RGP: Achieving Memory-Efficient Model Fine-tuning Via Randomized Gradient Projection

Training and fine-tuning Large Language Models (LLMs) require significant memory due to the substantial growth in the size of weight parameters and optimizer states. While methods like low-rank adaptation (LoRA), which introduce low-rank trainable modules in parallel to frozen pre-trained weights, effectively reduce memory usage, they often fail to preserve the optimization trajectory and are generally less effective for pre-training models. On the other hand, approaches, such as GaLore, that project gradients onto lower-dimensional spaces maintain the training trajectory and perform well in pre-training but suffer from high computational complexity, as they require repeated singular value decomposition on large matrices. In this work, we propose Randomized Gradient Projection (RGP), which outperforms GaLore, the current state-of-the-art in efficient fine-tuning, on the GLUE task suite, while being 74\% faster on average and requiring similar memory.