Stochastic gradient descent with backpropagation is the workhorse of
artificial neural networks. It has long been recognized that backpropagation
fails to be a biologically plausible algorithm. Fundamentally, it is a
non-local procedure -- updating one neuron's synaptic weights requires
knowledge of synaptic weights or receptive fields of downstream neurons. This
limits the use of artificial neural networks as a tool for understanding the
biological principles of information processing in the brain. Lillicrap et al.
(2016) propose a more biologically plausible "feedback alignment" algorithm
that uses random and fixed backpropagation weights, and show promising
simulations. In this paper we study the mathematical properties of the feedback
alignment procedure by analyzing convergence and alignment for two-layer
networks under squared error loss. In the overparameterized setting, we prove
that the error converges to zero exponentially fast, and also that
regularization is necessary in order for the parameters to become aligned with
the random backpropagation weights. Simulations are given that are consistent
with this analysis and suggest further generalizations. These results
contribute to our understanding of how biologically plausible algorithms might
carry out weight learning in a manner different from Hebbian learning, with
performance that is comparable with the full non-local backpropagation
algorithm.

该论文研究 “反馈对齐” 算法的数学特性，通过分析二层网络在平方误差损失下的收敛和对齐，证明在过度参数化的情况下，误差会以指数速度收敛，以及参数对齐需要正则化。该成果对我们理解生物学可行的算法如何不同于 Hebbian 学习方法，具有与非本地反向传播算法相当的性能提供了方法。