Given the task definition and input, reply with output. In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Predictive coding, within theoretical neuroscience, and variational autoencoders, within machine learning, both involve latent Gaussian models and variational inference. While these areas share a common origin, they have evolved largely independently. We outline connections and contrasts between these areas, using their relationships to identify new parallels between machine learning and neuroscience. We then discuss specific frontiers at this intersection: backpropagation, normalizing flows, and attention, with mutual benefits for both fields.
connections between predictive coding and VAEs + new frontiers