on (most cited first, 8 of 8)

- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [VeRA: Vector-based Random Matrix Adaptation](https://mlsanity.com/paper/2310.11454/) (2023)
- [Controlling Text-to-Image Diffusion by Orthogonal Finetuning](https://mlsanity.com/paper/2306.07280/) (2023)
- [Parameter-Efficient Orthogonal Finetuning via Butterfly Factorization](https://mlsanity.com/paper/2311.06243/) (2023)
- [MiLoRA: Harnessing Minor Singular Components for Parameter-Efficient LLM Finetuning](https://mlsanity.com/paper/2406.09044/) (2024)
- [AuroRA: Breaking Low-Rank Bottleneck of LoRA with Nonlinear Mapping](https://mlsanity.com/paper/2505.18738/) (2025)

## Abstract (arXiv)

Quantized orthogonal fine-tuning (qoft) enables parameter-efficient adaptation of low-bit language models by learning structured activation rotations before frozen quantized weights. However, its task-specific updates remain constrained to linear orthogonal transformations, limiting input-dependent nonlinear corrections. We introduce AuroOFT, which keeps qoft as a stable quantization-compatible branch while attaching a zero-start gated low-rank nonlinear residual to each adapted linear layer. AuroOFT maps activations into an RMS-normalized compact latent space and uses adaptive nonlinear bases with bounded or token-dependent gating. The zero-initialized up projection makes AuroOFT functionally identical to qoft at initialization, while orthogonality remains a branch-level stability property rather than a property of the combined nonlinear layer. Under matched data, optimization, decoding, and parser protocols, AuroOFT improves Macro-6 over matched qoft by 1.30-2.70% on the 1.5B/3B Qwen2.5 settings, exceeds QLoRA by 6.52-10.62%, and saves 32.3-44.7% trainable parameters relative to QLoRA in representative scales. The small exam-style multiple-choice math set is treated only as a protocol-sensitivity diagnostic. Our code is available at the anonymous repository: https://anonymous.4open.science/r/AuroOFT-F3FD.