Multilingual machine translation (MMT) benefits from cross-lingual transfer but is a challenging multitask optimization problem. This is partly because there is no clear framework to systematically learn language-specific parameters. Self-supervised learning (SSL) approaches that leverage large quantities of monolingual data (where parallel data is unavailable) have shown promise by improving translation performance as complementary tasks to the MMT task. However, jointly optimizing SSL and MMT tasks is even more challenging. In this work, we first investigate how to utilize **intra-distillation** to learn more *language-specific* parameters and then show the importance of these language-specific parameters. Next, we propose a novel but simple SSL task, **concurrent denoising**, that co-trains with the MMT task by concurrently denoising monolingual data on both the encoder and decoder. Finally, we apply **intra-distillation** to this co-training approach. Combining these two approaches significantly improves MMT performance, outperforming three state-of-the-art SSL methods by a large margin, e.g., 11.3{% and 3.7{% improvement on an 8-language and a 15-language benchmark compared with MASS, respectively.

Multi-task learning with an unbalanced data distribution skews model learning towards high resource tasks, especially when model capacity is fixed and fully shared across all tasks. Sparse scaling architectures, such as BASELayers, provide flexible mechanisms for different tasks to have a variable number of parameters, which can be useful to counterbalance skewed data distributions. We find that that sparse architectures for multilingual machine translation can perform poorly out of the box and propose two straightforward techniques to mitigate this — a temperature heating mechanism and dense pre-training. Overall, these methods improve performance on two multilingual translation benchmarks compared to standard BASELayers and Dense scaling baselines, and in combination, more than 2x model convergence speed.