# SPACE-LoRA: Allocating Activation-Subspace Protection for Continual Learning

arXiv: https://arxiv.org/abs/2609.34453 · HTML: https://mlsanity.com/paper/2609.34453/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 22 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 18 of 18)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [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)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Learning to Prompt for Continual Learning](https://mlsanity.com/paper/2112.08654/) (2021)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.10512/) (2023)
- [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)
- [InfLoRA: Interference-Free Low-Rank Adaptation for Continual Learning](https://mlsanity.com/paper/2404.00228/) (2024)
- [Progressive Prompts: Continual Learning for Language Models](https://mlsanity.com/paper/2301.12314/) (2023)
- [Training Networks in Null Space of Feature Covariance for Continual Learning](https://mlsanity.com/paper/2103.07113/) (2021)
- [SplitLoRA: Balancing Stability and Plasticity in Continual Learning Through Gradient Space Splitting](https://mlsanity.com/paper/2505.22370/) (2025)
- [PLAN: Proactive Low-Rank Allocation for Continual Learning](https://mlsanity.com/paper/2510.21188/) (2025)
- [Energy-Structured Low-Rank Adaptation for Continual Learning](https://mlsanity.com/paper/2605.27482/) (2026)
- [Janus-LoRA: A Balanced Low-Rank Adaptation for Continual Learning](https://mlsanity.com/paper/2605.28495/) (2026)
- [Adaptive Budget Allocation for Orthogonal-Subspace Adapter Tuning in LLMs Continual Learning](https://mlsanity.com/paper/2505.22358/) (2025)

## Abstract (arXiv)

This study addresses the catastrophic forgetting problem that occurs when sequentially learning successive tasks using Low-Rank Adaptation (LoRA) from a lifelong learning perspective. While existing approaches have primarily constrained parameter updates or learning subspaces to reduce interference with past knowledge, they have not fully considered additive interference. This occurs when a newly added residual adapter on top of a fixed past model generates non-zero responses along input directions important for old tasks, thereby altering previous predictions. To this end, we propose Subspace Protection with Allocated Capacity for Efficient Continual Adaptation (SPACE-LoRA). SPACE-LoRA directly suppresses the responses of the new residual branch along input activation directions that are important for old tasks and adaptively determines the protection coverage for each module based on past-task sensitivity estimated via a common Fisher sensitivity-based coverage target. Under a fixed LoRA rank, this approach adaptively adjusts module-specific protection coverage while suppressing interference along input directions sensitive to old tasks. We assess the effectiveness of activation-subspace protection in mitigating catastrophic forgetting and examine the role of sensitivity-guided protection in continual learning across diverse tasks. Code is available at https://anonymous.4open.science/r/SPACE-LoRA-7864.