# Mixture-of-Subspaces in Low-Rank Adaptation

arXiv: https://arxiv.org/abs/2406.11909 · HTML: https://mlsanity.com/paper/2406.11909/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- Placed in Image generation, text-to-image and editing, one of 14 directions in Diffusion models.
- Builds on 45 of its 63 references that are in the map.
- First posted on arXiv 16 Jun 2024.

## Placed in

- Diffusion models / [Image generation, text-to-image and editing](https://mlsanity.com/diffusion/image-generation-text-to-image-and-editing/)

## Builds on (most cited first, 30 of 45)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Improved Baselines with Visual Instruction Tuning](https://mlsanity.com/paper/2310.03744/) (2023)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (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)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Making the V in VQA Matter: Elevating the Role of Image Understanding in Visual Question Answering](https://mlsanity.com/paper/1612.00837/) (2016)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [MMBench: Is Your Multi-modal Model an All-around Player?](https://mlsanity.com/paper/2307.06281/) (2023)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [Towards VQA Models That Can Read](https://mlsanity.com/paper/1904.08920/) (2019)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [DeBERTaV3: Improving DeBERTa using ELECTRA-Style Pre-Training with Gradient-Disentangled Embedding Sharing](https://mlsanity.com/paper/2111.09543/) (2021)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [MM-Vet: Evaluating Large Multimodal Models for Integrated Capabilities](https://mlsanity.com/paper/2308.02490/) (2023)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [SEED-Bench: Benchmarking Multimodal LLMs with Generative Comprehension](https://mlsanity.com/paper/2307.16125/) (2023)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [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)

## Built on by (most cited first, 30 of 47)

- [A Survey on LoRA of Large Language Models](https://mlsanity.com/paper/2407.11046/) (2024)
- [K-LoRA: Unlocking Training-Free Fusion of Any Subject and Style LoRAs](https://mlsanity.com/paper/2502.18461/) (2025)
- [Parameter-Efficient Fine-Tuning for Foundation Models](https://mlsanity.com/paper/2501.13787/) (2025)
- [RobustMerge: Parameter-Efficient Model Merging for MLLMs with Direction Robustness](https://mlsanity.com/paper/2502.17159/) (2025)
- [AuroRA: Breaking Low-Rank Bottleneck of LoRA with Nonlinear Mapping](https://mlsanity.com/paper/2505.18738/) (2025)
- [Keeping Yourself is Important in Downstream Tuning Multimodal Large Language Model](https://mlsanity.com/paper/2503.04543/) (2025)
- [StelLA: Subspace Learning in Low-rank Adaptation using Stiefel Manifold](https://mlsanity.com/paper/2510.01938/) (2025)
- [Pareto Low-Rank Adapters: Efficient Multi-Task Learning with Preferences](https://mlsanity.com/paper/2407.08056/) (2024)
- [Flexora: Flexible Low Rank Adaptation for Large Language Models](https://mlsanity.com/paper/2408.10774/) (2024)
- [Federated Continual Instruction Tuning](https://mlsanity.com/paper/2503.12897/) (2025)
- [Low-Rank Interconnected Adaptation across Layers](https://mlsanity.com/paper/2407.09946/) (2024)
- [TeamLoRA: Boosting Low-Rank Adaptation with Expert Collaboration and Competition](https://mlsanity.com/paper/2408.09856/) (2024)
- [Shadow-FT: Tuning Instruct Model via Training on Paired Base Model](https://mlsanity.com/paper/2505.12716/) (2025)
- [A Stronger Mixture of Low-Rank Experts for Fine-Tuning Foundation Models](https://mlsanity.com/paper/2502.15828/) (2025)
- [RoCoFT: Efficient Finetuning of Large Language Models with Row-Column Updates](https://mlsanity.com/paper/2410.10075/) (2024)
- [GRAPHMOE: Amplifying Cognitive Depth of Mixture-of-Experts Network via Introducing Self-Rethinking Mechanism](https://mlsanity.com/paper/2501.07890/) (2025)
- [Collaborative Multi-LoRA Experts with Achievement-based Multi-Tasks Loss for Unified Multimodal Information Extraction](https://mlsanity.com/paper/2505.06303/) (2025)
- [Orthogonal Finetuning Made Scalable](https://mlsanity.com/paper/2506.19847/) (2025)
- [PaCA: Partial Connection Adaptation for Efficient Fine-Tuning](https://mlsanity.com/paper/2503.01905/) (2025)
- [Weight Spectra Induced Efficient Model Adaptation](https://mlsanity.com/paper/2505.23099/) (2025)
- [Little by Little: Continual Learning via Incremental Mixture of Rank-1 Associative Memory Experts](https://mlsanity.com/paper/2506.21035/) (2025)
- [FlexLoRA: Entropy-Guided Flexible Low-Rank Adaptation](https://mlsanity.com/paper/2601.22905/) (2026)
- [LLM-NEO: Parameter Efficient Knowledge Distillation for Large Language Models](https://mlsanity.com/paper/2411.06839/) (2024)
- [DenseLoRA: Dense Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2505.23808/) (2025)
- [S'MoRE: Structural Mixture of Residual Experts for Parameter-Efficient LLM Fine-tuning](https://mlsanity.com/paper/2504.06426/) (2025)
- [One Rank at a Time: Cascading Error Dynamics in Sequential Learning](https://mlsanity.com/paper/2505.22602/) (2025)
- [AgeBooth: Controllable Facial Aging and Rejuvenation via Diffusion Models](https://mlsanity.com/paper/2510.05715/) (2025)
- [UniARM: Towards a Unified Autoregressive Reward Model for Multi-Objective Test-Time Alignment](https://mlsanity.com/paper/2602.09538/) (2026)
- [Predicting Through Generation: Why Generation Is Better for Prediction](https://mlsanity.com/paper/2502.17817/) (2025)
- [HaLoRA: Hardware-aware Low-Rank Adaptation for Large Language Models Based on Hybrid Compute-in-Memory Architecture](https://mlsanity.com/paper/2502.19747/) (2025)

## Abstract (arXiv)

In this paper, we introduce a subspace-inspired Low-Rank Adaptation (LoRA) method, which is computationally efficient, easy to implement, and readily applicable to large language, multimodal, and diffusion models. Initially, we equivalently decompose the weights of LoRA into two subspaces, and find that simply mixing them can enhance performance. To study such a phenomenon, we revisit it through a fine-grained subspace lens, showing that such modification is equivalent to employing a fixed mixer to fuse the subspaces. To be more flexible, we jointly learn the mixer with the original LoRA weights, and term the method Mixture-of-Subspaces LoRA (MoSLoRA). MoSLoRA consistently outperforms LoRA on tasks in different modalities, including commonsense reasoning, visual instruction tuning, and subject-driven text-to-image generation, demonstrating its effectiveness and robustness. Codes are available at https://github.com/wutaiqiang/MoSLoRA.