Conservativeness of untied auto-encoders

Daniel Jiwoong Im, Mohamed Ishmael Belghazi, Roland Memisevic

Abstract:

We discuss necessary and sufficient conditions for an
auto-encoder to define a conservative vector field, in
which case it is associated with an energy function akin
to the unnormalized log-probability of the data. We
show that the conditions for conservativeness are more
general than for encoder and decoder weights to be the
same (“tied weights”), and that they also depend on the
form of the hidden unit activation function, but that contractive training criteria, such as denoising, will enforce
these conditions locally. Based on these observations,
we show how we can use auto-encoders to extract the
conservative component of a vector field.