ShapleyLaw: A Game-Theoretic Approach to Multilingual Scaling Laws

arXiv:2603.17945 · cs.CL · Submitted 2026-03-18 · Read on arXiv

cs.CL

Submitted: 2026-03-18

Updated: 2026-09-19

Comments: Accepted at EMNLP 2026 Main Conference. Camera-ready version; revised based on reviewer feedback

Code: https://github.com/llm-jp/llm-jp-tokenizer

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Cross-lingual Transfer — 68× in this paper · explained in 2 episodes
• Scaling Laws — 22× in this paper · explained in 4 episodes
• Accuracy — 21× in this paper · explained in 1 episode
• Downstream Tasks — 9× in this paper · explained in 2 episodes
• Benchmark — 8× in this paper · explained in 2 episodes
• Shapley values — 7× in this paper · explained in 2 episodes
• Cosine Similarity — 6× in this paper · explained in 3 episodes
• In-Run Data Shapley — 5× in this paper
• Multilingual Pretraining Game — 5× in this paper
• Alignment — 4× in this paper · explained in 1 episode
• Transferability — 4× in this paper · explained in 4 episodes
• Aggregation — 3× in this paper · explained in 1 episode
• Core — 3× in this paper · explained in 2 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Transformer — 3× in this paper · explained in 2 episodes
• Adam — 2× in this paper · explained in 2 episodes
• Calibration — 2× in this paper · explained in 7 episodes
• Transfer Learning — 2× in this paper · explained in 10 episodes
• Distribution Shift — 1× in this paper · explained in 6 episodes
• Few-Shot Learning — 1× in this paper · explained in 4 episodes
• Foundation Model — 1× in this paper · explained in 3 episodes
• Foundation Models — 1× in this paper · explained in 7 episodes
• Generative AI — 1× in this paper · explained in 2 episodes
• Hyperparameters — 1× in this paper · explained in 2 episodes
• Large Language Models (LLMs) — 1× in this paper · explained in 6 episodes
• Low-Resource Languages — 1× in this paper · explained in 4 episodes
• Reinforcement Learning — 1× in this paper · explained in 4 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Tokenization — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Scaling Laws for Predicting Downstream Performance in LLMs
• Scaling Laws for Neural Language Models
• LLM-jp: A Cross-organizational Project for the Research and Development of Fully Open Japanese LLMs
• FineWeb2: One Pipeline to Scale Them All -- Adapting Pre-Training Data Processing to Every Language
• Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism
• Scaling Laws for Optimal Data Mixtures
• Llama 2: Open Foundation and Fine-Tuned Chat Models

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