Gradient Descent with Polyak's Momentum Finds Flatter Minima via Large Catapults
This provides insights into optimization dynamics for machine learning practitioners, but it is incremental as it builds on prior work like the self-stabilization effect.
The paper tackles the problem of understanding how gradient descent with Polyak's momentum affects training trajectories, showing empirically that it drives iterates towards flatter minima than gradient descent via large catapults, with evidence from linear diagonal and nonlinear neural networks.
Although gradient descent with Polyak's momentum is widely used in modern machine and deep learning, a concrete understanding of its effects on the training trajectory remains elusive. In this work, we empirically show that for linear diagonal networks and nonlinear neural networks, momentum gradient descent with a large learning rate displays large catapults, driving the iterates towards much flatter minima than those found by gradient descent. We hypothesize that the large catapult is caused by momentum "prolonging" the self-stabilization effect (Damian et al., 2023). We provide theoretical and empirical support for our hypothesis in a simple toy example and empirical evidence supporting our hypothesis for linear diagonal networks.