The paper introduces a new approach named Gradient Low-Rank Projection (GaLore) to train large language models (LLMs) with full parameter learning while being significantly more memory-efficient than existing techniques. GaLore dynamically switches between multiple low-rank subspaces to represent the gradient during training, enabling the exploration of different directions while maintaining memory savings. GaLore offers a breakthrough in memory-efficient LLM training by reducing memory usage significantly while achieving performance comparable to full-rank training. It enables training of large models on limited hardware resources, democratizing LLM research and development. Future research directions include applying GaLore to various model architectures, enhancing memory efficiency further, and exploring elastic data distributed training using consumer-grade hardware.