# CORA: Per-Slice Coherent Orthogonal Rotation for SVD-based Low-Rank Adaptation

arXiv: https://arxiv.org/abs/2607.02576 · HTML: https://mlsanity.com/paper/2607.02576/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 27 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Builds on (most cited first, 23 of 23)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.10512/) (2023)
- [LLM-Adapters: An Adapter Family for Parameter-Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2304.01933/) (2023)
- [PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models](https://mlsanity.com/paper/2404.02948/) (2024)
- [Controlling Text-to-Image Diffusion by Orthogonal Finetuning](https://mlsanity.com/paper/2306.07280/) (2023)
- [LoftQ: LoRA-Fine-Tuning-Aware Quantization for Large Language Models](https://mlsanity.com/paper/2310.08659/) (2023)
- [LoRA-GA: Low-Rank Adaptation with Gradient Approximation](https://mlsanity.com/paper/2407.05000/) (2024)
- [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)
- [LoRA-Pro: Are Low-Rank Adapters Properly Optimized?](https://mlsanity.com/paper/2407.18242/) (2024)
- [SVFT: Parameter-Efficient Fine-Tuning with Singular Vectors](https://mlsanity.com/paper/2405.19597/) (2024)
- [CorDA: Context-Oriented Decomposition Adaptation of Large Language Models for Task-Aware Parameter-Efficient Fine-tuning](https://mlsanity.com/paper/2406.05223/) (2024)
- [Reparameterized LLM Training via Orthogonal Equivalence Transformation](https://mlsanity.com/paper/2506.08001/) (2025)
- [KaSA: Knowledge-Aware Singular-Value Adaptation of Large Language Models](https://mlsanity.com/paper/2412.06071/) (2024)
- [Orthogonal Finetuning Made Scalable](https://mlsanity.com/paper/2506.19847/) (2025)
- [Efficient Orthogonal Fine-Tuning with Principal Subspace Adaptation](https://mlsanity.com/paper/2505.11235/) (2025)
- [DiaBlo: Diagonal Blocks Are Sufficient For Finetuning](https://mlsanity.com/paper/2506.03230/) (2025)
- [Geometric and Spectral Alignment for Deep Neural Network II](https://mlsanity.com/paper/2605.02111/) (2026)

## Built on by (most cited first, 1 of 1)

- [CHASE: Channel-Aligned Structure Exploitation for Geometry-Aware Model Engineering](https://mlsanity.com/paper/2610.09476/) (2026)

## Abstract (arXiv)

Parameter-Efficient Fine-Tuning (PEFT) commonly adapts pretrained weights through low-rank updates, and recent methods further exploit the singular value decomposition (SVD) of the base weight for initialization or subspace selection. However, these methods do not explicitly preserve the coupled geometry between the pretrained left and right singular bases. Motivated by recent minimum-perturbation theory, which shows that stable finetuning follows a coherent SVD rotation in which a single orthogonal Q acts on both the left singular basis U0 and the right singular basis V0, we prove a per-slice analogue: each row slice of W0 can be adapted by a shared orthogonal rotation Qi on its left basis Ui and right basis Vi together with a diagonal spectrum shift. We implement this form as CORA (Coherent Orthogonal Rotation Adaptation), which applies per-slice orthogonal rotations and a per-layer diagonal scale to the rank-r SVD truncation of W0. CORA uses tfrac12m(r-1) trainable parameters per linear layer, about 4× fewer than LoRA at the same rank. CORA outperforms LoRA, DoRA, PiSSA, and MiLoRA on commonsense reasoning and code generation while using about 8× fewer parameters.