# Towards Greater Leverage: Scaling Laws for Efficient Mixture-of-Experts Language Models

arXiv: https://arxiv.org/abs/2507.17702 · HTML: https://mlsanity.com/paper/2507.17702/

## Key facts

- Cited by 45 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 53 of its 59 references that are in the map.
- First posted on arXiv 23 Jul 2025.

## Placed in

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

## Builds on (most cited first, 30 of 53)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [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)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Neural Machine Translation of Rare Words with Subword Units](https://mlsanity.com/paper/1508.07909/) (2015)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [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)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [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)
- [RACE: Large-scale ReAding Comprehension Dataset From Examinations](https://mlsanity.com/paper/1704.04683/) (2017)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [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)
- [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)

## Built on by (most cited first, 30 of 45)

- [Beyond Language Modeling: An Exploration of Multimodal Pretraining](https://mlsanity.com/paper/2603.03276/) (2026)
- [SonicMoE: Accelerating MoE with IO and Tile-aware Optimizations](https://mlsanity.com/paper/2512.14080/) (2025)
- [On the origin of neural scaling laws: from random graphs to natural language](https://mlsanity.com/paper/2601.10684/) (2026)
- [Every Attention Matters: An Efficient Hybrid Architecture for Long-Context Reasoning](https://mlsanity.com/paper/2510.19338/) (2025)
- [Training Matryoshka Mixture-of-Experts for Elastic Inference-Time Expert Utilization](https://mlsanity.com/paper/2509.26520/) (2025)
- [Mixture of Neuron Experts](https://mlsanity.com/paper/2510.05781/) (2025)
- [Information Capacity: Evaluating the Efficiency of Large Language Models via Text Compression](https://mlsanity.com/paper/2511.08066/) (2025)
- [RouteHijack: Routing-Aware Attack on Mixture-of-Experts LLMs](https://mlsanity.com/paper/2605.02946/) (2026)
- [Training Foundation Models on a Full-Stack AMD Platform: Compute, Networking, and System Design](https://mlsanity.com/paper/2511.17127/) (2025)
- [Synergistic Intra- and Cross-Layer Regularization Losses for MoE Expert Specialization](https://mlsanity.com/paper/2602.14159/) (2026)
- [φ-Balancing for Mixture-of-Experts Training](https://mlsanity.com/paper/2605.15403/) (2026)
- [Revealing the Challenges of Attention-FFN Disaggregation for Modern MoE Models and Hardware Systems](https://mlsanity.com/paper/2602.09721/) (2026)
- [ZAYA1-8B Technical Report](https://mlsanity.com/paper/2605.05365/) (2026)
- [Scaling Laws for Code: A More Data-Hungry Regime](https://mlsanity.com/paper/2510.08702/) (2025)
- [Theoretical Foundations of Scaling Law in Familial Models](https://mlsanity.com/paper/2512.23407/) (2025)
- [JTok: On Token Embedding as another Axis of Scaling Law via Joint Token Self-modulation](https://mlsanity.com/paper/2602.00800/) (2026)
- [Marco-MoE: Open Multilingual Mixture-of-Expert Language Models with Efficient Upcycling](https://mlsanity.com/paper/2604.25578/) (2026)
- [DAG-MoE: From Simple Mixture to Structural Aggregation in Mixture-of-Experts](https://mlsanity.com/paper/2606.01062/) (2026)
- [Holistic Scaling Laws for Optimal Mixture-of-Experts Architecture Optimization](https://mlsanity.com/paper/2603.21862/) (2026)
- [Geometric Routing Enables Causal Expert Control in Mixture of Experts](https://mlsanity.com/paper/2604.14434/) (2026)
- [Slicing and Dicing: Configuring Optimal Mixtures of Experts](https://mlsanity.com/paper/2605.11689/) (2026)
- [Scale Weight Decay and Train Better](https://mlsanity.com/paper/2607.23777/) (2026)
- [EngGPT2: Sovereign, Efficient and Open Intelligence](https://mlsanity.com/paper/2603.16430/) (2026)
- [Equifinality in Mixture of Experts: Routing Topology Does Not Determine Language Modeling Quality](https://mlsanity.com/paper/2604.14419/) (2026)
- [Expert Upcycling: Shifting the Compute-Efficient Frontier of Mixture-of-Experts](https://mlsanity.com/paper/2604.19835/) (2026)
- [Optimus: Elastic Decoding for Efficient Diffusion LLM Serving](https://mlsanity.com/paper/2605.24832/) (2026)
- [LLaDA MoE v2: Scaling Mixture-of-Experts Diffusion Language Models](https://mlsanity.com/paper/2608.03457/) (2026)
- [Scaling Laws for Looped Mixture of Experts](https://mlsanity.com/paper/2609.40316/) (2026)
- [Towards Principled Design of Mixture-of-Experts Language Models under Memory and Inference Constraints](https://mlsanity.com/paper/2601.08215/) (2026)
- [A.X K1 Technical Report](https://mlsanity.com/paper/2601.09200/) (2026)

## Abstract (arXiv)

Mixture-of-Experts (MoE) has become a dominant architecture for scaling Large Language Models (LLMs) efficiently by decoupling total parameters from computational cost. However, this decoupling creates a critical challenge: predicting the model capacity of a given MoE configurations (e.g., expert activation ratio and granularity) remains an unresolved problem. To address this gap, we introduce Efficiency Leverage (EL), a metric quantifying the computational advantage of an MoE model over a dense equivalent. We conduct a large-scale empirical study, training over 300 models up to 28B parameters, to systematically investigate the relationship between MoE architectural configurations and EL. Our findings reveal that EL is primarily driven by the expert activation ratio and the total compute budget, both following predictable power laws, while expert granularity acts as a non-linear modulator with a clear optimal range. We integrate these discoveries into a unified scaling law that accurately predicts the EL of an MoE architecture based on its configuration. To validate our derived scaling laws, we designed and trained Ling-mini-beta, a pilot model for Ling-2.0 series with only 0.85B active parameters, alongside a 6.1B dense model for comparison. When trained on an identical 1T high-quality token dataset, Ling-mini-beta matched the performance of the 6.1B dense model while consuming over 7x fewer computational resources, thereby confirming the accuracy of our scaling laws. This work provides a principled and empirically-grounded foundation for the scaling of efficient MoE models.