# Eigenvectors of Experts are Training-free Non-collapsing Routers

arXiv: https://arxiv.org/abs/2605.30992 · HTML: https://mlsanity.com/paper/2605.30992/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Expert routing strategies, one of 12 directions in Mixture-of-experts.
- Builds on 36 of its 58 references that are in the map.
- First posted on arXiv 29 May 2026.

## Placed in

- Mixture-of-experts / [Expert routing strategies](https://mlsanity.com/moe/expert-routing-strategies/)

## Builds on (most cited first, 30 of 36)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [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)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Flickr30k Entities: Collecting Region-to-Phrase Correspondences for Richer Image-to-Sentence Models](https://mlsanity.com/paper/1505.04870/) (2015)
- [ShareGPT4V: Improving Large Multi-Modal Models with Better Captions](https://mlsanity.com/paper/2311.12793/) (2023)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [Scaling Vision with Sparse Mixture of Experts](https://mlsanity.com/paper/2106.05974/) (2021)
- [MTEB: Massive Text Embedding Benchmark](https://mlsanity.com/paper/2210.07316/) (2022)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2403.07378/) (2024)
- [On the Representation Collapse of Sparse Mixture of Experts](https://mlsanity.com/paper/2204.09179/) (2022)
- [Uni-MoE: Scaling Unified Multimodal LLMs with Mixture of Experts](https://mlsanity.com/paper/2405.11273/) (2024)
- [StableMoE: Stable Routing Strategy for Mixture of Experts](https://mlsanity.com/paper/2204.08396/) (2022)
- [Scaling Vision-Language Models with Sparse Mixture of Experts](https://mlsanity.com/paper/2303.07226/) (2023)
- [Scaling Sentence Embeddings with Large Language Models](https://mlsanity.com/paper/2307.16645/) (2023)
- [SVD-LLM V2: Optimizing Singular Value Truncation for Large Language Model Compression](https://mlsanity.com/paper/2503.12340/) (2025)
- [Your Mixture-of-Experts LLM Is Secretly an Embedding Model For Free](https://mlsanity.com/paper/2410.10814/) (2024)
- [Accuracy is Not All You Need](https://mlsanity.com/paper/2407.09141/) (2024)
- [Dropping Experts, Recombining Neurons: Retraining-Free Pruning for Sparse Mixture-of-Experts LLMs](https://mlsanity.com/paper/2509.10377/) (2025)
- [CLIP-MoE: Towards Building Mixture of Experts for CLIP with Diversified Multiplet Upcycling](https://mlsanity.com/paper/2409.19291/) (2024)
- [Random matrix analysis of deep neural network weight matrices](https://mlsanity.com/paper/2203.14661/) (2022)

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

- [Beyond Independent Optimization: Compression, MoE Routing, and Quantization Interactions in Multimodal Edge Intelligence](https://mlsanity.com/paper/2607.20981/) (2026)

## Abstract (arXiv)

Sparse Mixture of Experts (SMoE) architectures improve the training efficiency of Large Language Models (LLMs) by routing input tokens to a selected subset of specialized experts. Despite their remarkable success, both training and inference in SMoE models suffer from the expert collapse issue (Chi et al., 2022), which degrades model performance. Prior studies primarily focus on improving the router; however, such methods rely on training from scratch or fine-tuning, which requires high computational and data-processing costs. Furthermore, we demonstrate that, despite these efforts, the issue persists when advancing well-pretrained SMoE models, as evidenced by both theoretical and empirical results. To fill that gap, we analyze the advanced SMoE models and observe that the eigenvectors of expert weight matrices encode rich semantic information, pointing to an effective alternative to conventional routing strategies. Building on this insight, we propose Singular Value Decomposition SMoE (SSMoE), a novel and training-free framework that leverages spectral properties of the expert weights to address the collapse issue and enhance model performance. Extensive experiments across diverse language and vision tasks, under both clean and corrupt data settings, demonstrate the strong generalization and robustness of SSMoE. Our findings highlight how a deeper understanding of model internals can guide the development of more effective SMoE architectures. Our implementation is publicly available at https://github.com/giangdip2410/SSMoE.