  The success of deep learning, a brain-inspired form of AI, has sparked
interest in understanding how the brain could similarly learn across multiple
layers of neurons. However, the majority of biologically-plausible learning
algorithms have not yet reached the performance of backpropagation (BP), nor
are they built on strong theoretical foundations. Here, we analyze target
propagation (TP), a popular but not yet fully understood alternative to BP,
from the standpoint of mathematical optimization. Our theory shows that TP is
closely related to Gauss-Newton optimization and thus substantially differs
from BP. Furthermore, our analysis reveals a fundamental limitation of
difference target propagation (DTP), a well-known variant of TP, in the
realistic scenario of non-invertible neural networks. We provide a first
solution to this problem through a novel reconstruction loss that improves
feedback weight training, while simultaneously introducing architectural
flexibility by allowing for direct feedback connections from the output to each
hidden layer. Our theory is corroborated by experimental results that show
significant improvements in performance and in the alignment of forward weight
updates with loss gradients, compared to DTP.
