# Function Over Form: Distributional Orthogonalization in Mixture-of-Experts with Replica Expert Mechanism

arXiv: https://arxiv.org/abs/2609.32398 · HTML: https://mlsanity.com/paper/2609.32398/

## 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 25 of its 32 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Placed in

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

## Builds on (most cited first, 25 of 25)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models](https://mlsanity.com/paper/2304.06364/) (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)
- [DeepSpeed-MoE: Advancing Mixture-of-Experts Inference and Training to Power Next-Generation AI Scale](https://mlsanity.com/paper/2201.05596/) (2022)
- [ST-MoE: Designing Stable and Transferable Sparse Expert Models](https://mlsanity.com/paper/2202.08906/) (2022)
- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [Auxiliary-Loss-Free Load Balancing Strategy for Mixture-of-Experts](https://mlsanity.com/paper/2408.15664/) (2024)
- [Demons in the Detail: On Implementing Load Balancing Loss for Training Specialized Mixture-of-Expert Models](https://mlsanity.com/paper/2501.11873/) (2025)
- [Advancing Expert Specialization for Better MoE](https://mlsanity.com/paper/2505.22323/) (2025)
- [Diversifying the Mixture-of-Experts Representation for Language Models with Orthogonal Optimizer](https://mlsanity.com/paper/2310.09762/) (2023)
- [Coupling Experts and Routers in Mixture-of-Experts via an Auxiliary Loss](https://mlsanity.com/paper/2512.23447/) (2025)
- [Prediction Is All MoE Needs: Expert Load Distribution Goes from Fluctuating to Stabilizing](https://mlsanity.com/paper/2404.16914/) (2024)
- [Pro-Prophet: A Systematic Load Balancing Method for Efficient Parallel Training of Large-scale MoE Models](https://mlsanity.com/paper/2411.10003/) (2024)

## Abstract (arXiv)

The scaling of LLMs increasingly relies on MoE architectures to decouple active computation from total parameter count. However, the efficacy of MoE is often constrained by expert collapse and representation redundancy, both leading to underutilization of model capacity. To address these challenges, this paper proposes Distributional Orthogonalization Loss (DO-loss), an auxiliary regularization that shifts the focus from static weight diversity to dynamic routing behavior. By representing each expert's token assignment history as a high-dimensional binary load signature, DO-loss penalizes signature overlap to prevent expert collapse while encouraging functional specialization. To align this algorithmic design with system efficiency, we further introduce the Replica Expert Mechanism (REM), which improves load balancing through a two-tiered strategy: adjusting replica expert placement at the global-batch level and performing real-time token dispatching at the micro-batch level. Empirical evaluations demonstrate that our method outperforms the evaluated routing algorithms on downstream tasks for both 4.8BA0.5B and 30BA3B MoE models, while maintaining comparable training efficiency.