CocktailSGD is a novel communication-efficient training framework designed to train large language models (LLMs) over slow networks, such as 500Mbps connections. This approach combines three distinct compression techniques - random sparsification, top-K sparsification, and quantization - to achieve much greater compression than individual techniques alone. Theoretical analysis justifies the benefit of this hybrid approach, while empirical results show that CocktailSGD achieves up to 117x compression in fine-tuning LLMs without compromising convergence. On a slow network, CocktailSGD only incurs a small slowdown compared to data center networks. The RedPajama-V2 Dataset is conceptualized as a foundation for creating high-quality datasets, and its use requires filtering out data using quality signals that accompany it, depending on the intended application.