Computer Science > Machine Learning
arXiv:2603.09453 (cs)
[Submitted on 10 Mar 2026]
Title:Variational Routing: A Scalable Bayesian Framework for Calibrated Mixture-of-Experts Transformers
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Abstract:Foundation models are increasingly being deployed in contexts where understanding the uncertainty of their outputs is critical to ensuring responsible deployment. While Bayesian methods offer a principled approach to uncertainty quantification, their computational overhead renders their use impractical for training or inference at foundation model scale. State-of-the-art models achieve parameter counts in the trillions through carefully engineered sparsity including Mixture-of-Experts (MoE) layers. In this work, we demonstrate calibrated uncertainty at scale by introducing Variational Mixture-of-Experts Routing (VMoER), a structured Bayesian approach for modelling uncertainty in MoE layers. VMoER confines Bayesian inference to the expert-selection stage which is typically done by a deterministic routing network. We instantiate VMoER using two inference strategies: amortised variational inference over routing logits and inferring a temperature parameter for stochastic expert selection. Across tested foundation models, VMoER improves routing stability under noise by 38\%, reduces calibration error by 94\%, and increases out-of-distribution AUROC by 12\%, while incurring less than 1\% additional FLOPs. These results suggest VMoER offers a scalable path toward robust and uncertainty-aware foundation models.
| Comments: | |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML) |
| Cite as: | arXiv:2603.09453 [cs.LG] |
| (or arXiv:2603.09453v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2603.09453
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View a PDF of the paper titled Variational Routing: A Scalable Bayesian Framework for Calibrated Mixture-of-Experts Transformers, by Albus Yizhuo Li and 1 other authors
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