Learn how to address catastrophic forgetting in Large Language Models through a conference talk that presents a novel full-parameter continual learning method using adaptive Singular Value Decomposition (SVD). Discover how to dynamically identify and protect task-critical subspaces while constraining updates to orthogonal low-rank directions, enabling models to retain previous knowledge without adding extra parameters. Explore the methodology that achieves up to 7% higher accuracy compared to strong baselines like O-LoRA while maintaining general language capabilities and safety. Examine the theoretical foundations and extensive empirical results that demonstrate a scalable approach toward continually evolving LLMs, presented by Nikhil Shivakumar Nayak at DevConf.US 2025.