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    <abstract>In this paper, we study a fundamental design problem in pretraining Large Language Models (LLMs) for low-resource language regimes, focusing on cross-family language pairs in which English serves as the high-resource language. Existing works adopt multi-epoch, multi-lingual, and multi-stage training to utilize the limited target-language corpus efficiently, but no prior scaling law can compare recipes spanning these approaches under the same compute budget C and target-language corpus size D_T, leaving the optimal training setup unclear. To address this gap, we propose the M³ Scaling Law, a unified predictive model parameterized by the model scale, the number of target-corpus epochs k, the average target-language ratio r, and the final-stage target-language ratio r_f, which places monolingual single-stage, multi-lingual single-stage, and multi-lingual multi-stage recipes on a single target-language validation-loss surface. Across three language pairs (English paired with Japanese, Indonesian, and Swahili), it extrapolates to unseen hyperparameter regions more accurately than existing scaling laws. Using M³ as a surrogate objective, we derive two practical guidelines for low-resource LLM pretraining: (i) as D_T decreases, the optimal recipe shifts directly from monolingual single-stage to multi-lingual two-stage training at a compute-budget-dependent threshold, with multi-lingual single-stage never optimal in our experimental grid; and (ii) the optimal number of epochs collapses onto a single curve in the scarcity variable D_T/D^\*(C), where D^\*(C) \propto C^α/(α+β) is the monolingual compute-optimal corpus size.</abstract>
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%0 Conference Proceedings
%T M³ Scaling Law: Optimizing Multi-Epoch, Multi-Lingual, and Multi-Stage Training for Low-Resource Language Models
%A Akimoto, Kosuke
%A Miyagawa, Taiki
%A Oyamada, Masafumi
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Findings of the Association for Computational Linguistics: EMNLP 2026
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-462-0
%F akimoto-etal-2026-m3
%X In this paper, we study a fundamental design problem in pretraining Large Language Models (LLMs) for low-resource language regimes, focusing on cross-family language pairs in which English serves as the high-resource language. Existing works adopt multi-epoch, multi-lingual, and multi-stage training to utilize the limited target-language corpus efficiently, but no prior scaling law can compare recipes spanning these approaches under the same compute budget C and target-language corpus size D_T, leaving the optimal training setup unclear. To address this gap, we propose the M³ Scaling Law, a unified predictive model parameterized by the model scale, the number of target-corpus epochs k, the average target-language ratio r, and the final-stage target-language ratio r_f, which places monolingual single-stage, multi-lingual single-stage, and multi-lingual multi-stage recipes on a single target-language validation-loss surface. Across three language pairs (English paired with Japanese, Indonesian, and Swahili), it extrapolates to unseen hyperparameter regions more accurately than existing scaling laws. Using M³ as a surrogate objective, we derive two practical guidelines for low-resource LLM pretraining: (i) as D_T decreases, the optimal recipe shifts directly from monolingual single-stage to multi-lingual two-stage training at a compute-budget-dependent threshold, with multi-lingual single-stage never optimal in our experimental grid; and (ii) the optimal number of epochs collapses onto a single curve in the scarcity variable D_T/D^\*(C), where D^\*(C) \propto C^α/(α+β) is the monolingual compute-optimal corpus size.
%U https://aclanthology.org/2026.findings-emnlp.2315/
%P 49689-49729

Markdown (Informal)

[M3 Scaling Law: Optimizing Multi-Epoch, Multi-Lingual, and Multi-Stage Training for Low-Resource Language Models](https://aclanthology.org/2026.findings-emnlp.2315/) (Akimoto et al., Findings 2026)

• M3 Scaling Law: Optimizing Multi-Epoch, Multi-Lingual, and Multi-Stage Training for Low-Resource Language Models (Akimoto et al., Findings 2026)

ACL

• Kosuke Akimoto, Taiki Miyagawa, and Masafumi Oyamada. 2026. M3 Scaling Law: Optimizing Multi-Epoch, Multi-Lingual, and Multi-Stage Training for Low-Resource Language Models. In Findings of the Association for Computational Linguistics: EMNLP 2026, pages 49689–49729, Budapest, Hungary. Association for Computational Linguistics.