  This paper reviews predictive coding, from theoretical neuroscience, and
variational autoencoders, from machine learning, identifying the common origin
and mathematical framework underlying both areas. As each area is prominent
within its respective field, more firmly connecting these areas could prove
useful in the dialogue between neuroscience and machine learning. After
reviewing each area, we discuss two possible correspondences implied by this
perspective: cortical pyramidal dendrites as analogous to (non-linear) deep
networks and lateral inhibition as analogous to normalizing flows. These
connections may provide new directions for further investigations in each
field.
