Largest Eigenvalue

The largest eigenvalue of a matrix is a fundamental concept with broad applications, particularly in analyzing the stability and performance of complex systems. Current research focuses on understanding the behavior of largest eigenvalues in high-dimensional settings, such as those arising in neural network training and distributed optimization algorithms. This includes investigating the dynamics of eigenvalues during optimization processes and exploring alternative metrics beyond the second-largest eigenvalue modulus for characterizing network performance in distributed systems. These investigations are crucial for improving the efficiency and stability of machine learning algorithms and distributed computing frameworks.