# Expert Divergence Learning for MoE-based Language Models

arXiv: https://arxiv.org/abs/2603.00054 · HTML: https://mlsanity.com/paper/2603.00054/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in MoE large language models, one of 12 directions in Mixture-of-experts.
- Builds on 29 of its 36 references that are in the map.
- First posted on arXiv 10 Feb 2026.

## Placed in

- Mixture-of-experts / [MoE large language models](https://mlsanity.com/moe/moe-large-language-models/)

## Builds on (most cited first, 29 of 29)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [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)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [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)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [RACE: Large-scale ReAding Comprehension Dataset From Examinations](https://mlsanity.com/paper/1704.04683/) (2017)
- [Towards General Text Embeddings with Multi-stage Contrastive Learning](https://mlsanity.com/paper/2308.03281/) (2023)
- [C-Eval: A Multi-Level Multi-Discipline Chinese Evaluation Suite for Foundation Models](https://mlsanity.com/paper/2305.08322/) (2023)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [CMMLU: Measuring massive multitask language understanding in Chinese](https://mlsanity.com/paper/2306.09212/) (2023)
- [SmolLM2: When Smol Goes Big -- Data-Centric Training of a Small Language Model](https://mlsanity.com/paper/2502.02737/) (2025)
- [Unified Scaling Laws for Routed Language Models](https://mlsanity.com/paper/2202.01169/) (2022)
- [A Survey on Mixture of Experts in Large Language Models](https://mlsanity.com/paper/2407.06204/) (2024)
- [Auxiliary-Loss-Free Load Balancing Strategy for Mixture-of-Experts](https://mlsanity.com/paper/2408.15664/) (2024)
- [Efficient Large Scale Language Modeling with Mixtures of Experts](https://mlsanity.com/paper/2112.10684/) (2021)
- [Nemotron-CC: Transforming Common Crawl into a Refined Long-Horizon Pretraining Dataset](https://mlsanity.com/paper/2412.02595/) (2024)
- [On the Representation Collapse of Sparse Mixture of Experts](https://mlsanity.com/paper/2204.09179/) (2022)
- [Beyond Distillation: Task-level Mixture-of-Experts for Efficient Inference](https://mlsanity.com/paper/2110.03742/) (2021)
- [Organize the Web: Constructing Domains Enhances Pre-Training Data Curation](https://mlsanity.com/paper/2502.10341/) (2025)
- [Task-Specific Expert Pruning for Sparse Mixture-of-Experts](https://mlsanity.com/paper/2206.00277/) (2022)
- [Demons in the Detail: On Implementing Load Balancing Loss for Training Specialized Mixture-of-Expert Models](https://mlsanity.com/paper/2501.11873/) (2025)
- [Lory: Fully Differentiable Mixture-of-Experts for Autoregressive Language Model Pre-training](https://mlsanity.com/paper/2405.03133/) (2024)
- [OpenCSG Chinese Corpus: A Series of High-quality Chinese Datasets for LLM Training](https://mlsanity.com/paper/2501.08197/) (2025)
- [Improving Expert Specialization in Mixture of Experts](https://mlsanity.com/paper/2302.14703/) (2023)

## Built on by (most cited first, 4 of 4)

- [The Myth of Expert Specialization in MoEs: Why Routing Reflects Geometry, Not Necessarily Domain Expertise](https://mlsanity.com/paper/2604.09780/) (2026)
- [Task-Aware Federated Fine-Tuning for MoE-based Large Language Models](https://mlsanity.com/paper/2609.13395/) (2026)
- [Cross-Entropy Guided Routing in Mixture-of-Experts Large Language Models](https://mlsanity.com/paper/2609.37751/) (2026)
- [Overcoming Data Imbalances with Expert Selection Biases](https://mlsanity.com/paper/2610.13370/) (2026)

## Abstract (arXiv)

The Mixture-of-Experts (MoE) architecture is a powerful technique for scaling language models, yet it often suffers from expert homogenization, where experts learn redundant functionalities, thereby limiting MoE's full potential. To address this, we introduce Expert Divergence Learning, a novel pre-training strategy that explicitly encourages functional specialization among experts. Our method incorporates a label-driven auxiliary loss that leverages domain labels inherent in pre-training corpora to maximize the Jensen-Shannon Divergence between the expert routing distributions of different data domains. This optimization objective guides the model to develop diverged routing policies for varied domains and closer routing policies for the same domain, which leads to emergent and organized expert specialization. We validate our approach by pre-training MoE models of up to 15 billion parameters from scratch. Experimental results demonstrate that models trained with Expert Divergence Learning not only achieve a lower language modeling loss but also exhibit significant performance improvements across a diverse range of downstream benchmarks. Further analysis confirms that our method effectively mitigates expert homogenization and brings greater functional specialization, all with negligible computational overhead during training.