The Adam Optimizer (DL 21) | Highlights and Annotations by Gistr.

This segment details the common pitfalls of gradient descent, including getting stuck in local minima, plateaus, and saddle points in both one and higher dimensions. It explains how these points lead to zero gradients, hindering the optimization process and slowing down learning, particularly in high-dimensional spaces where saddle points become more prevalent. The explanation includes visual examples and clarifies why stochasticity can sometimes, but not always, help overcome these challenges. Adam optimizer improves upon stochastic gradient descent by addressing its weaknesses. It uses momentum (a moving average of gradients) to escape plateaus and saddle points, and adaptive learning rates (using a moving average of squared gradients) to normalize steps across dimensions, preventing zigzagging and overshooting. This results in faster and more stable neural network training. This segment introduces the Adam optimizer and its two key components: momentum and adaptive learning rates. It explains how momentum helps to overcome plateaus and saddle points by continuing movement in a consistent direction, and how adaptive learning rates, calculated using moving averages of the partial derivatives and their squares, address the issue of overshooting and zigzagging caused by differing scales of partial derivatives across dimensions. The segment concludes by describing the Adam update rule, including a crucial detail about handling potential division by zero.