The training of large models demands substantial computational resources, typically available only in data centers with high-bandwidth interconnects. However, reducing the reliance on high-bandwidth interconnects between nodes enables the use of distributed compute resources as an alternative to centralized data center training. Building on recent advances in distributed model training, we propose an approach that further reduces communication by combining infrequent synchronizations across distributed model replicas with gradient momentum compression. In particular, we treat the optimizer momentum as a signal and decompose the Nesterov momentum into high- and low-frequency components via the discrete cosine transform (DCT). Only the high-frequency components are synchronized across model replicas every $H$ steps. Empirically, our method achieves up to a $16\times$ reduction in communication compared to the baseline DiLoCo, and it generalizes across architectures, including transformer-based language models and convolutional neural networks for images. Overall, this work advances the feasibility of training large models on distributed nodes with low-bandwidth interconnects.

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