Despite the dominance and effectiveness of scaling, resulting in large networks with hundreds of billions of parameters, the necessity to train overparametrized models remains poorly understood, while training costs grow exponentially. In this paper, we explore parameter-efficient training techniques as an approach to training large neural networks. We introduce a novel method called ReLoRA, which utilizes low-rank updates to train high-rank networks. We apply ReLoRA to training transformer language models with up to 1.3B parameters and demonstrate comparable performance to regular neural network training. ReLoRA saves up to 5.5Gb of RAM per GPU and improves training speed by 9-40% depending on 10 the model size and hardware setup. Our findings show the potential of parameter-efficient techniques for large-scale pre-training.