# Dynamic Context-oriented Decomposition for Task-aware Low-rank Adaptation with Less Forgetting and Faster Convergence

arXiv: https://arxiv.org/abs/2506.13187 · HTML: https://mlsanity.com/paper/2506.13187/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 101 of its 115 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Builds on (most cited first, 30 of 101)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Improved Baselines with Visual Instruction Tuning](https://mlsanity.com/paper/2310.03744/) (2023)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (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)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Making the V in VQA Matter: Elevating the Role of Image Understanding in Visual Question Answering](https://mlsanity.com/paper/1612.00837/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [MMBench: Is Your Multi-modal Model an All-around Player?](https://mlsanity.com/paper/2307.06281/) (2023)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Towards VQA Models That Can Read](https://mlsanity.com/paper/1904.08920/) (2019)

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

- [A Guardrail for Safety Preservation: When Safety-Sensitive Subspace Meets Harmful-Resistant Null-Space](https://mlsanity.com/paper/2510.14301/) (2025)
- [Purifying Task Vectors in Knowledge-Aware Subspace for Model Merging](https://mlsanity.com/paper/2510.14697/) (2025)
- [Spectral Surgery: Training-Free Refinement of LoRA via Gradient-Guided Singular Value Reweighting](https://mlsanity.com/paper/2603.03995/) (2026)
- [CCF: A Context Compression Framework for Efficient Long-Sequence Language Modeling](https://mlsanity.com/paper/2509.09199/) (2025)

## Abstract (arXiv)

Conventional low-rank adaptation methods build adapters without considering data context, leading to sub-optimal fine-tuning performance and severe forgetting of inherent world knowledge. In this paper, we propose context-oriented decomposition adaptation (CorDA), a novel method that initializes adapters in a task-aware manner. Concretely, we develop context-oriented singular value decomposition, where we collect covariance matrices of input activations for each linear layer using sampled data from the target task, and apply SVD to the product of weight matrix and its corresponding covariance matrix. By doing so, the task-specific capability is compacted into the principal components. Thanks to the task awareness, our method enables two optional adaptation modes, knowledge-preserved mode (KPM) and instruction-previewed mode (IPM), providing flexibility to choose between freezing the principal components to preserve their associated knowledge or adapting them to better learn a new task. We further develop CorDA++ by deriving a metric that reflects the compactness of task-specific principal components, and then introducing dynamic covariance selection and dynamic rank allocation strategies based on the same metric. The two strategies provide each layer with the most representative covariance matrix and a proper rank allocation. Experimental results show that CorDA++ outperforms CorDA by a significant margin. CorDA++ in KPM not only achieves better fine-tuning performance than LoRA, but also mitigates the forgetting of pre-trained knowledge in both large language models and vision language models. For IPM, our method exhibits faster convergence, e.g., 4.5x speedup over QLoRA, and improves adaptation performance in various scenarios, outperforming strong baseline methods. Our method has been integrated into the PEFT library developed by Hugging Face.