  We propose to exploit {\em reconstruction} as a layer-local training signal
for deep learning. Reconstructions can be propagated in a form of target
propagation playing a role similar to back-propagation but helping to reduce
the reliance on derivatives in order to perform credit assignment across many
levels of possibly strong non-linearities (which is difficult for
back-propagation). A regularized auto-encoder tends produce a reconstruction
that is a more likely version of its input, i.e., a small move in the direction
of higher likelihood. By generalizing gradients, target propagation may also
allow to train deep networks with discrete hidden units. If the auto-encoder
takes both a representation of input and target (or of any side information) in
input, then its reconstruction of input representation provides a target
towards a representation that is more likely, conditioned on all the side
information. A deep auto-encoder decoding path generalizes gradient propagation
in a learned way that can could thus handle not just infinitesimal changes but
larger, discrete changes, hopefully allowing credit assignment through a long
chain of non-linear operations. In addition to each layer being a good
auto-encoder, the encoder also learns to please the upper layers by
transforming the data into a space where it is easier to model by them,
flattening manifolds and disentangling factors. The motivations and theoretical
justifications for this approach are laid down in this paper, along with
conjectures that will have to be verified either mathematically or
experimentally, including a hypothesis stating that such auto-encoder mediated
target propagation could play in brains the role of credit assignment through
many non-linear, noisy and discrete transformations.
