Characterizing Optimizer-Dependent Training Dynamics Through Hessian Eigenvector Displacement and Localization

Hessian spectral properties are a standard tool in analysing neural-network training, with eigenvalues linked to sharpness, generalization, and optimization dynamics. Eigenvalues quantify curvature magnitude, while eigenvectors identify which parameters generate that curvature. In this work, we study how the leading Hessian eigenvectors evolve during training and how they affect the learning trajectories. We track the training dynamics of multilayer perceptrons on a classification problem and measure eigenvector dynamics through two complementary statistics: (i) displacement over time, inspire