Hyperparameter Transfer with Mixture-of-Expert Layers
On the map: Mixture-of-experts → MoE theory and gating functions
Abstract (arXiv)
Mixture-of-Experts (MoE) layers have emerged as an important tool in scaling up modern neural networks by decoupling total trainable parameters from activated parameters in the forward pass for each token. However, sparse MoEs add complexity to training due to (i) new trainable parameters (router weights) that, like all other parameter groups, require hyperparameter (HP) tuning; (ii) new architecture scale dimensions (number of and size of experts) that must be chosen and potentially taken large. To make HP selection cheap and reliable, we propose a new parameterization for transformer models with MoE layers when scaling model width, depth, number of experts, and expert (hidden) size. Our parameterization is justified by a novel dynamical mean-field theory (DMFT) analysis. When varying different model dimensions trained at a fixed token budget, we find empirically that our parameterization enables reliable HP transfer across models from 51M to over 2B total parameters. We further take HPs identified from sweeping small models on a short token horizon to train larger models on longer horizons and report performant model behaviors.
Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Placed in MoE theory and gating functions, one of 12 directions in Mixture-of-experts. Builds on 46 of its 70 references that are in the map. First posted on arXiv 28 Jan 2026.
Builds on
46 of 70 references.
Closest ancestors · 1
Same direction, newest first
Other references · 45
- 2019Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformercited by 14,491
- 2020Scaling Laws for Neural Language Modelscited by 6,411
- 2017Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layercited by 3,413
- 2021Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsitycited by 3,014
- 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,597
- 2020GShard: Scaling Giant Models with Conditional Computation and Automatic Shardingcited by 1,601
- 2024DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Modelscited by 834
- 2018On Lazy Training in Differentiable Programmingcited by 671
- 2022Mixture-of-Experts with Expert Choice Routingcited by 611
- 2018signSGD: Compressed Optimisation for Non-Convex Problemscited by 561
- 2017Deep Learning Scaling is Predictable, Empiricallycited by 556
- 2018A Mean Field View of the Landscape of Two-Layers Neural Networkscited by 463
33 more
- 2022ST-MoE: Designing Stable and Transferable Sparse Expert Modelscited by 391
- 2022Unified Scaling Laws for Routed Language Modelscited by 249
- 2024Auxiliary-Loss-Free Load Balancing Strategy for Mixture-of-Expertscited by 191
- 2021The Principles of Deep Learning Theorycited by 169
- 2024Scaling Laws for Fine-Grained Mixture of Expertscited by 166
- 2020Infinite attention: NNGP and NTK for deep attention networkscited by 117
- 2018Trainability and Accuracy of Neural Networks: An Interacting Particle System Approachcited by 105
- 2022Self-Consistent Dynamical Field Theory of Kernel Evolution in Wide Neural Networkscited by 104
- 2023A Spectral Condition for Feature Learningcited by 101
- 2023Tensor Programs VI: Feature Learning in Infinite-Depth Neural Networkscited by 94
- 2025Don't be lazy: CompleteP enables compute-efficient deep transformerscited by 69
- 2023Depthwise Hyperparameter Transfer in Residual Networks: Dynamics and Scaling Limitcited by 64
- 2024Scalable Optimization in the Modular Normcited by 64
- 2020Dynamical mean-field theory for stochastic gradient descent in Gaussian mixture classificationcited by 60
- 2025Step-3 is Large yet Affordable: Model-system Co-design for Cost-effective Decodingcited by 52
- 2023Dynamics of Finite Width Kernel and Prediction Fluctuations in Mean Field Neural Networkscited by 42
- 2024How to set AdamW's weight decay as you scale model and dataset sizecited by 42
- 2025Power Lines: Scaling Laws for Weight Decay and Batch Size in LLM Pre-trainingcited by 41
- 2024Infinite Limits of Multi-head Transformer Dynamicscited by 38
- 2025Predictable Scale: Part I, Step Law -- Optimal Hyperparameter Scaling Law in Large Language Model Pretrainingcited by 30
- 2023Effective Theory of Transformers at Initializationcited by 21
- 2025Why Gradients Rapidly Increase Near the End of Trainingcited by 21
- 2025Scaling Collapse Reveals Universal Dynamics in Compute-Optimally Trained Neural Networkscited by 21
- 2025Weight Decay may matter more than muP for Learning Rate Transfer in Practicecited by 20
- 2022Meta-Principled Family of Hyperparameter Scaling Strategiescited by 18
- 2025Unveiling Super Experts in Mixture-of-Experts Large Language Modelscited by 15
- 2025The Hidden Width of Deep ResNets: Tight Error Bounds and Phase Diagramcited by 13
- 2025The power of fine-grained experts: Granularity boosts expressivity in Mixture of Expertscited by 9
- 2025Towards a Comprehensive Scaling Law of Mixture-of-Expertscited by 9
- 2025Scaling with Collapse: Efficient and Predictable Training of LLM Familiescited by 8
- 2025Understanding the Mechanisms of Fast Hyperparameter Transfercited by 6
- 2019Exact Convergence Rates of the Neural Tangent Kernel in the Large Depth Limitcited by 5
- 2026Disordered Dynamics in High Dimensions: Connections to Random Matrices and Machine Learningcited by 4
Built on by
Citing papers per year: 2026: 10.
