Why are optimization algorithms slower at critical points?
In that simulation, the movement speed is a proxy for step size. The step size is a function of learning rate (v) and the approximate gradient of the function at that point ($\frac{\partial L}{\partial w}$). The learning rate can be constant. However, the approximate gradient is not constant. The approximate gradient is typically smaller closer to a critical point (i.e., the valley starts to gradually level out). Thus, the computed update value is smaller and the movement speed slows down.