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Language Modeling on Multilingual Held-out Corpus Unweighted Sum

18.289CE LossShapleyLaw
18.2462818.5346418.82319.11136Mar 18, 2026

Evaluation results

MethodLinks
ShapleyLawLanguage Mixture Ratio (en)=1.8, Language Mixture Ratio (de)=16.9, Language Mixture Ratio (fr)=12.6, Language Mixture Ratio (es)=9.6, Language Mixture Ratio (zh)=20.1, Language Mixture Ratio (ja)=19.8, Language Mixture Ratio (ko)=19.22026.0318.289
α = 0.5Language Mixture Ratio (en)=14.8, Language Mixture Ratio (de)=14.8, Language Mixture Ratio (fr)=16.2, Language Mixture Ratio (es)=14.1, Language Mixture Ratio (zh)=15.2, Language Mixture Ratio (ja)=21.4, Language Mixture Ratio (ko)=12.82026.0318.349
UniformLanguage Mixture Ratio (en)=14.3, Language Mixture Ratio (de)=14.3, Language Mixture Ratio (fr)=14.3, Language Mixture Ratio (es)=14.3, Language Mixture Ratio (zh)=14.3, Language Mixture Ratio (ja)=14.3, Language Mixture Ratio (ko)=14.22026.0318.354
FamilyLawLanguage Mixture Ratio (en)=8.1, Language Mixture Ratio (de)=8.1, Language Mixture Ratio (fr)=8.1, Language Mixture Ratio (es)=8.1, Language Mixture Ratio (zh)=24.2, Language Mixture Ratio (ja)=23.1, Language Mixture Ratio (ko)=20.32026.0318.435
Common CrawlLanguage Mixture Ratio (en)=44.4, Language Mixture Ratio (de)=12.1, Language Mixture Ratio (fr)=9.8, Language Mixture Ratio (es)=9.5, Language Mixture Ratio (zh)=12.0, Language Mixture Ratio (ja)=10.7, Language Mixture Ratio (ko)=1.52026.0318.679
FineWeb-2Language Mixture Ratio (en)=81.3, Language Mixture Ratio (de)=3.3, Language Mixture Ratio (fr)=2.3, Language Mixture Ratio (es)=2.7, Language Mixture Ratio (zh)=6.8, Language Mixture Ratio (ja)=3.1, Language Mixture Ratio (ko)=0.52026.0319.357