# Spectral Imbalance Causes Forgetting in Low-Rank Continual Adaptation

arXiv: https://arxiv.org/abs/2602.00722 · HTML: https://mlsanity.com/paper/2602.00722/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 76 references that are in the map.
- First posted on arXiv 31 Jan 2026.

## Builds on (most cited first, 30 of 55)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Making the V in VQA Matter: Elevating the Role of Image Understanding in Visual Question Answering](https://mlsanity.com/paper/1612.00837/) (2016)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Flickr30k Entities: Collecting Region-to-Phrase Correspondences for Richer Image-to-Sentence Models](https://mlsanity.com/paper/1505.04870/) (2015)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Learning to Prompt for Continual Learning](https://mlsanity.com/paper/2112.08654/) (2021)
- [Generation and Comprehension of Unambiguous Object Descriptions](https://mlsanity.com/paper/1511.02283/) (2015)
- [VizWiz Grand Challenge: Answering Visual Questions from Blind People](https://mlsanity.com/paper/1802.08218/) (2018)
- [A Diagram Is Worth A Dozen Images](https://mlsanity.com/paper/1603.07396/) (2016)
- [DualPrompt: Complementary Prompting for Rehearsal-free Continual Learning](https://mlsanity.com/paper/2204.04799/) (2022)
- [PathVQA: 30000+ Questions for Medical Visual Question Answering](https://mlsanity.com/paper/2003.10286/) (2020)
- [CODA-Prompt: COntinual Decomposed Attention-based Prompting for Rehearsal-Free Continual Learning](https://mlsanity.com/paper/2211.13218/) (2022)
- [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)
- [IconQA: A New Benchmark for Abstract Diagram Understanding and Visual Language Reasoning](https://mlsanity.com/paper/2110.13214/) (2021)
- [RSVQA: Visual Question Answering for Remote Sensing Data](https://mlsanity.com/paper/2003.07333/) (2020)
- [Boosting Continual Learning of Vision-Language Models via Mixture-of-Experts Adapters](https://mlsanity.com/paper/2403.11549/) (2024)
- [Continual Pre-training of Language Models](https://mlsanity.com/paper/2302.03241/) (2023)
- [InfLoRA: Interference-Free Low-Rank Adaptation for Continual Learning](https://mlsanity.com/paper/2404.00228/) (2024)
- [Continual Learning with Pre-Trained Models: A Survey](https://mlsanity.com/paper/2401.16386/) (2024)
- [Multimodal ArXiv: A Dataset for Improving Scientific Comprehension of Large Vision-Language Models](https://mlsanity.com/paper/2403.00231/) (2024)
- [CLEVR-Math: A Dataset for Compositional Language, Visual and Mathematical Reasoning](https://mlsanity.com/paper/2208.05358/) (2022)
- [Preventing Zero-Shot Transfer Degradation in Continual Learning of Vision-Language Models](https://mlsanity.com/paper/2303.06628/) (2023)
- [Fine-tuning can cripple your foundation model; preserving features may be the solution](https://mlsanity.com/paper/2308.13320/) (2023)

## Built on by (most cited first, 5 of 5)

- [RL Forgets! Towards Continual Policy Optimization](https://mlsanity.com/paper/2607.04364/) (2026)
- [Bilinear Optimization Divergence: Diagnosing Factor-Constrained LoRA Continual Learning](https://mlsanity.com/paper/2609.23594/) (2026)
- [KeepLoRA++: Continual Learning with Layer-Scaled Residual Gradient Adaptation](https://mlsanity.com/paper/2606.16256/) (2026)
- [OrthoSkillVLA: Continual Skill Learning via Gradient-Informed Skill Subspace Adaptation](https://mlsanity.com/paper/2608.19589/) (2026)
- [MuLoRA: Spectrally Balanced Low-Rank Adaptation for Continual Learning](https://mlsanity.com/paper/2610.02283/) (2026)

## Abstract (arXiv)

Parameter-efficient continual learning aims to adapt pre-trained models to sequential tasks without forgetting previously acquired knowledge. Most existing approaches treat continual learning as avoiding interference with past updates, rather than considering what properties make the current task-specific update naturally preserve previously acquired knowledge. From a knowledge-decomposition perspective, we observe that low-rank adaptations exhibit highly imbalanced singular value spectra: a few dominant components absorb most of the adaptation energy, thereby (i) more likely to disrupt previously acquired knowledge and (ii) making the update more vulnerable to interference from subsequent tasks. To enable explicit balance among components, we decouple the magnitude of the task update from its directional structure and formulate it as a constrained optimization problem on a restricted Stiefel manifold. We address this problem using a projected first-order method compatible with standard deep-learning optimizers used in vision-language models. Our method mitigates both backward and forward forgetting, consistently outperforming continual learning baselines. The implementation code is available at https://github.com/haodotgu/EBLoRA.