Reparameterization Tricks: Variance Reduction by Smarter Gradients

The reparameterization trick is a technique that enables training models like Variational Autoencoders (VAEs) with standard stochastic gradient descent. It works by moving randomness outside the computation graph, expressing a random variable as a deterministic, differentiable function of its parameters and an independent noise variable. This reformulation allows gradients to be computed directly through the sampling process using the chain rule, creating a "pathwise derivative." This method significantly reduces the variance of gradient estimates compared to alternatives like the score function estimator (REINFORCE), resulting in more stable and faster model training.