10 papers.
- 2026There Will Be a Scientific Theory of Deep Learningcited by 21
- 2026Hyperparameter Transfer Laws for Non-Recurrent Multi-Path Neural Networkscited by 1
- 2026Quantifying Hyperparameter Transfer and the Importance of Embedding Layer Learning Ratecited by 1
- 2026Complete-muE: Optimal Hyperparameter Transfer and Scaling for MoE Modelscited by 1
- 2026Abra: Scaling Diffusion Image Trainingcited by 1
- 2026How to Scale Mixture-of-Experts: From muP to the Maximally Scale-Stable Parameterizationcited by 0
- 2026Beyond Modality Fusion: Deep Ensembles for Multimodal Classificationcited by 0
- 2026Compute-Optimal Is Not Cluster-Optimal: Systems-Aware Scaling for Sparse Mixture-of-Expertscited by 0
- 2026Hyperparameter Scaling Laws Across MoE Sparsitycited by 0
- 2026MoRE: Scaling mixture of experts with hardware-aware low-rank routingcited by 0
- 2026MoRE: Scaling mixture of experts with hardware-aware low-rank routing28 Sep 2026
- 2026Hyperparameter Scaling Laws Across MoE Sparsity8 Sep 2026
- 2026Abra: Scaling Diffusion Image Training18 Aug 2026
- 2026Compute-Optimal Is Not Cluster-Optimal: Systems-Aware Scaling for Sparse Mixture-of-Experts11 Aug 2026
- 2026Beyond Modality Fusion: Deep Ensembles for Multimodal Classification6 Jul 2026
- 2026Complete-muE: Optimal Hyperparameter Transfer and Scaling for MoE Models22 May 2026
- 2026Quantifying Hyperparameter Transfer and the Importance of Embedding Layer Learning Rate20 May 2026
- 2026How to Scale Mixture-of-Experts: From muP to the Maximally Scale-Stable Parameterization13 May 2026
- 2026There Will Be a Scientific Theory of Deep Learning23 Apr 2026
- 2026Hyperparameter Transfer Laws for Non-Recurrent Multi-Path Neural Networks7 Feb 2026
Similar, not cited
Close in wording, no citation either way
- 2026Let's Scale Step by Step: Compute-Efficient Hyperparameter Transfer for Large-Scale Mixture-of-Experts
- 2025μ-Parametrization for Mixture of Experts
- 2025Symphony-MoE: Harmonizing Disparate Pre-trained Models into a Coherent Mixture-of-Experts
- 2026Generalization and Scaling Laws for Mixture-of-Experts Transformers
- 2025Mixture-of-Experts Operator Transformer for Large-Scale PDE Pre-Training
- 2026Optimal Expert-Attention Allocation in Mixture-of-Experts: A Scalable Law for Dynamic Model Design
- 2025Dense Backpropagation Improves Training for Sparse Mixture-of-Experts
- 2023Pushing Mixture of Experts to the Limit: Extremely Parameter Efficient MoE for Instruction Tuning