Training large language models (LLMs) is like feeding a hungry giant—it demands enormous resources, especially memory. As these models grow larger, training them becomes increasingly challenging, limited to those with the most powerful hardware. But what if there was a way to train these giants more efficiently, using less memory without sacrificing performance? That's the promise of BlockLLM, a novel approach inspired by a classic optimization technique called block coordinate descent. Instead of updating all the model's parameters at once, BlockLLM strategically selects and updates only a small subset. This clever trick dramatically reduces the memory footprint by storing gradients and optimizer states only for the chosen parameters. Imagine focusing your efforts on the most critical parts of a complex puzzle—that's essentially what BlockLLM does. It identifies the most impactful parameters at different stages of training, ensuring efficient updates without wasting resources on less important parts. The results are impressive. In tests on fine-tuning and pre-training tasks, BlockLLM achieves state-of-the-art performance while using significantly less memory than existing methods. This means researchers and developers with limited resources can now participate in the exciting world of LLM training, pushing the boundaries of AI. BlockLLM isn't just a memory saver; it also maintains the model's original architecture and doesn't restrict its learning potential. This flexibility makes it suitable for various LLMs and tasks. While BlockLLM demonstrates impressive results, the research is ongoing. Future work includes exploring alternative parameter selection criteria and integrating BlockLLM with other memory optimization techniques. BlockLLM represents a significant step toward democratizing LLM training, opening doors for broader participation and accelerating AI advancements. By training smarter, not just bigger, we can unlock the full potential of these powerful language models.