What is the role of the step size hyperparameter (η) in Langevin dynamics as described in the chapter?

The step size hyperparameter (η) in Langevin dynamics determines the size of each update step during the sampling process. If η is too large, the algorithm may skip over minima, and if it is too small, the convergence will be slow.

In Langevin dynamics, the step size hyperparameter (η) is crucial because it controls how much the input is adjusted in each iteration of the sampling process. This adjustment is made in the direction of the negative gradient of the energy function with respect to the input. A properly tuned η ensures efficient convergence to a low-energy state, balancing between making meaningful progress and avoiding overshooting the minima. If the step size is too large, the algorithm might jump over the minima, missing potential solutions. Conversely, if the step size is too small, the algorithm will take longer to converge, making the process inefficient.