Imagine training massive AI models on a single GPU, a feat once deemed impossible. Recent research suggests that a new approach, called Weight Low-Rank Projection (WeLore), is changing the game. Large Language Models (LLMs) like the ones powering ChatGPT, are built on gigantic matrices with billions of elements. This complexity demands colossal resources for storage and training. WeLore tackles this head-on by strategically compressing these matrices, making them leaner and more efficient. The key insight? Not all parts of these models contribute equally to learning. WeLore identifies and focuses on the 'Low-Rank Components' (LRCs), the parts responsible for the most effective learning. By targeting only these LRCs for fine-tuning, WeLore unlocks significant memory and compute savings. The results are striking. Experiments on standard language tasks demonstrate that WeLore fine-tuning performs similarly to traditional methods but requires only a fraction of the resources. In some cases, it even outperforms full fine-tuning. For example, with the LLaMa-2 7B model, WeLore achieves similar performance using only about 35% of trainable parameters while achieving three times better throughput and requiring only 60% of the GPU memory. This method opens doors for deploying state-of-the-art LLMs on consumer-grade hardware, democratizing access to powerful AI tools. Moreover, by focusing on the components with the greatest learning potential, WeLore points toward a future of AI where large models can adapt to new tasks quickly and efficiently. The implications for training LLMs from scratch remain an exciting direction for further research.