  Traditional backpropagation of error, though a highly successful algorithm
for learning in artificial neural network models, includes features which are
biologically implausible for learning in real neural circuits. An alternative
called target propagation proposes to solve this implausibility by using a
top-down model of neural activity to convert an error at the output of a neural
network into layer-wise and plausible 'targets' for every unit. These targets
can then be used to produce weight updates for network training. However, thus
far, target propagation has been heuristically proposed without demonstrable
equivalence to backpropagation. Here, we derive an exact correspondence between
backpropagation and a modified form of target propagation (GAIT-prop) where the
target is a small perturbation of the forward pass. Specifically,
backpropagation and GAIT-prop give identical updates when synaptic weight
matrices are orthogonal. In a series of simple computer vision experiments, we
show near-identical performance between backpropagation and GAIT-prop with a
soft orthogonality-inducing regularizer.
