# Holistic Scaling Laws for Optimal Mixture-of-Experts Architecture Optimization

arXiv: https://arxiv.org/abs/2603.21862 · HTML: https://mlsanity.com/paper/2603.21862/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Expert routing strategies, one of 12 directions in Mixture-of-experts.
- Builds on 34 of its 38 references that are in the map.
- First posted on arXiv 23 Mar 2026.

## Placed in

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

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [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)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [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)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [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)
- [Unified Scaling Laws for Routed Language Models](https://mlsanity.com/paper/2202.01169/) (2022)
- [Scaling Laws for Fine-Grained Mixture of Experts](https://mlsanity.com/paper/2402.07871/) (2024)
- [Beyond Chinchilla-Optimal: Accounting for Inference in Language Model Scaling Laws](https://mlsanity.com/paper/2401.00448/) (2023)
- [Observational Scaling Laws and the Predictability of Language Model Performance](https://mlsanity.com/paper/2405.10938/) (2024)
- [Language models scale reliably with over-training and on downstream tasks](https://mlsanity.com/paper/2403.08540/) (2024)
- [Parameters vs FLOPs: Scaling Laws for Optimal Sparsity for Mixture-of-Experts Language Models](https://mlsanity.com/paper/2501.12370/) (2025)
- [Scaling Laws for Predicting Downstream Performance in LLMs](https://mlsanity.com/paper/2410.08527/) (2024)
- [Towards Greater Leverage: Scaling Laws for Efficient Mixture-of-Experts Language Models](https://mlsanity.com/paper/2507.17702/) (2025)
- [Predictable Scale: Part I, Step Law -- Optimal Hyperparameter Scaling Law in Large Language Model Pretraining](https://mlsanity.com/paper/2503.04715/) (2025)
- [Joint MoE Scaling Laws: Mixture of Experts Can Be Memory Efficient](https://mlsanity.com/paper/2502.05172/) (2025)
- [Scaling Laws Across Model Architectures: A Comparative Analysis of Dense and MoE Models in Large Language Models](https://mlsanity.com/paper/2410.05661/) (2024)

## Built on by (most cited first, 2 of 2)

- [Compute-Optimal Is Not Cluster-Optimal: Systems-Aware Scaling for Sparse Mixture-of-Experts](https://mlsanity.com/paper/2608.10605/) (2026)
- [Scaling Laws for Multimodal Data Mixtures](https://mlsanity.com/paper/2610.14423/) (2026)

## Abstract (arXiv)

Scaling laws govern macroscopic resource allocation for LLMs, yet precise architectural configurations for Mixture-of-Experts (MoE) models remain guided by heuristics. Existing MoE scaling studies either incorporate MoE-specific variables into scaling formulas, causing fitted coefficients to grow rapidly without proportional experimental support, or fix all non-MoE factors, implicitly assuming global architecture does not influence local MoE scaling. We propose a reusable framework for holistic MoE architectural optimization. We first show that MoE architectures decouple FLOPs per token (M), active parameters (Na), and total parameters (N), which serve as distinct proxies for computation, weight access, and parameter storage. We therefore establish a joint constraint triad of M, active parameters (Na), and total parameters (N) for rigorous MoE characterization. To tame the resulting O(n16) search space, we employ mathematical decoupling: structural constraints and a rank-preserving property of the hidden dimension factorize the optimization into an O(n3) + O(n2) two-phase search. Through extensive validation across 670+ MoE models spanning 1018 to 3 × 1020 FLOPs, we derive globally applicable scaling laws mapping any compute budget to its optimal architecture. A key finding is that the near-optimal configuration band widens with scale, providing a quantitative basis for trade-offs between scaling law recommendations and engineering constraints. Our work delivers actionable blueprints for optimal MoE design under arbitrary compute budgets.