# Two Is Better Than One: Rotations Scale LoRAs

arXiv: https://arxiv.org/abs/2505.23184 · HTML: https://mlsanity.com/paper/2505.23184/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mixture of LoRA experts, one of 12 directions in Mixture-of-experts.
- Builds on 29 of its 34 references that are in the map.
- First posted on arXiv 29 May 2025.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [DeepSpeed Inference: Enabling Efficient Inference of Transformer Models at Unprecedented Scale](https://mlsanity.com/paper/2207.00032/) (2022)
- [LoraHub: Efficient Cross-Task Generalization via Dynamic LoRA Composition](https://mlsanity.com/paper/2307.13269/) (2023)
- [Tutel: Adaptive Mixture-of-Experts at Scale](https://mlsanity.com/paper/2206.03382/) (2022)
- [Mixture of LoRA Experts](https://mlsanity.com/paper/2404.13628/) (2024)
- [Scaling Laws for Fine-Grained Mixture of Experts](https://mlsanity.com/paper/2402.07871/) (2024)
- [Composing Parameter-Efficient Modules with Arithmetic Operations](https://mlsanity.com/paper/2306.14870/) (2023)
- [HydraLoRA: An Asymmetric LoRA Architecture for Efficient Fine-Tuning](https://mlsanity.com/paper/2404.19245/) (2024)
- [FastMoE: A Fast Mixture-of-Expert Training System](https://mlsanity.com/paper/2103.13262/) (2021)
- [Pre-gated MoE: An Algorithm-System Co-Design for Fast and Scalable Mixture-of-Expert Inference](https://mlsanity.com/paper/2308.12066/) (2023)
- [Multi-LoRA Composition for Image Generation](https://mlsanity.com/paper/2402.16843/) (2024)
- [Towards Modular LLMs by Building and Reusing a Library of LoRAs](https://mlsanity.com/paper/2405.11157/) (2024)
- [Flex-MoE: Modeling Arbitrary Modality Combination via the Flexible Mixture-of-Experts](https://mlsanity.com/paper/2410.08245/) (2024)
- [FuseMoE: Mixture-of-Experts Transformers for Fleximodal Fusion](https://mlsanity.com/paper/2402.03226/) (2024)
- [Uni-Perceiver-MoE: Learning Sparse Generalist Models with Conditional MoEs](https://mlsanity.com/paper/2206.04674/) (2022)
- [MTLoRA: A Low-Rank Adaptation Approach for Efficient Multi-Task Learning](https://mlsanity.com/paper/2403.20320/) (2024)
- [Evaluating the Efficacy of Open-Source LLMs in Enterprise-Specific RAG Systems: A Comparative Study of Performance and Scalability](https://mlsanity.com/paper/2406.11424/) (2024)
- [OMoE: Diversifying Mixture of Low-Rank Adaptation by Orthogonal Finetuning](https://mlsanity.com/paper/2501.10062/) (2025)
- [Nexus: Specialization meets Adaptability for Efficiently Training Mixture of Experts](https://mlsanity.com/paper/2408.15901/) (2024)
- [MoDE: Effective Multi-task Parameter Efficient Fine-Tuning with a Mixture of Dyadic Experts](https://mlsanity.com/paper/2408.01505/) (2024)
- [Matrix-Transformation Based Low-Rank Adaptation (MTLoRA): A Brain-Inspired Method for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2403.07440/) (2024)

## Abstract (arXiv)

Scaling Low-Rank Adaptation (LoRA)-based Mixture-of-Experts (MoE) facilitates large language models (LLMs) to efficiently adapt to diverse tasks. However, traditional gating mechanisms that route inputs to the best experts may fundamentally hinder LLMs' scalability, leading to poor generalization and underfitting issues. We identify that the root cause lies in the restricted expressiveness of existing weighted-sum mechanisms, both within and outside the convex cone of LoRA representations. This motivates us to propose RadarGate, a novel geometrically inspired gating method that introduces rotational operations of LoRAs representations to boost the expressiveness and facilitate richer feature interactions among multiple LoRAs for scalable LLMs. Specifically, we first fuse each LoRA representation to other LoRAs using a learnable component and then feed the output to a rotation matrix. This matrix involves learnable parameters that define the relative angular relationship between LoRA representations. Such a simple yet effective mechanism provides an extra degree of freedom, facilitating the learning of cross-LoRA synergies and properly tracking the challenging poor generalization and underfitting issues as the number of LoRA grows. Extensive experiments on 6 public benchmarks across 21 tasks show the effectiveness of our RadarGate for scaling LoRAs. We also provide valuable insights, revealing that the rotations to each pair of representations are contrastive, encouraging closer alignment of semantically similar representations during geometrical transformation while pushing distance ones further apart. We will release our code to the community.