# Cross-Entropy Guided Routing in Mixture-of-Experts Large Language Models

arXiv: https://arxiv.org/abs/2609.37751 · HTML: https://mlsanity.com/paper/2609.37751/

## 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 23 of its 32 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [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)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [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)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [MedMCQA : A Large-scale Multi-Subject Multi-Choice Dataset for Medical domain Question Answering](https://mlsanity.com/paper/2203.14371/) (2022)
- [Hybrid LLM: Cost-Efficient and Quality-Aware Query Routing](https://mlsanity.com/paper/2404.14618/) (2024)
- [Learning Loss for Active Learning](https://mlsanity.com/paper/1905.03677/) (2019)
- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [ReMoE: Fully Differentiable Mixture-of-Experts with ReLU Routing](https://mlsanity.com/paper/2412.14711/) (2024)
- [Ada-K Routing: Boosting the Efficiency of MoE-based LLMs](https://mlsanity.com/paper/2410.10456/) (2024)
- [Coupling Experts and Routers in Mixture-of-Experts via an Auxiliary Loss](https://mlsanity.com/paper/2512.23447/) (2025)
- [When Are Experts Misrouted? Counterfactual Routing Analysis in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2605.07260/) (2026)
- [From Dense to Dynamic: Token-Difficulty Driven MoEfication of Pre-Trained LLMs](https://mlsanity.com/paper/2502.12325/) (2025)
- [Expert Divergence Learning for MoE-based Language Models](https://mlsanity.com/paper/2603.00054/) (2026)
- [Variational Routing: A Scalable Bayesian Framework for Calibrated Mixture-of-Experts Transformers](https://mlsanity.com/paper/2603.09453/) (2026)
- [MoGU: Mixture-of-Gaussians with Uncertainty-based Gating for Time Series Forecasting](https://mlsanity.com/paper/2510.07459/) (2025)
- [Grassmannian Mixture-of-Experts: Concentration-Controlled Routing on Subspace Manifolds](https://mlsanity.com/paper/2602.17798/) (2026)
- [Uncertainty Is Not Enough: Value-of-Information Routing for Mixtures of LoRA Experts](https://mlsanity.com/paper/2608.02528/) (2026)

## Abstract (arXiv)

Sparse mixture-of-experts (MoE) large language models scale model capacity by routing each token to a small subset of experts. Their routers are regularized with load balancing terms and learn affinity scores through the language-model objective. However, these objectives do not provide direct alignment between routing affinities and token-level error. We introduce token-error supervision for sparse routing in two forms. The first form predicts an error score per expert. The affinity-weighted aggregate of these scores is aligned to the next-token cross-entropy loss, while the individual scores attenuate affinity before top-K selection. The second directly aligns the router's affinities to the model's objective without requiring an additional head or inference-time modification. Both formulations use the Itakura--Saito divergence or an exponential negative log-likelihood for aligning affinities and token errors. Across two sparse MoE backbones and four multiple-choice question-answering benchmarks, we evaluate both supervision mechanisms. On Granite, our method improves accuracy by approximately 2.3 percentage points on average over a parameter-matched routing baseline. With stronger supervision, the gain on ARC-Challenge reaches 2.94 points. Both mechanisms preserve the native sparse execution budget and aggregation policy. Our code is available in the supplementary materials.