{"paper":{"title":"How to Scale Mixture-of-Experts: From muP to the Maximally Scale-Stable Parameterization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Mixture-of-Experts models require a Maximally Scale-Stable Parameterization to restore learning-rate transfer and monotonic gains at scale.","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Alessandro Breccia, Leena Chennuru Vankadara, Luke Hayward, Moritz Haas, Sebastian Bordt","submitted_at":"2026-05-13T23:32:00Z","abstract_excerpt":"Recent frontier large language models predominantly rely on Mixture-of-Experts (MoE) architectures. Despite empirical progress, there is still no principled understanding of how hyperparameters should scale with network width $N$, expert width $N_e$, number of experts $M$, sparsity $K$, and depth $L$ to ensure both stability and optimal performance at scale. We take a principled step toward resolving this gap by analyzing three different scaling regimes: (I) co-scaling $N\\asymp N_e$, (II) co-scaling $N\\asymp M\\asymp K$, and (III) full proportional scaling of $N, N_e, M$, and $K$. For each regi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Experiments verify that MSSP robustly recovers learning rate transfer and monotonic improvement with scale across regimes. Combined with existing depth-scaling theory, these results provide a complete scaling prescription for MoE architectures as a function of width, depth, expert width, and number of experts.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The DMFT description of limiting training dynamics accurately captures the scale-dependent observables in the aggregation dynamics of MoE models in all three regimes, and that the maximal scale stability desiderata are the right refinement of muP.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The authors derive a Maximally Scale-Stable Parameterization (MSSP) for MoE models that achieves robust learning-rate transfer and monotonic performance gains with scale across co-scaling regimes of width, experts, and sparsity.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Mixture-of-Experts models require a Maximally Scale-Stable Parameterization to restore learning-rate transfer and monotonic gains at scale.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"df1ed8f1f7b36e9ce117ae9f7fd9c175ebc98dea20197fd95b39e369892f9100"},"source":{"id":"2605.14200","kind":"arxiv","version":1},"verdict":{"id":"645bc396-a8cb-41b0-b98b-00ebd4de8ae5","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T04:42:00.533798Z","strongest_claim":"Experiments verify that MSSP robustly recovers learning rate transfer and monotonic improvement with scale across regimes. Combined with existing depth-scaling theory, these results provide a complete scaling prescription for MoE architectures as a function of width, depth, expert width, and number of experts.","one_line_summary":"The authors derive a Maximally Scale-Stable Parameterization (MSSP) for MoE models that achieves robust learning-rate transfer and monotonic performance gains with scale across co-scaling regimes of width, experts, and sparsity.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The DMFT description of limiting training dynamics accurately captures the scale-dependent observables in the aggregation dynamics of MoE models in all three regimes, and that the maximal scale stability desiderata are the right refinement of muP.","pith_extraction_headline":"Mixture-of-Experts models require a Maximally Scale-Stable Parameterization to restore learning-rate transfer and monotonic gains at scale."},"references":{"count":300,"sample":[{"doi":"","year":null,"title":"arXiv preprint arXiv:2512.22768 , year=","work_id":"8057482a-2cb6-42e6-a46f-e6542c181011","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"CS 231N , volume=","work_id":"dd43a69f-c43e-4948-8ec1-87068c776a10","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2026,"title":"Generalization and Scaling Laws for Mixture-of-Experts Transformers , author=. 2026 , note=","work_id":"6f68a207-1758-4f32-84da-3b1817876228","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"arXiv preprint arXiv:2407.04153 , year=","work_id":"edf386eb-cf36-47f2-b15f-fad92344ed8a","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"arXiv preprint arXiv:2402.07871 , year=","work_id":"e67733fa-7550-4e7a-b1e0-d65341a18264","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":300,"snapshot_sha256":"a9c5da219652f2822c95c9c4ef54db647fa1c5c3d0b13e2b1be9e00dedeea2e5","internal_anchors":13},"formal_canon":{"evidence_count":2,"snapshot_sha256":"e6bb6c8203a02a28edbd308837a7eb343dbcfd2de8b3452e62a25eebdf5d3d0c"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}