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Language Modeling on WikiText2 (train)

5.3073Final Train LossDF-Muon
4.8594567.88240310.9053513.928297Dec 15, 2025Jan 9, 2026Feb 4, 2026Mar 2, 2026Mar 27, 2026Apr 22, 2026May 18, 2026

Evaluation results

MethodLinks
DF-MuonMean base η=0.02022026.055.3073—————
SC-MuonMean base η=0.02022026.055.4122—————
DA-MuonMean base η=0.03002026.055.4445—————
Best fixed MuonMean base η=0.01502026.055.4489—————
AdamWMean base η=0.00102026.055.5576—————
QKV111H×L=4×6, T=512, d=2562025.1214.6401—0———
[1,1,1,1]H×L=4×6, T=512, d=2562025.1214.8002—-1.093———
[1,0,0,0]H×L=4×6, T=512, d=2562025.1214.8139—-1.186———
[0,0,0,0]H×L=4×6, T=512, d=2562025.1215.0499—-2.799———
[1,1,1,1]H×L=16×6, T=512, d=2562025.1215.1213—0.8328———
QKV111H×L=16×6, T=512, d=2562025.1215.2483—0———
[1,0,0,0]H×L=16×6, T=512, d=2562025.1215.3293—-0.531———
[1,0,0,0]H×L=1×1, T=512, d=2562025.1216.4084—0.241———
QKV111H×L=1×1, T=512, d=2562025.1216.4481—0———
[1,1,1,1]H×L=1×1, T=512, d=2562025.1216.4519—-0.023———
[0,0,0,0]H×L=1×1, T=512, d=2562025.1216.5034—-0.336———
AQ-SGDNetwork Bandwidth=100 Mbps, Backbone=GPT2-1.5B, Pipeline Config=fw4 bw82022.06—3————
DirectQNetwork Bandwidth=10 Gbps, Backbone=GPT2-1.5B, Pipeline Config=fw4 bw82022.06—4.1————
FP32Network Bandwidth=10 Gbps, Backbone=GPT2-1.5B, Precision=FP322022.06—3.8————
MeBPModel=0.5B, Sequence length=2562026.02———360.80.68—
MeBPModel=1.5B, Sequence length=2562026.02———516.21.66—
MeBPModel=3B, Sequence length=2562026.02———637.63.21—
MeSPModel=0.5B, Sequence length=2562026.02———136.20.8662
MeSPModel=1.5B, Sequence length=2562026.02———262.62.1749
MeSPModel=3B, Sequence length=2562026.02———368.44.0942
MeZOModel=0.5B, Sequence length=2562026.02———2430.5133
MeZOModel=1.5B, Sequence length=2562026.02———3761.2127
MeZOModel=3B, Sequence length=2562026.02———479.22.2425