# SplitLoRA: Balancing Stability and Plasticity in Continual Learning Through Gradient Space Splitting

arXiv: https://arxiv.org/abs/2505.22370 · HTML: https://mlsanity.com/paper/2505.22370/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 56 references that are in the map.
- First posted on arXiv 28 May 2025.

## Builds on (most cited first, 30 of 50)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (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)
- [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)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Visual Prompt Tuning](https://mlsanity.com/paper/2203.12119/) (2022)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [Learning to Prompt for Continual Learning](https://mlsanity.com/paper/2112.08654/) (2021)
- [AdaptFormer: Adapting Vision Transformers for Scalable Visual Recognition](https://mlsanity.com/paper/2205.13535/) (2022)
- [DualPrompt: Complementary Prompting for Rehearsal-free Continual Learning](https://mlsanity.com/paper/2204.04799/) (2022)
- [ImageNet-21K Pretraining for the Masses](https://mlsanity.com/paper/2104.10972/) (2021)
- [Knowledge Neurons in Pretrained Transformers](https://mlsanity.com/paper/2104.08696/) (2021)
- [Gradient based sample selection for online continual learning](https://mlsanity.com/paper/1903.08671/) (2019)
- [Compacter: Efficient Low-Rank Hypercomplex Adapter Layers](https://mlsanity.com/paper/2106.04647/) (2021)
- [CODA-Prompt: COntinual Decomposed Attention-based Prompting for Rehearsal-Free Continual Learning](https://mlsanity.com/paper/2211.13218/) (2022)
- [Online Continual Learning with Maximally Interfered Retrieval](https://mlsanity.com/paper/1908.04742/) (2019)
- [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)
- [Orthogonal Subspace Learning for Language Model Continual Learning](https://mlsanity.com/paper/2310.14152/) (2023)
- [Learn to Grow: A Continual Structure Learning Framework for Overcoming Catastrophic Forgetting](https://mlsanity.com/paper/1904.00310/) (2019)
- [Compacting, Picking and Growing for Unforgetting Continual Learning](https://mlsanity.com/paper/1910.06562/) (2019)

## Built on by (most cited first, 10 of 10)

- [Bilinear Optimization Divergence: Diagnosing Factor-Constrained LoRA Continual Learning](https://mlsanity.com/paper/2609.23594/) (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)
- [SR2-LoRA: Self-Rectifying Inter-layer Relations in Low-Rank Adaptation for Class-Incremental Learning](https://mlsanity.com/paper/2605.07420/) (2026)
- [iGSP:Implicit Gradient Subspace Projection for Efficient Continual Learning of Vision-Language Models](https://mlsanity.com/paper/2605.19301/) (2026)
- [SPACE-LoRA: Allocating Activation-Subspace Protection for Continual Learning](https://mlsanity.com/paper/2609.34453/) (2026)
- [Distribution-Conditioned Task Routing for Class-Incremental Learning](https://mlsanity.com/paper/2609.34503/) (2026)
- [Generalized Residual Closure: General Learning Dynamics for Stability-Plasticity Compatibility](https://mlsanity.com/paper/2609.38911/) (2026)
- [MuLoRA: Spectrally Balanced Low-Rank Adaptation for Continual Learning](https://mlsanity.com/paper/2610.02283/) (2026)
- [Text-Centric Post-Training for Omni-Modal Reasoning](https://mlsanity.com/paper/2610.02819/) (2026)
- [Stable-Plastic Subspace Construction for Differentially Private Continual LoRA](https://mlsanity.com/paper/2610.17904/) (2026)

## Abstract (arXiv)

Continual Learning requires a model to learn multiple tasks in sequence while maintaining both stability:preserving knowledge from previously learned tasks, and plasticity:effectively learning new tasks. Gradient projection has emerged as an effective and popular paradigm in CL, where it partitions the gradient space of previously learned tasks into two orthogonal subspaces: a primary subspace and a minor subspace. New tasks are learned effectively within the minor subspace, thereby reducing interference with previously acquired knowledge. However, existing Gradient Projection methods struggle to achieve an optimal balance between plasticity and stability, as it is hard to appropriately partition the gradient space. In this work, we consider a continual learning paradigm based on Low-Rank Adaptation, which has gained considerable attention due to its efficiency and wide applicability, and propose a novel approach for continual learning, called SplitLoRA. We first provide a theoretical analysis of how subspace partitioning affects model stability and plasticity. Informed by this analysis, we then introduce an effective method that derives the optimal partition of the gradient space for previously learned tasks. This approach effectively balances stability and plasticity in continual learning. Experimental results on multiple datasets demonstrate that the proposed method achieves state-of-the-art performance.