Conservativeness of untied auto-encoders
This work addresses theoretical conditions for auto-encoders in machine learning, but it appears incremental as it builds on existing concepts of conservativeness and training methods.
The paper tackles the problem of determining when auto-encoders define conservative vector fields, which relate to energy functions for data probability, and shows that contractive training criteria like denoising enforce these conditions locally, enabling extraction of conservative components from vector fields.
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.