# PaLoRA: Paced Low-Rank Adaptation for Continual Learning

arXiv: https://arxiv.org/abs/2610.04226 · HTML: https://mlsanity.com/paper/2610.04226/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 52 of its 62 references that are in the map.
- First posted on arXiv 3 Oct 2026.

## Builds on (most cited first, 30 of 52)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [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)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Transformers in Vision: A Survey](https://mlsanity.com/paper/2101.01169/) (2021)
- [Learning to Prompt for Continual Learning](https://mlsanity.com/paper/2112.08654/) (2021)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [GPT Understands, Too](https://mlsanity.com/paper/2103.10385/) (2021)
- [A Survey on Visual Transformer](https://mlsanity.com/paper/2012.12556/) (2020)
- [DualPrompt: Complementary Prompting for Rehearsal-free Continual Learning](https://mlsanity.com/paper/2204.04799/) (2022)
- [End-to-End Incremental Learning](https://mlsanity.com/paper/1807.09536/) (2018)
- [Gradient based sample selection for online continual learning](https://mlsanity.com/paper/1903.08671/) (2019)
- [How to train your ViT? Data, Augmentation, and Regularization in Vision Transformers](https://mlsanity.com/paper/2106.10270/) (2021)
- [CODA-Prompt: COntinual Decomposed Attention-based Prompting for Rehearsal-Free Continual Learning](https://mlsanity.com/paper/2211.13218/) (2022)
- [Class-incremental learning: survey and performance evaluation on image classification](https://mlsanity.com/paper/2010.15277/) (2020)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [Measuring Catastrophic Forgetting in Neural Networks](https://mlsanity.com/paper/1708.02072/) (2017)
- [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)
- [VeRA: Vector-based Random Matrix Adaptation](https://mlsanity.com/paper/2310.11454/) (2023)
- [PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models](https://mlsanity.com/paper/2404.02948/) (2024)
- [Learning without Memorizing](https://mlsanity.com/paper/1811.08051/) (2018)
- [A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA](https://mlsanity.com/paper/2312.03732/) (2023)
- [LST: Ladder Side-Tuning for Parameter and Memory Efficient Transfer Learning](https://mlsanity.com/paper/2206.06522/) (2022)

## Abstract (arXiv)

LoRA-based continual learning methods mitigate catastrophic forgetting through various mechanisms, yet nearly all complement these with small learning rates as a heuristic to restrict gradient scaling magnitude. Such fixed heuristics lack theoretical guidance on how the strength of this restriction should evolve as tasks accumulate. We reveal that even under directional constraints such as nullspace projection, finite-precision updates inevitably leak into the subspace of accumulated prior knowledge along multiple directions. While small learning rates attenuate such leakage, they cannot prevent the accumulated forgetting from intensifying as the effective rank of historical knowledge grows. We show that the optimal magnitude restriction should adaptively increase with this effective rank to balance stability and plasticity, i.e., preservation of previous knowledge and acquisition of new task information. Under an anisotropic leakage model, we derive a pacing law s^*=√R/c that characterizes the optimal scaling of gradient steps, i.e., the magnitude restriction itself, where R is the effective rank of past updates. Based on this insight, we propose PaLoRA, which compresses historical knowledge via adaptive SVD truncation, projects gradients onto the nullspace of prior tasks, and applies rank-aware adaptive pacing. Experiments demonstrate consistent improvements over prior methods, with particularly strong performance in long-horizon settings, achieving substantial gains of 4% accuracy on challenging 50-task ImageNet-A and ImageNet-R benchmarks.