  The state-of-the art machine learning approach to training deep neural
networks, backpropagation, is implausible for real neural networks: neurons
need to know their outgoing weights; training alternates between a bottom-up
forward pass (computation) and a top-down backward pass (learning); and the
algorithm often needs precise labels of many data points. Biologically
plausible approximations to backpropagation, such as feedback alignment, solve
the weight transport problem, but not the other two. Thus, fully biologically
plausible learning rules have so far remained elusive. Here we present a family
of learning rules that does not suffer from any of these problems. It is
motivated by the information bottleneck principle (extended with kernel
methods), in which networks learn to compress the input as much as possible
without sacrificing prediction of the output. The resulting rules have a
3-factor Hebbian structure: they require pre- and post-synaptic firing rates
and an error signal - the third factor - consisting of a global teaching signal
and a layer-specific term, both available without a top-down pass. They do not
require precise labels; instead, they rely on the similarity between pairs of
desired outputs. Moreover, to obtain good performance on hard problems and
retain biological plausibility, our rules need divisive normalization - a known
feature of biological networks. Finally, simulations show that our rules
perform nearly as well as backpropagation on image classification tasks.
