E = T*H/(O+B): A Dimensionless Control Parameter for Mixture-of-Experts Ecology
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866916040330444800 |
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| author | Zhang, Qingjun |
| author_facet | Zhang, Qingjun |
| contents | We introduce E = T*H/(O+B), a dimensionless control parameter that predicts whether Mixture-of-Experts (MoE) models will develop a healthy expert ecology or collapse into dead experts. E combines four hyperparameters -- routing temperature T, routing entropy weight H, oracle weight O, and balance weight B -- into a single quantity. Through 12 controlled experiments (8 vision, 4 language) totaling over 11,000 training epochs, we establish that E >= 0.5 alone is sufficient to guarantee zero dead experts, removing the necessity for handcrafted load-balancing auxiliary losses. We validate this cross-modally on CIFAR-10, CIFAR-100, TinyImageNet-200, WikiText-2, and WikiText-103. Six additional findings emerge: (1) dead experts can resuscitate -- triggered by balance loss driving router re-exploration; (2) ortho toxicity is dataset-dependent, not universal; (3) task complexity shifts the critical E threshold; (4) model overfitting is decoupled from expert ecological health; (5) three-tier MoE spontaneously collapses into a two-tier functional structure; (6) ecological structure is temperature-invariant across a 50x range. We propose that E serves as a unified diagnostic for MoE training, analogous to the Reynolds number in fluid dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06415 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | E = T*H/(O+B): A Dimensionless Control Parameter for Mixture-of-Experts Ecology Zhang, Qingjun Machine Learning Artificial Intelligence Computation and Language Computer Vision and Pattern Recognition I.2.6; I.2.10 We introduce E = T*H/(O+B), a dimensionless control parameter that predicts whether Mixture-of-Experts (MoE) models will develop a healthy expert ecology or collapse into dead experts. E combines four hyperparameters -- routing temperature T, routing entropy weight H, oracle weight O, and balance weight B -- into a single quantity. Through 12 controlled experiments (8 vision, 4 language) totaling over 11,000 training epochs, we establish that E >= 0.5 alone is sufficient to guarantee zero dead experts, removing the necessity for handcrafted load-balancing auxiliary losses. We validate this cross-modally on CIFAR-10, CIFAR-100, TinyImageNet-200, WikiText-2, and WikiText-103. Six additional findings emerge: (1) dead experts can resuscitate -- triggered by balance loss driving router re-exploration; (2) ortho toxicity is dataset-dependent, not universal; (3) task complexity shifts the critical E threshold; (4) model overfitting is decoupled from expert ecological health; (5) three-tier MoE spontaneously collapses into a two-tier functional structure; (6) ecological structure is temperature-invariant across a 50x range. We propose that E serves as a unified diagnostic for MoE training, analogous to the Reynolds number in fluid dynamics. |
| title | E = T*H/(O+B): A Dimensionless Control Parameter for Mixture-of-Experts Ecology |
| topic | Machine Learning Artificial Intelligence Computation and Language Computer Vision and Pattern Recognition I.2.6; I.2.10 |
| url | https://arxiv.org/abs/2605.06415 |