# Continual Gradient Low-Rank Projection Fine-Tuning for LLMs

arXiv: https://arxiv.org/abs/2507.02503 · HTML: https://mlsanity.com/paper/2507.02503/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 47 references that are in the map.
- First posted on arXiv 3 Jul 2025.

## Builds on (most cited first, 30 of 40)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (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)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [Learning to Prompt for Continual Learning](https://mlsanity.com/paper/2112.08654/) (2021)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [Orthogonal Gradient Descent for Continual Learning](https://mlsanity.com/paper/1910.07104/) (2019)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [Orthogonal Subspace Learning for Language Model Continual Learning](https://mlsanity.com/paper/2310.14152/) (2023)
- [In-Context Learning Creates Task Vectors](https://mlsanity.com/paper/2310.15916/) (2023)
- [In-context Vectors: Making In Context Learning More Effective and Controllable Through Latent Space Steering](https://mlsanity.com/paper/2311.06668/) (2023)
- [Continual Learning of Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2404.16789/) (2024)
- [ReLoRA: High-Rank Training Through Low-Rank Updates](https://mlsanity.com/paper/2307.05695/) (2023)
- [Progressive Prompts: Continual Learning for Language Models](https://mlsanity.com/paper/2301.12314/) (2023)
- [Episodic Memory in Lifelong Language Learning](https://mlsanity.com/paper/1906.01076/) (2019)
- [Training Networks in Null Space of Feature Covariance for Continual Learning](https://mlsanity.com/paper/2103.07113/) (2021)
- [Continual Diffusion: Continual Customization of Text-to-Image Diffusion with C-LoRA](https://mlsanity.com/paper/2304.06027/) (2023)
- [Mitigating Catastrophic Forgetting in Large Language Models with Self-Synthesized Rehearsal](https://mlsanity.com/paper/2403.01244/) (2024)
- [Flora: Low-Rank Adapters Are Secretly Gradient Compressors](https://mlsanity.com/paper/2402.03293/) (2024)
- [LFPT5: A Unified Framework for Lifelong Few-shot Language Learning Based on Prompt Tuning of T5](https://mlsanity.com/paper/2110.07298/) (2021)
- [TRGP: Trust Region Gradient Projection for Continual Learning](https://mlsanity.com/paper/2202.02931/) (2022)
- [Chain of LoRA: Efficient Fine-tuning of Language Models via Residual Learning](https://mlsanity.com/paper/2401.04151/) (2024)
- [Beyond Not-Forgetting: Continual Learning with Backward Knowledge Transfer](https://mlsanity.com/paper/2211.00789/) (2022)
- [Towards Better Plasticity-Stability Trade-off in Incremental Learning: A Simple Linear Connector](https://mlsanity.com/paper/2110.07905/) (2021)

## Built on by (most cited first, 11 of 11)

- [When Continual Learning Moves to Memory: A Study of Experience Reuse in LLM Agents](https://mlsanity.com/paper/2604.27003/) (2026)
- [Decomposing the Basic Abilities of Large Language Models: Mitigating Cross-Task Interference in Multi-Task Instruct-Tuning](https://mlsanity.com/paper/2605.05676/) (2026)
- [Rotation-Preserving Supervised Fine-Tuning](https://mlsanity.com/paper/2605.10973/) (2026)
- [Collaborative Parameter Learning: Mitigating Forgetting via Parameter-Level Gradient Analysis](https://mlsanity.com/paper/2601.21577/) (2026)
- [SAE-FD: Sparse Autoencoder Feature Distillation for Continual Learning of Large Language Models](https://mlsanity.com/paper/2605.25525/) (2026)
- [Make LLM Learn to Synthesize from Streaming Experiences through Feedback](https://mlsanity.com/paper/2605.29940/) (2026)
- [MemTrapBench: Benchmarking Cognitive Traps in LLM Memory Use](https://mlsanity.com/paper/2608.20202/) (2026)
- [Estimating and Orthogonalizing Unknown Pre-training Gradients for Continual Fine-tuning of Large Language Models](https://mlsanity.com/paper/2609.30935/) (2026)
- [Hidden Failure Modes of Gradient Modification under Adam in Continual Learning, and Adaptive Decoupled Moment Routing as a Repair](https://mlsanity.com/paper/2604.22407/) (2026)
- [Generalizable Lifelong Model Editing via Preference Optimization](https://mlsanity.com/paper/2609.36748/) (2026)
- [Static Gradient Attribution Underperforms a Density-Matched Random Mask on Loss-Based Forgetting Within LoRA B-Matrix](https://mlsanity.com/paper/2610.12744/) (2026)

## Abstract (arXiv)

Continual fine-tuning of Large Language Models (LLMs) is hampered by the trade-off between efficiency and expressiveness. Low-Rank Adaptation (LoRA) offers efficiency but constrains the model's ability to learn new tasks and transfer knowledge due to its low-rank nature and reliance on explicit parameter constraints. We propose GORP (Gradient LOw Rank Projection) for Continual Learning, a novel training strategy that overcomes these limitations by synergistically combining full and low-rank parameters and jointly updating within a unified low-rank gradient subspace. GORP expands the optimization space while preserving efficiency and mitigating catastrophic forgetting. Extensive experiments on continual learning benchmarks demonstrate GORP's superior performance compared to existing state-of-the-art approaches. Code is available at https://github.com/Wcxwcxw/GORP.