# When Are Experts Misrouted? Counterfactual Routing Analysis in Mixture-of-Experts Language Models

arXiv: https://arxiv.org/abs/2605.07260 · HTML: https://mlsanity.com/paper/2605.07260/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Expert routing strategies, one of 12 directions in Mixture-of-experts.
- Builds on 27 of its 31 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, 27 of 27)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [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)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [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)
- [From Sparse to Soft Mixtures of Experts](https://mlsanity.com/paper/2308.00951/) (2023)
- [Auxiliary-Loss-Free Load Balancing Strategy for Mixture-of-Experts](https://mlsanity.com/paper/2408.15664/) (2024)
- [OpenMoE: An Early Effort on Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2402.01739/) (2024)
- [Direct Preference Optimization with an Offset](https://mlsanity.com/paper/2402.10571/) (2024)
- [StableMoE: Stable Routing Strategy for Mixture of Experts](https://mlsanity.com/paper/2204.08396/) (2022)
- [Critical Tokens Matter: Token-Level Contrastive Estimation Enhances LLM's Reasoning Capability](https://mlsanity.com/paper/2411.19943/) (2024)
- [WPO: Enhancing RLHF with Weighted Preference Optimization](https://mlsanity.com/paper/2406.11827/) (2024)
- [ReMoE: Fully Differentiable Mixture-of-Experts with ReLU Routing](https://mlsanity.com/paper/2412.14711/) (2024)
- [Let the Expert Stick to His Last: Expert-Specialized Fine-Tuning for Sparse Architectural Large Language Models](https://mlsanity.com/paper/2407.01906/) (2024)
- [R2-T2: Re-Routing in Test-Time for Multimodal Mixture-of-Experts](https://mlsanity.com/paper/2502.20395/) (2025)
- [Defending MoE LLMs against Harmful Fine-Tuning via Safety Routing Alignment](https://mlsanity.com/paper/2509.22745/) (2025)
- [C3PO: Critical-Layer, Core-Expert, Collaborative Pathway Optimization for Test-Time Expert Re-Mixing](https://mlsanity.com/paper/2504.07964/) (2025)
- [MoE-GRPO: Optimizing Mixture-of-Experts via Reinforcement Learning in Vision-Language Models](https://mlsanity.com/paper/2603.24984/) (2026)
- [Certain Head, Uncertain Tail: Expert-Sample for Test-Time Scaling in Fine-Grained MoE](https://mlsanity.com/paper/2602.02443/) (2026)

## Built on by (most cited first, 9 of 9)

- [Evidence for Shared Routing Geometry and Dynamics in Sparse Mixture-of-Experts](https://mlsanity.com/paper/2609.02404/) (2026)
- [Beyond Geometric Complementarity: Coherent Overlap in Sparse Mixture-of-Experts Routing](https://mlsanity.com/paper/2607.28308/) (2026)
- [Learning to Orchestrate Vision Foundation Models for Multi-Task Dense Prediction](https://mlsanity.com/paper/2606.15765/) (2026)
- [Beyond Routing: Decoupling Expert Dispatch and Aggregation in Sparse Mixture-of-Experts](https://mlsanity.com/paper/2608.08853/) (2026)
- [Routing Divergence Is Not Evidence of Behavioral Influence in Same-Weight MoE Self-Distillation](https://mlsanity.com/paper/2608.15787/) (2026)
- [Towards a Statistical Understanding of Mixture-of-Experts](https://mlsanity.com/paper/2609.03501/) (2026)
- [From Concentration to Differentiation and Back: Routing Effective Rank in MoE Reasoning Cohorts](https://mlsanity.com/paper/2609.06403/) (2026)
- [Cross-Entropy Guided Routing in Mixture-of-Experts Large Language Models](https://mlsanity.com/paper/2609.37751/) (2026)
- [How Sparse Probability Maps Shape Mixture-of-Experts Routing](https://mlsanity.com/paper/2610.06677/) (2026)

## Abstract (arXiv)

Mixture-of-Experts (MoE) language models route each token to a small subset of experts, but whether the routes selected by a trained top-k router are good ones is rarely evaluated directly. Holding the model fixed, we compare each standard route against sampled equal-compute alternatives for the same token and score each by the next-token probability it assigns to the realized token in a verified reasoning trajectory. The result is sharply token-conditional: the standard router is well-aligned with route utility on confident tokens but uninformative on the fragile tokens that drive hard reasoning, where lower-loss equal-compute routes consistently exist inside the frozen model but are not selected. The same pattern holds across Qwen3-30B-A3B, GPT-OSS-20B, DeepSeek-V2-Lite, and OLMoE-1B-7B, and follows structurally from how standard top-k training evaluates routing decisions: the language modeling loss scores only the executed route, and load balancing depends only on aggregate routing statistics. A minimal router-only update to the final-layer router, leaving every expert and every other router frozen, is sufficient to shift pass@K on AIME 2024+2025 and HMMT 2025 for both Qwen3-30B-A3B and GPT-OSS-20B, suggesting that at least part of the failure reflects router-reachable misallocation rather than expert capacity alone.