Exponential Growth

Exponential growth, the rapid increase of a quantity over time, is a fundamental concept studied across diverse scientific fields. Current research focuses on understanding and managing exponential growth in various contexts, including optimization algorithms (e.g., gradient descent with adaptive step sizes), material science (e.g., automated semiconductor growth using machine learning), and large language models (analyzing the exponential growth of linear regions and singular vector alignment). These investigations are crucial for improving the efficiency and scalability of computational methods, accelerating materials development, and enhancing our understanding of complex systems like LLMs, ultimately impacting fields ranging from computer science to astrophysics.