# CorDA: Context-Oriented Decomposition Adaptation of Large Language Models for Task-Aware Parameter-Efficient Fine-tuning

arXiv: https://arxiv.org/abs/2406.05223 · HTML: https://mlsanity.com/paper/2406.05223/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- Builds on 64 of its 84 references that are in the map.
- First posted on arXiv 7 Jun 2024.

## Builds on (most cited first, 30 of 64)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [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)
- [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)
- [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)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [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)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [Latent Retrieval for Weakly Supervised Open Domain Question Answering](https://mlsanity.com/paper/1906.00300/) (2019)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)

## Built on by (most cited first, 30 of 44)

- [Keeping Yourself is Important in Downstream Tuning Multimodal Large Language Model](https://mlsanity.com/paper/2503.04543/) (2025)
- [LoRA meets Riemannion: Muon Optimizer for Parametrization-independent Low-Rank Adapters](https://mlsanity.com/paper/2507.12142/) (2025)
- [LoRASculpt: Sculpting LoRA for Harmonizing General and Specialized Knowledge in Multimodal Large Language Models](https://mlsanity.com/paper/2503.16843/) (2025)
- [Merge before Forget: A Single LoRA Continual Learning via Continual Merging](https://mlsanity.com/paper/2512.23017/) (2025)
- [Learning Rate Matters: Vanilla LoRA May Suffice for LLM Fine-tuning](https://mlsanity.com/paper/2602.04998/) (2026)
- [SelfAug: Mitigating Catastrophic Forgetting in Retrieval-Augmented Generation via Distribution Self-Alignment](https://mlsanity.com/paper/2509.03934/) (2025)
- [OSCAR: Offline Spectral Covariance-Aware Rotation for 2-bit KV Cache Quantization](https://mlsanity.com/paper/2605.17757/) (2026)
- [Mamba-FSCIL: Dynamic Adaptation with Selective State Space Model for Few-Shot Class-Incremental Learning](https://mlsanity.com/paper/2407.06136/) (2024)
- [BA-LoRA: Bias-Alleviating Low-Rank Adaptation to Mitigate Catastrophic Inheritance in Large Language Models](https://mlsanity.com/paper/2408.04556/) (2024)
- [Enhancing Online Continual Learning with Plug-and-Play State Space Model and Class-Conditional Mixture of Discretization](https://mlsanity.com/paper/2412.18177/) (2024)
- [LatentLLM: Attention-Aware Joint Tensor Compression](https://mlsanity.com/paper/2505.18413/) (2025)
- [The Primacy of Magnitude in Low-Rank Adaptation](https://mlsanity.com/paper/2507.06558/) (2025)
- [PMSS: Pretrained Matrices Skeleton Selection for LLM Fine-tuning](https://mlsanity.com/paper/2409.16722/) (2024)
- [SC-LoRA: Balancing Efficient Fine-tuning and Knowledge Preservation via Subspace-Constrained LoRA](https://mlsanity.com/paper/2505.23724/) (2025)
- [COALA: Numerically Stable and Efficient Framework for Context-Aware Low-Rank Approximation](https://mlsanity.com/paper/2507.07580/) (2025)
- [CARE: Covariance-Aware and Rank-Enhanced Decomposition for Enabling Multi-Head Latent Attention](https://mlsanity.com/paper/2603.17946/) (2026)
- [Dynamic Context-oriented Decomposition for Task-aware Low-rank Adaptation with Less Forgetting and Faster Convergence](https://mlsanity.com/paper/2506.13187/) (2025)
- [ThanoRA: Task Heterogeneity-Aware Multi-Task Low-Rank Adaptation](https://mlsanity.com/paper/2505.18640/) (2025)
- [Optimization-Inspired Few-Shot Adaptation for Large Language Models](https://mlsanity.com/paper/2505.19107/) (2025)
- [Purifying Task Vectors in Knowledge-Aware Subspace for Model Merging](https://mlsanity.com/paper/2510.14697/) (2025)
- [ConsNoTrainLoRA: Data-driven Weight Initialization of Low-rank Adapters using Constraints](https://mlsanity.com/paper/2507.08044/) (2025)
- [A Unified Study of LoRA Variants: Taxonomy, Review, Codebase, and Empirical Evaluation](https://mlsanity.com/paper/2601.22708/) (2026)
- [Sparsity Outperforms Low-Rank Projections in Few-Shot Adaptation](https://mlsanity.com/paper/2504.12436/) (2025)
- [Memory-Free Continual Learning with Null Space Adaptation for Zero-Shot Vision-Language Models](https://mlsanity.com/paper/2510.21175/) (2025)
- [CORA: Per-Slice Coherent Orthogonal Rotation for SVD-based Low-Rank Adaptation](https://mlsanity.com/paper/2607.02576/) (2026)
- [AWARe: Mitigating Catastrophic Forgetting via Activation-Weighted Adaptive REtention](https://mlsanity.com/paper/2608.11758/) (2026)
- [TuneComp: Joint Fine-tuning and Compression for Large Foundation Models](https://mlsanity.com/paper/2505.21835/) (2025)
- [GenFT: A Generative Parameter-Efficient Fine-Tuning Method for Pretrained Foundation Models](https://mlsanity.com/paper/2506.11042/) (2025)
- [PLATE: Plasticity-Tunable Efficient Adapters for Geometry-Aware Continual Learning](https://mlsanity.com/paper/2602.03846/) (2026)
- [GiVA: Gradient-Informed Bases for Vector-Based Adaptation](https://mlsanity.com/paper/2604.21901/) (2026)

## Abstract (arXiv)

Current parameter-efficient fine-tuning (PEFT) methods build adapters widely agnostic of the context of downstream task to learn, or the context of important knowledge to maintain. As a result, there is often a performance gap compared to full-parameter fine-tuning, and meanwhile the fine-tuned model suffers from catastrophic forgetting of the pre-trained world knowledge. In this paper, we propose CorDA, a Context-oriented Decomposition Adaptation method that builds learnable task-aware adapters from weight decomposition oriented by the context of downstream task or the world knowledge to maintain. Concretely, we collect a few data samples, and perform singular value decomposition for each linear layer of a pre-trained LLM multiplied by the covariance matrix of the input activation using these samples. The inverse of the covariance matrix is multiplied with the decomposed components to reconstruct the original weights. By doing so, the context of the representative samples is captured through deciding the factorizing orientation. Our method enables two options, the knowledge-preserved adaptation and the instruction-previewed adaptation. For the former, we use question-answering samples to obtain the covariance matrices, and use the decomposed components with the smallest r singular values to initialize a learnable adapter, with the others frozen such that the world knowledge is better preserved. For the latter, we use the instruction data from the fine-tuning task, such as math or coding, to orientate the decomposition and train the largest r components that most correspond to the task to learn. We conduct extensive experiments on Math, Code, and Instruction Following tasks.