In this work, we provide a large-scale empirical study of the scaling properties of multilingual neural machine translation models. We examine how increases in the model size affect the model performance and investigate the role of the training mixture composition on the scaling behavior. We find that changing the weightings of the individual language pairs in the training mixture only affect the multiplicative factor of the scaling law. In particular, we observe that multilingual models trained using different mixing rates all exhibit the same scaling exponent. Through a novel joint scaling law formulation, we compute the effective number of parameters allocated to each language pair and examine the role of language similarity in the scaling behavior of our models. We find little evidence that language similarity has any impact. In contrast, the direction of the multilinguality plays a significant role, with models translating from multiple languages into English having a larger number of effective parameters per task than their reversed counterparts. Finally, we leverage our observations to predict the performance of multilingual models trained with any language weighting at any scale, significantly reducing efforts required for language balancing in large multilingual models. Our findings apply to both in-domain and out-of-domain test sets and to multiple evaluation metrics, such as ChrF and BLEURT.

本研究提供了一个大规模的实证研究，研究了多语言神经机器翻译模型的缩放特性，包括模型规模对模型性能的影响，训练混合物组成对缩放行为的作用，以及语言相似性在模型缩放中的作用。通过新颖的联合缩放定律公式，我们计算了每个语言对分配的有效参数数量，并发现了翻译多个语言到英语的模型比反向模型具有更多的任务有效参数。最终，我们利用这些发现预测了任何规模的带有任何语言加权的多语言模型的性能，显著减少了大型多语言模型中语言平衡所需的工作量。

多语言神经机器翻译的规模定律