# Calibrating and Rotating: A Unified Framework for Weight Conditioning in PEFT

arXiv: https://arxiv.org/abs/2511.00051 · HTML: https://mlsanity.com/paper/2511.00051/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 48 references that are in the map.
- First posted on arXiv 28 Oct 2025.

## Builds on (most cited first, 30 of 36)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [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)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Muon is Scalable for LLM Training](https://mlsanity.com/paper/2502.16982/) (2025)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [VeRA: Vector-based Random Matrix Adaptation](https://mlsanity.com/paper/2310.11454/) (2023)
- [A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA](https://mlsanity.com/paper/2312.03732/) (2023)
- [Controlling Text-to-Image Diffusion by Orthogonal Finetuning](https://mlsanity.com/paper/2306.07280/) (2023)
- [WinoGrande: An Adversarial Winograd Schema Challenge at Scale](https://mlsanity.com/paper/1907.10641/) (2019)
- [ReLoRA: High-Rank Training Through Low-Rank Updates](https://mlsanity.com/paper/2307.05695/) (2023)
- [LoRA-GA: Low-Rank Adaptation with Gradient Approximation](https://mlsanity.com/paper/2407.05000/) (2024)
- [Orthogonalizing Convolutional Layers with the Cayley Transform](https://mlsanity.com/paper/2104.07167/) (2021)
- [Skew Orthogonal Convolutions](https://mlsanity.com/paper/2105.11417/) (2021)
- [Riemannian Preconditioned LoRA for Fine-Tuning Foundation Models](https://mlsanity.com/paper/2402.02347/) (2024)
- [LoRA Done RITE: Robust Invariant Transformation Equilibration for LoRA Optimization](https://mlsanity.com/paper/2410.20625/) (2024)
- [PoLAR: Polar-Decomposed Low-Rank Adapter Representation](https://mlsanity.com/paper/2506.03133/) (2025)

## Built on by (most cited first, 4 of 4)

- [Localizing Credit at the Divergence: Path-Conditioned Self-Distillation for LLM Reasoning](https://mlsanity.com/paper/2606.15576/) (2026)
- [MINT: Minimal Information Neuro-Symbolic Tree for Objective-Driven Knowledge-Gap Reasoning and Active Elicitation](https://mlsanity.com/paper/2602.05048/) (2026)
- [ACDZero: MCTS Agent for Mastering Automated Cyber Defense](https://mlsanity.com/paper/2601.02196/) (2026)
- [A Note on Stability for Orthogonalized Matrix Momentum with Client Sampling](https://mlsanity.com/paper/2606.01720/) (2026)

## Abstract (arXiv)

Parameter-Efficient Fine-Tuning (PEFT) methods are crucial for adapting large pre-trained models. Among these, LoRA is considered a foundational approach. Building on this, the influential DoRA method enhances performance by decomposing weight updates into magnitude and direction. However, its underlying mechanism remains unclear, and it introduces significant computational overhead. In this work, we first identify that DoRA's success stems from its capacity to increase the singular value entropy of the weight update matrix, which promotes a more uniform update distribution akin to full fine-tuning. We then reformulate DoRA into a mathematically equivalent and more efficient matrix form, revealing it as a learnable weight conditioning method. Based on this insight, we propose a unified framework for designing advanced PEFT methods by exploring two orthogonal dimensions: the architectural placement and the transformation type of the conditioning matrix. Within this framework, we introduce two novel methods: (1) Pre-Diag, which applies a diagonal conditioning matrix before the LoRA update to efficiently calibrate the pre-trained weights, thereby enhancing performance while reducing training time; and (2) Skewed Orthogonal Rotation Adaptation (SORA), which employs a parameter-efficient orthogonal rotation to perform a more powerful, norm-preserving transformation of the feature space. Extensive experiments on natural language understanding and generation tasks demonstrate that our proposed methods achieve superior performance and efficiency compared to both LoRA and DoRA. The code is available at https://github.com/MaeChd/SORA.