# L2R: Low-Rank and Lipschitz-Controlled Routing for Mixture-of-Experts

arXiv: https://arxiv.org/abs/2601.21349 · HTML: https://mlsanity.com/paper/2601.21349/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Vision mixture-of-experts, one of 12 directions in Mixture-of-experts.
- Builds on 30 of its 37 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Placed in

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

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

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [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)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [Scaling Vision with Sparse Mixture of Experts](https://mlsanity.com/paper/2106.05974/) (2021)
- [ST-MoE: Designing Stable and Transferable Sparse Expert Models](https://mlsanity.com/paper/2202.08906/) (2022)
- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [A Survey on Mixture of Experts in Large Language Models](https://mlsanity.com/paper/2407.06204/) (2024)
- [MegaBlocks: Efficient Sparse Training with Mixture-of-Experts](https://mlsanity.com/paper/2211.15841/) (2022)
- [Tutel: Adaptive Mixture-of-Experts at Scale](https://mlsanity.com/paper/2206.03382/) (2022)
- [On the Representation Collapse of Sparse Mixture of Experts](https://mlsanity.com/paper/2204.09179/) (2022)
- [OLMES: A Standard for Language Model Evaluations](https://mlsanity.com/paper/2406.08446/) (2024)
- [Multi-Head Mixture-of-Experts](https://mlsanity.com/paper/2404.15045/) (2024)
- [Yuan 2.0-M32: Mixture of Experts with Attention Router](https://mlsanity.com/paper/2405.17976/) (2024)
- [Statistical Advantages of Perturbing Cosine Router in Mixture of Experts](https://mlsanity.com/paper/2405.14131/) (2024)
- [Adaptive Shared Experts with LoRA-Based Mixture of Experts for Multi-Task Learning](https://mlsanity.com/paper/2510.00570/) (2025)
- [Router Upcycling: Leveraging Mixture-of-Routers in Mixture-of-Experts Upcycling](https://mlsanity.com/paper/2509.00679/) (2025)

## Built on by (most cited first, 1 of 1)

- [MoRE: Scaling mixture of experts with hardware-aware low-rank routing](https://mlsanity.com/paper/2609.36301/) (2026)

## Abstract (arXiv)

Mixture-of-Experts (MoE) models scale neural networks by conditionally activating a small subset of experts, where the router plays a central role in determining expert specialization and overall model performance. However, many modern MoE systems still adopt linear routers in raw high-dimensional representation spaces, where representation mismatch, angular concentration, and scale-sensitive scoring can jointly undermine routing discriminability and stable expert specialization. In this work, we propose Low-rank & Lipschitz-controlled Routing (L2R), a unified routing framework that reshapes both the routing space and scoring geometry. L2R performs expert assignment in a shared low-rank latent routing space and introduces Saturated Inner-Product Scoring (SIPS) to explicitly control the Lipschitz behavior of routing functions, yielding smoother and more stable routing geometry. In addition, L2R incorporates a parameter-efficient multi-anchor routing mechanism to enhance expert expressiveness. Experiments on an OLMoE-based language MoE model and a ViT-based ImageNet setting show improved overall performance in both domains; OLMoE diagnostics further show improved routing geometry and expert discrimination.