MoE Models Show Shared Routing Dynamics Across Layers

Kirill Labzin, Stepan Kulibaba, Artem Dzhalilov, Artem Gorokhov· September 3, 2026 View original

Key takeaways

  • Sparse Mixture-of-Experts (MoE) models exhibit shared routing geometry across layers.
  • A single linear model can predict much of the routing state evolution after alignment.
  • This suggests a reusable routing process across the depth of MoE architectures.
  • Understanding this can lead to more efficient and compact MoE designs.

Who benefits

AI DevelopmentLarge Language ModelsCloud ComputingData Centers

Summary

This research provides evidence that sparse Mixture-of-Experts (MoE) models exhibit shared geometric structure and dynamics in their routing decisions across different layers. By aligning layer-specific control subspaces, a single linear transition can predict much of the routing state evolution, suggesting a reusable process.

Sparse Mixture-of-Experts (MoE) models typically employ independent routers at each layer to select specialized experts for processing tokens. Previous observations hinted that routing decisions across layers might not be entirely independent, but the underlying structure remained unclear. This study reveals that the states relevant to routing across different layers share a common geometric structure, which is often obscured by the unique coordinate systems of each layer. The researchers isolated the control subspace for each router and aligned these spaces into a unified, canonical representation using generalized orthogonal Procrustes analysis. After this alignment, a single linear transition model could predict a significant portion (R^2=0.39-0.71) of the routing state evolution, retaining 79-90% of the predictive power of layer-specific dynamics. This indicates that a substantial part of how routing states evolve follows a reusable process across the model's depth. Further analysis differentiated this routing-specific information from generic cross-layer predictability of residual representations, confirming that the shared dynamics are indeed specific to expert selection.

Why it matters

Understanding the shared dynamics in MoE routing can lead to more efficient, compact, and potentially more performant MoE architectures, reducing redundancy and improving training.

How to implement this in your domain

  1. 1Investigate the potential for designing MoE models with shared or learned routing dynamics across layers to reduce parameter count.
  2. 2Explore methods for aligning and transferring routing knowledge between different layers or even different MoE models.
  3. 3Develop diagnostic tools to visualize and analyze the geometric structure of routing decisions within MoE layers.
  4. 4Consider how a more unified routing mechanism could simplify the training and fine-tuning of large MoE models.

Original post by Kirill Labzin, Stepan Kulibaba, Artem Dzhalilov, Artem Gorokhov

"arXiv:2609.02404v1 Announce Type: new Abstract: Sparse mixture-of-experts (MoE) models use an independently parameterized router at each sparse layer to select experts for every token. Prior work has shown that routing decisions across depth can often be predicted from earlier ro…"

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Originally posted by Kirill Labzin, Stepan Kulibaba, Artem Dzhalilov, Artem Gorokhov on X · view source

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