How to Train a Model on a Cheap Cluster with Low Cost using Block Coordinate Descent (2506.12037v1)

Abstract: Training LLMs typically demands extensive GPU memory and substantial financial investment, which poses a barrier for many small- to medium-sized teams. In this paper, we present a full-parameter pre-training framework based on block coordinate descent (BCD), augmented with engineering optimizations, to efficiently train large models on affordable RTX 4090 GPU clusters. BCD ensures model convergence based on block coordinate descent theory and performs gradient computation and update at the level of parameter blocks. Experiments show that 1) Lower cost of Same-Device: BCD significantly reduces pre-training cost. For the 7B model, under identical hardware settings, BCD lowers training costs to approximately 33% on A100,A800 clusters on 7B model averagely and to approximately 2.6% on RTX 4090 clusters on 7B model, compared to traditional full-parameter training. 2) Cross-Device Transfer: By leveraging BCD, large-scale models previously trainable only on high-end A100 clusters can be seamlessly migrated and pre-trained on 4090 clusters-whose hourly cost is only one-quarter that of A100-without requiring expensive hardware. 3) Accuracy Retention: In both scenarios, BCD training achieves the same level of model accuracy as full-parameter pre-training.