Task-Driven Subspace Decomposition for Knowledge Sharing and Isolation in LoRA-based Continual Learning

2026-02-26

AI Summary

This work addresses the challenge in existing LoRA-based continual learning methods of balancing knowledge sharing and isolation across tasks, which often leads to insufficient transfer or severe interference. To resolve this, the authors propose Low-rank Decomposition with Adaptation (LoDA), a novel approach that decouples shared and task-specific knowledge by decomposing LoRA weights into orthogonal subspaces guided by task-driven projection energy analysis. LoDA uniquely integrates energy-aware subspace decomposition, Gradient Alignment Optimization (GAO), and a closed-form calibration for the shared component updates. Extensive experiments on multiple continual learning benchmarks demonstrate that LoDA significantly outperforms current state-of-the-art methods, effectively enhancing knowledge transfer while mitigating catastrophic interference across sequential tasks.

Technology Category

Machine Learning: Transfer, Domain Adaptation, Multi-Task LearningIntelligent Robots: Learning & Optimization for ROBNatural Language Processing: Learning & Optimization for NLP

Application Category

Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMsGraph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Continual Learning (CL) requires models to sequentially adapt to new tasks without forgetting old knowledge. Recently, Low-Rank Adaptation (LoRA), a representative Parameter-Efficient Fine-Tuning (PEFT) method, has gained increasing attention in CL. Several LoRA-based CL methods reduce interference across tasks by separating their update spaces, typically building the new space from the estimated null space of past tasks. However, they (i) overlook task-shared directions, which suppresses knowledge transfer, and (ii) fail to capture truly effective task-specific directions since these ``null bases" of old tasks can remain nearly inactive for new task under correlated tasks. To address this, we study LoRA learning capability from a projection energy perspective, and propose Low-rank Decomposition and Adaptation (LoDA). It performs a task-driven decomposition to build general and truly task-specific LoRA subspaces by solving two energy-based objectives, decoupling directions for knowledge sharing and isolation. LoDA fixes LoRA down-projections on two subspaces and learns robust up-projections via a Gradient-Aligned Optimization (GAO) approach. After each task, before integrating the LoRA updates into the backbone, LoDA derives a closed-form recalibration for the general update, approximating a feature-level joint optimum along this task-shared direction. Experiments indicate that LoDA outperforms existing CL methods.

Problem

• Continual Learning
• Low-Rank Adaptation
• Knowledge Sharing
• Task Interference
• Subspace Decomposition

Innovation

• LoRA
• Continual Learning
• Subspace Decomposition
• Knowledge Sharing
• Gradient-Aligned Optimization