  Learning depends on changes in synaptic connections deep inside the brain. In
multilayer networks, these changes are triggered by error signals fed back from
the output, generally through a stepwise inversion of the feedforward
processing steps. The gold standard for this process -- backpropagation --
works well in artificial neural networks, but is biologically implausible.
Several recent proposals have emerged to address this problem, but many of
these biologically-plausible schemes are based on learning an independent set
of feedback connections. This complicates the assignment of errors to each
synapse by making it dependent upon a second learning problem, and by fitting
inversions rather than guaranteeing them. Here, we show that feedforward
network transformations can be effectively inverted through dynamics. We derive
this dynamic inversion from the perspective of feedback control, where the
forward transformation is reused and dynamically interacts with fixed or random
feedback to propagate error signals during the backward pass. Importantly, this
scheme does not rely upon a second learning problem for feedback because
accurate inversion is guaranteed through the network dynamics. We map these
dynamics onto generic feedforward networks, and show that the resulting
algorithm performs well on several supervised and unsupervised datasets.
Finally, we discuss potential links between dynamic inversion and second-order
optimization. Overall, our work introduces an alternative perspective on credit
assignment in the brain, and proposes a special role for temporal dynamics and
feedback control during learning.
