  In recent years, there has been an intense debate about how learning in
biological neural networks (BNNs) differs from learning in artificial neural
networks. It is often argued that the updating of connections in the brain
relies only on local information, and therefore a stochastic gradient-descent
type optimization method cannot be used. In this paper, we study a stochastic
model for supervised learning in BNNs. We show that a (continuous) gradient
step occurs approximately when each learning opportunity is processed by many
local updates. This result suggests that stochastic gradient descent may indeed
play a role in optimizing BNNs.
