# Geometric Asymmetry in MoE Specialization: Functional Decorrelation and Representational Overlap

arXiv: https://arxiv.org/abs/2605.16349 · HTML: https://mlsanity.com/paper/2605.16349/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Expert routing strategies, one of 12 directions in Mixture-of-experts.
- Builds on 17 of its 20 references that are in the map.
- First posted on arXiv 8 May 2026.

## Placed in

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

## Builds on (most cited first, 17 of 17)

- [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)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [ST-MoE: Designing Stable and Transferable Sparse Expert Models](https://mlsanity.com/paper/2202.08906/) (2022)
- [Sensitivity and Generalization in Neural Networks: an Empirical Study](https://mlsanity.com/paper/1802.08760/) (2018)
- [Scaling Laws for Fine-Grained Mixture of Experts](https://mlsanity.com/paper/2402.07871/) (2024)
- [All Bark and No Bite: Rogue Dimensions in Transformer Language Models Obscure Representational Quality](https://mlsanity.com/paper/2109.04404/) (2021)
- [The Emergence of Spectral Universality in Deep Networks](https://mlsanity.com/paper/1802.09979/) (2018)
- [MoE-I2: Compressing Mixture of Experts Models through Inter-Expert Pruning and Intra-Expert Low-Rank Decomposition](https://mlsanity.com/paper/2411.01016/) (2024)
- [Mixture Compressor for Mixture-of-Experts LLMs Gains More](https://mlsanity.com/paper/2410.06270/) (2024)
- [Sub-MoE: Efficient Mixture-of-Expert LLMs Compression via Subspace Expert Merging](https://mlsanity.com/paper/2506.23266/) (2025)
- [Improving Expert Specialization in Mixture of Experts](https://mlsanity.com/paper/2302.14703/) (2023)
- [MergeMoE: Efficient Compression of MoE Models via Expert Output Merging](https://mlsanity.com/paper/2510.14436/) (2025)
- [On the Stability of the Jacobian Matrix in Deep Neural Networks](https://mlsanity.com/paper/2506.08764/) (2025)
- [Mixture-of-Clustered-Experts: Advancing Expert Specialization and Generalization in Instruction Tuning](https://mlsanity.com/paper/2509.10513/) (2025)

## Abstract (arXiv)

Mixture-of-Experts (MoE) architectures achieve scalable capacity through sparse routing, yet the geometric structure of expert specialization remains poorly understood. We introduce a unified Jacobian-PCA-Grassmann framework for analyzing MoE layers in both function space and representation space. Across pretrained MoE Transformers (Mistral, Qwen), we find a consistent structural asymmetry: experts exhibit strong functional decorrelation (consistently low, near-zero cross-expert Jacobian alignment) while their routed representations occupy distinct but partially overlapping subspaces. This indicates that functional decorrelation and representation overlap coexist rather than coincide in MoE specialization. Controlled routing experiments further indicate that routing sparsity appears to be a key factor shaping this geometry: top-k routing induces sharper functional separation and larger subspace divergence, whereas fully soft routing yields more entangled expert structure. Together, these results suggest a geometric interpretation in which MoE layers may be viewed as implementing locally decorrelated operators over overlapping submanifolds on a shared representation manifold, and provide a general diagnostic framework for studying conditional computation in modern Transformer architectures.