# Beyond Geometric Complementarity: Coherent Overlap in Sparse Mixture-of-Experts Routing

arXiv: https://arxiv.org/abs/2607.28308 · HTML: https://mlsanity.com/paper/2607.28308/

## 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 35 of its 45 references that are in the map.
- First posted on arXiv 30 Jul 2026.

## Placed in

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

## Builds on (most cited first, 30 of 35)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [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)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [Enhancing Chat Language Models by Scaling High-quality Instructional Conversations](https://mlsanity.com/paper/2305.14233/) (2023)
- [CodeSearchNet Challenge: Evaluating the State of Semantic Code Search](https://mlsanity.com/paper/1909.09436/) (2019)
- [A Discourse-Aware Attention Model for Abstractive Summarization of Long Documents](https://mlsanity.com/paper/1804.05685/) (2018)
- [Insights on representational similarity in neural networks with canonical correlation](https://mlsanity.com/paper/1806.05759/) (2018)
- [BASE Layers: Simplifying Training of Large, Sparse Models](https://mlsanity.com/paper/2103.16716/) (2021)
- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [Unified Scaling Laws for Routed Language Models](https://mlsanity.com/paper/2202.01169/) (2022)
- [Hash Layers For Large Sparse Models](https://mlsanity.com/paper/2106.04426/) (2021)
- [Scaling Laws for Fine-Grained Mixture of Experts](https://mlsanity.com/paper/2402.07871/) (2024)
- [On the Representation Collapse of Sparse Mixture of Experts](https://mlsanity.com/paper/2204.09179/) (2022)
- [Not All Experts are Equal: Efficient Expert Pruning and Skipping for Mixture-of-Experts Large Language Models](https://mlsanity.com/paper/2402.14800/) (2024)
- [A Closer Look into Mixture-of-Experts in Large Language Models](https://mlsanity.com/paper/2406.18219/) (2024)
- [AdaMoE: Token-Adaptive Routing with Null Experts for Mixture-of-Experts Language Models](https://mlsanity.com/paper/2406.13233/) (2024)
- [Diversifying the Expert Knowledge for Task-Agnostic Pruning in Sparse Mixture-of-Experts](https://mlsanity.com/paper/2407.09590/) (2024)
- [STUN: Structured-Then-Unstructured Pruning for Scalable MoE Pruning](https://mlsanity.com/paper/2409.06211/) (2024)
- [Diversifying the Mixture-of-Experts Representation for Language Models with Orthogonal Optimizer](https://mlsanity.com/paper/2310.09762/) (2023)
- [Sub-MoE: Efficient Mixture-of-Expert LLMs Compression via Subspace Expert Merging](https://mlsanity.com/paper/2506.23266/) (2025)
- [EAC-MoE: Expert-Selection Aware Compressor for Mixture-of-Experts Large Language Models](https://mlsanity.com/paper/2508.01625/) (2025)
- [Probing Semantic Routing in Large Mixture-of-Expert Models](https://mlsanity.com/paper/2502.10928/) (2025)
- [The Myth of Expert Specialization in MoEs: Why Routing Reflects Geometry, Not Necessarily Domain Expertise](https://mlsanity.com/paper/2604.09780/) (2026)
- [Mosaic Pruning: A Hierarchical Framework for Generalizable Pruning of Mixture-of-Experts Models](https://mlsanity.com/paper/2511.19822/) (2025)
- [When Are Experts Misrouted? Counterfactual Routing Analysis in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2605.07260/) (2026)

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

- [DIET: Deletion-response Expert Trimming for Video Diffusion Transformers](https://mlsanity.com/paper/2609.37829/) (2026)

## Abstract (arXiv)

Sparse mixture-of-experts (MoE) language models route each token to multiple experts, suggesting a geometric account of their benefit: co-selected experts should contribute distinct representation directions. Existing evidence often conflates route coherence, candidate quality, and candidate-by-context interaction. We distinguish these quantities using an Expert Subspace Separation Index (ESSI), matched-route residuals, and a prefix-controlled 2×2 factorial; frozen-route interventions and a controlled Top-k study assess functional value. Three paired contrasts organize the findings. First, across six MoE architectures, expert subspaces overlap substantially, yet actual routes explain token representations better than matched alternatives. Second, across the 39 factorial cells in OLMoE, Mixtral, and DeepSeek, the selected candidate explains more of the residual representation than the strongest unselected rival in every cell, yet the actual prefix narrows this advantage throughout: all interactions are negative, and every 95% confidence interval lies below zero. Third, this geometric narrowing does not imply functional redundancy: adding later experts improves next-token prediction in 24 of 39 frozen-route comparisons, while the other 15 estimates are inconclusive; a controlled training study also favors Top-2 over Top-1 in all three seeds. We call this joint pattern coherent overlap: routing selects token-relevant experts from a shared geometric neighborhood, while useful multi-expert computation persists without disjoint linear coverage. Separating these quantities clarifies why geometric similarity alone cannot determine redundancy or pruning value.