# Muon Can Outperform Dedicated Continual Learning Methods

arXiv: https://arxiv.org/abs/2609.24678 · HTML: https://mlsanity.com/paper/2609.24678/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 17 references that are in the map.
- First posted on arXiv 21 Sep 2026.

## Builds on (most cited first, 13 of 13)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [CodeXGLUE: A Machine Learning Benchmark Dataset for Code Understanding and Generation](https://mlsanity.com/paper/2102.04664/) (2021)
- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)
- [Orthogonal Subspace Learning for Language Model Continual Learning](https://mlsanity.com/paper/2310.14152/) (2023)
- [NumGLUE: A Suite of Fundamental yet Challenging Mathematical Reasoning Tasks](https://mlsanity.com/paper/2204.05660/) (2022)
- [MeetingBank: A Benchmark Dataset for Meeting Summarization](https://mlsanity.com/paper/2305.17529/) (2023)
- [Trillion Dollar Words: A New Financial Dataset, Task & Market Analysis](https://mlsanity.com/paper/2305.07972/) (2023)
- [TRACE: A Comprehensive Benchmark for Continual Learning in Large Language Models](https://mlsanity.com/paper/2310.06762/) (2023)
- [PolarGrad: A Class of Matrix-Gradient Optimizers from a Unifying Preconditioning Perspective](https://mlsanity.com/paper/2505.21799/) (2025)
- [ELLA: Efficient Lifelong Learning for Adapters in Large Language Models](https://mlsanity.com/paper/2601.02232/) (2026)

## Abstract (arXiv)

Continual learning with Low-Rank Adapters (LoRA) typically mitigates forgetting by penalizing the overlap between a new update and the accumulated past weights, which discourages certain update directions without controlling how an update distributes its energy over the ones that remain. We ask whether that restriction has to be task-aware, or whether a generic one supplied by the optimizer is enough. We train a plain incremental LoRA (IncLoRA) with Muon, which orthogonalizes each update, and compare it against O-LoRA and ELLA over five seeds and three task orders on the Standard CL Benchmark and three seeds on TRACE. IncLoRA+Muon reaches the accuracy band of the dedicated methods on Standard CL and improves on every AdamW configuration on TRACE. One update-constraining mechanism is enough, whether it comes from the loss or from the optimizer; on Standard CL a second one does not help, and for the most restrictive method it costs 8.4 points of accuracy and the plasticity to fit each task. What separates the two optimizers is not the size of the update, which under Muon is 0.91 to 2.06 times that under AdamW, but how it is distributed. AdamW confines it to between 1.4 and 1.8 effective singular directions, Muon spreads it over 7.0, and the two do not overlap in any tracked run. Part of the advantage usually attributed to dedicated CL methods may therefore be explained by the geometry of the optimizer's updates.