# CoDe-LoRA: Mitigating the Orthogonality Dilemma in Continual Learning of LLMs via Knowledge Consolidation and Decoupling

arXiv: https://arxiv.org/abs/2610.08312 · HTML: https://mlsanity.com/paper/2610.08312/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 6 Oct 2026.

## Builds on (most cited first, 12 of 12)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [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)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [Orthogonal Subspace Learning for Language Model Continual Learning](https://mlsanity.com/paper/2310.14152/) (2023)
- [Progressive Prompts: Continual Learning for Language Models](https://mlsanity.com/paper/2301.12314/) (2023)
- [LFPT5: A Unified Framework for Lifelong Few-shot Language Learning Based on Prompt Tuning of T5](https://mlsanity.com/paper/2110.07298/) (2021)
- [TRACE: A Comprehensive Benchmark for Continual Learning in Large Language Models](https://mlsanity.com/paper/2310.06762/) (2023)

## Abstract (arXiv)

Continual learning (CL) is essential for Large Language Models (LLMs) to sequentially adapt to evolving tasks. To mitigate catastrophic forgetting, recent advances implement low-rank adaptation with orthogonal projections (e.g., O-LoRA) to isolate task parameters. However, we reveal that such strict geometric constraints trigger an "Orthogonality Dilemma": rigid parameter isolation impedes the transfer and accumulation of shared representations across semantically related tasks. In this work, we propose a new replay-free method, called Consolidation and Decoupling LoRA (CoDe-LoRA), for CL of LLMs. CoDe-LoRA disentangles the learning process into Consolidating Universal Knowledge and Decoupling Task-Specific Knowledge. To achieve this, CoDe-LoRA leverages an adaptive null space projection mechanism and semantic routing to balance knowledge accumulation with task-specific adaptation. Experimental results across four backbones and three CL benchmarks show that CoDe-LoRA achieves the best average accuracy. Our code is available at https://github.com/Estrellajer/CoDe-LoRA.