# Synergistic Intra- and Cross-Layer Regularization Losses for MoE Expert Specialization

arXiv: https://arxiv.org/abs/2602.14159 · HTML: https://mlsanity.com/paper/2602.14159/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Expert routing strategies, one of 12 directions in Mixture-of-experts.
- Builds on 43 of its 46 references that are in the map.
- First posted on arXiv 15 Feb 2026.

## Placed in

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

## Builds on (most cited first, 30 of 43)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [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)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [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)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space](https://mlsanity.com/paper/2203.14680/) (2022)
- [ST-MoE: Designing Stable and Transferable Sparse Expert Models](https://mlsanity.com/paper/2202.08906/) (2022)
- [BASE Layers: Simplifying Training of Large, Sparse Models](https://mlsanity.com/paper/2103.16716/) (2021)
- [Unified Scaling Laws for Routed Language Models](https://mlsanity.com/paper/2202.01169/) (2022)
- [Hash Layers For Large Sparse Models](https://mlsanity.com/paper/2106.04426/) (2021)
- [MiniCache: KV Cache Compression in Depth Dimension for Large Language Models](https://mlsanity.com/paper/2405.14366/) (2024)
- [Taming Sparsely Activated Transformer with Stochastic Experts](https://mlsanity.com/paper/2110.04260/) (2021)

## Built on by (most cited first, 5 of 5)

- [Grouter: Decoupling Routing from Representation for Accelerated MoE Training](https://mlsanity.com/paper/2603.06626/) (2026)
- [Tying the Loop -- Tied Expert Layers in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2606.16825/) (2026)
- [LiMoDE: Rethinking Lifelong Robot Manipulation from a Mixture-of-Dynamic-Experts Perspective](https://mlsanity.com/paper/2606.26183/) (2026)
- [GNMR: Runtime Stability Control for Low-Precision Large Language Model Training](https://mlsanity.com/paper/2606.00539/) (2026)
- [HERO-MoE: Historical Expert Routing with Scale-Preserving Fusion](https://mlsanity.com/paper/2609.32581/) (2026)

## Abstract (arXiv)

Sparse Mixture-of-Experts (MoE) models scale Transformers efficiently but suffer from expert overlap -- redundant representations across experts and routing ambiguity, resulting in severely underutilized model capacity. While architectural solutions like DeepSeekMoE promote specialization, they require substantial structural modifications and rely solely on intra-layer signals. In this paper, we propose two plug-and-play regularization losses that enhance MoE specialization and routing efficiency without modifying router or model architectures. First, an intra-layer specialization loss penalizes cosine similarity between experts' SwiGLU activations on identical tokens, encouraging experts to specialize in complementary knowledge. Second, a cross-layer coupling loss maximizes joint Top-k routing probabilities across adjacent layers, establishing coherent expert pathways through network depth while reinforcing intra-layer expert specialization. Both losses are orthogonal to the standard load-balancing loss and compatible with both the shared-expert architecture in DeepSeekMoE and vanilla top-k MoE architectures. We implement both losses as a drop-in Megatron-LM module. Extensive experiments across pre-training, fine-tuning, and zero-shot benchmarks demonstrate consistent task gains, higher expert specialization, and lower-entropy routing; together, these improvements translate into faster inference via more stable expert pathways.