# A Stronger Mixture of Low-Rank Experts for Fine-Tuning Foundation Models

arXiv: https://arxiv.org/abs/2502.15828 · HTML: https://mlsanity.com/paper/2502.15828/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Mixture of LoRA experts, one of 12 directions in Mixture-of-experts.
- Builds on 39 of its 51 references that are in the map.
- First posted on arXiv 20 Feb 2025.

## Placed in

- Mixture-of-experts / [Mixture of LoRA experts](https://mlsanity.com/moe/mixture-of-lora-experts/)

## Builds on (most cited first, 30 of 39)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Visual Genome: Connecting Language and Vision Using Crowdsourced Dense Image Annotations](https://mlsanity.com/paper/1602.07332/) (2016)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [Visual7W: Grounded Question Answering in Images](https://mlsanity.com/paper/1511.03416/) (2015)
- [A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA](https://mlsanity.com/paper/2312.03732/) (2023)
- [Mixture of LoRA Experts](https://mlsanity.com/paper/2404.13628/) (2024)
- [Pushing Mixture of Experts to the Limit: Extremely Parameter Efficient MoE for Instruction Tuning](https://mlsanity.com/paper/2309.05444/) (2023)
- [MixLoRA: Enhancing Large Language Models Fine-Tuning with LoRA-based Mixture of Experts](https://mlsanity.com/paper/2404.15159/) (2024)
- [LoRA-GA: Low-Rank Adaptation with Gradient Approximation](https://mlsanity.com/paper/2407.05000/) (2024)
- [AdaMix: Mixture-of-Adaptations for Parameter-efficient Model Tuning](https://mlsanity.com/paper/2210.17451/) (2022)
- [HydraLoRA: An Asymmetric LoRA Architecture for Efficient Fine-Tuning](https://mlsanity.com/paper/2404.19245/) (2024)
- [Mixture of Cluster-conditional LoRA Experts for Vision-language Instruction Tuning](https://mlsanity.com/paper/2312.12379/) (2023)
- [Higher Layers Need More LoRA Experts](https://mlsanity.com/paper/2402.08562/) (2024)
- [MiLoRA: Harnessing Minor Singular Components for Parameter-Efficient LLM Finetuning](https://mlsanity.com/paper/2406.09044/) (2024)
- [LLaVA-MoLE: Sparse Mixture of LoRA Experts for Mitigating Data Conflicts in Instruction Finetuning MLLMs](https://mlsanity.com/paper/2401.16160/) (2024)
- [LoRA-Pro: Are Low-Rank Adapters Properly Optimized?](https://mlsanity.com/paper/2407.18242/) (2024)
- [MoRAL: MoE Augmented LoRA for LLMs' Lifelong Learning](https://mlsanity.com/paper/2402.11260/) (2024)
- [Riemannian Preconditioned LoRA for Fine-Tuning Foundation Models](https://mlsanity.com/paper/2402.02347/) (2024)
- [Mixture-of-Subspaces in Low-Rank Adaptation](https://mlsanity.com/paper/2406.11909/) (2024)
- [Parameter-Efficient Fine-Tuning for Foundation Models](https://mlsanity.com/paper/2501.13787/) (2025)
- [LoRA Dropout as a Sparsity Regularizer for Overfitting Control](https://mlsanity.com/paper/2404.09610/) (2024)
- [Mixture-of-Domain-Adapters: Decoupling and Injecting Domain Knowledge to Pre-trained Language Models Memories](https://mlsanity.com/paper/2306.05406/) (2023)
- [SiRA: Sparse Mixture of Low Rank Adaptation](https://mlsanity.com/paper/2311.09179/) (2023)
- [Automated Generation of Challenging Multiple-Choice Questions for Vision Language Model Evaluation](https://mlsanity.com/paper/2501.03225/) (2025)
- [Low-Rank Matrix Recovery with Scaled Subgradient Methods: Fast and Robust Convergence Without the Condition Number](https://mlsanity.com/paper/2010.13364/) (2020)

## Built on by (most cited first, 9 of 9)

- [Revisiting semi-supervised learning in the era of foundation models](https://mlsanity.com/paper/2503.09707/) (2025)
- [W2T: LoRA Weights Already Know What They Can Do](https://mlsanity.com/paper/2603.15990/) (2026)
- [PASs-MoE: Mitigating Misaligned Co-drift among Router and Experts via Pathway Activation Subspaces for Continual Learning](https://mlsanity.com/paper/2601.13020/) (2026)
- [Breaking the MoE LLM Trilemma: Dynamic Expert Clustering with Structured Compression](https://mlsanity.com/paper/2510.02345/) (2025)
- [C-Flat++: Towards a More Efficient and Powerful Framework for Continual Learning](https://mlsanity.com/paper/2508.18860/) (2025)
- [RotMoLE: Enhancing Mixture of Low-Rank Experts through Rotational Gating Mechanism](https://mlsanity.com/paper/2605.25565/) (2026)
- [Mixture of Debaters: Learn to Debate at Architectural Level in Multi-Agent Reasoning](https://mlsanity.com/paper/2606.29425/) (2026)
- [InstructMoLE: Instruction-Guided Mixture of Low-rank Experts for Multi-Conditional Image Generation](https://mlsanity.com/paper/2512.21788/) (2025)
- [FourierMoE: Fourier Mixture-of-Experts Adaptation of Large Language Models](https://mlsanity.com/paper/2604.01762/) (2026)

## Abstract (arXiv)

In order to streamline the fine-tuning of foundation models, Low-Rank Adapters (LoRAs) have been substantially adopted across various fields, including instruction tuning and domain adaptation. The underlying concept of LoRA involves decomposing a full-rank matrix into the product of two lower-rank matrices, which reduces storage consumption and accelerates the training process. Furthermore, to address the limited expressive capacity of LoRA, the Mixture-of-Expert (MoE) has been introduced for incorporating multiple LoRA adapters. The integration of LoRA experts leads to a visible improvement across several downstream scenes. However, the mixture of LoRAs (MoE-LoRA) still exhibits its low robustness during tuning and inferring. Inspired by the Riemannian Preconditioners which train LoRA as a sub-space projector, we propose a new training strategy for MoE-LoRA, to stabilize and boost its feature learning procedure by multi-space projections. Examinations on SGD and AdamW optimizers demonstrate the effectiveness of our methodology. Source code is available at https://github.com/THUDM/MoELoRA_Riemannian.