# Routing Divergence Is Not Evidence of Behavioral Influence in Same-Weight MoE Self-Distillation

arXiv: https://arxiv.org/abs/2608.15787 · HTML: https://mlsanity.com/paper/2608.15787/

## 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 37 of its 40 references that are in the map.
- First posted on arXiv 16 Aug 2026.

## Placed in

- Mixture-of-experts / [Expert routing strategies](https://mlsanity.com/moe/expert-routing-strategies/)
- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 30 of 37)

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- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [PubMedQA: A Dataset for Biomedical Research Question Answering](https://mlsanity.com/paper/1909.06146/) (2019)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Models](https://mlsanity.com/paper/2508.06471/) (2025)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [Sparse Upcycling: Training Mixture-of-Experts from Dense Checkpoints](https://mlsanity.com/paper/2212.05055/) (2022)
- [Arcee's MergeKit: A Toolkit for Merging Large Language Models](https://mlsanity.com/paper/2403.13257/) (2024)
- [Branch-Train-Merge: Embarrassingly Parallel Training of Expert Language Models](https://mlsanity.com/paper/2208.03306/) (2022)
- [DEMix Layers: Disentangling Domains for Modular Language Modeling](https://mlsanity.com/paper/2108.05036/) (2021)
- [Branch-Train-MiX: Mixing Expert LLMs into a Mixture-of-Experts LLM](https://mlsanity.com/paper/2403.07816/) (2024)
- [StableMoE: Stable Routing Strategy for Mixture of Experts](https://mlsanity.com/paper/2204.08396/) (2022)
- [Self-Distillation Bridges Distribution Gap in Language Model Fine-Tuning](https://mlsanity.com/paper/2402.13669/) (2024)
- [Stabilizing MoE Reinforcement Learning by Aligning Training and Inference Routers](https://mlsanity.com/paper/2510.11370/) (2025)
- [Upcycling Large Language Models into Mixture of Experts](https://mlsanity.com/paper/2410.07524/) (2024)
- [Mixture of Experts Made Intrinsically Interpretable](https://mlsanity.com/paper/2503.07639/) (2025)
- [Load Balancing Mixture of Experts with Similarity Preserving Routers](https://mlsanity.com/paper/2506.14038/) (2025)
- [BAM! Just Like That: Simple and Efficient Parameter Upcycling for Mixture of Experts](https://mlsanity.com/paper/2408.08274/) (2024)
- [When Are Experts Misrouted? Counterfactual Routing Analysis in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2605.07260/) (2026)

## Abstract (arXiv)

Two Mixture-of-Experts (MoE) forward passes can share every weight yet route the same token through different experts. This creates a possible blind spot in same-weight self-distillation, where a demonstration-conditioned teacher supervises a query-only student. We study this mismatch in its single-step form, with frozen weights rather than as a proxy for a full training trajectory. An exact blockwise decomposition separates a routing term, which changes gates at fixed content, from a dense-like content term. Across seven open-weight checkpoints and two domains, the routing term spans only 1.6× as a fraction of block output, while its residual-stream exposure spans 3.2×. Exposure is ordered by the routed block's share of the residual. Scaling the always-on backbone in two confirmatory models moves exposure monotonically; common-mode controls support a mass-and-coherence mechanism rather than denominator dilution alone. Preregistered PubMedQA patches on three models show that the full routing term moves outputs by less than half the natural context effect and is largely reproduced by matched-norm noise, whereas the content term is strongly direction-specific. Scale and merged-expert probes show that the narrow block-level range is not universal, although exposure remains small at the tested boundaries. Router movement alone is therefore not evidence of behavioral influence: measure exposure first, and use a behavioral intervention when the decision matters.