uniform, zero-mean, distribution whose max/min values depend on the number of neurons in the source and target layers according to the scheme in [@Glorot_Bengio10].

We compare our approach to the feedback alignment training method [@Lillicrap_etal16] in which random fixed weights are used to backpropagate the error layer-by-layer from the top layer. The layer’s activation derivative is still used when backpropagating errors. In the presence of max-pooling layers, errors only backpropagate through the winner(max) neuron in each pooling window. When using feedback alignment training in the presence of dropout, a neuron that is dropped during the forward pass is also dropped during the backward pass. When using convolutional layers, we use fixed random filters that we convolve with the errors of one convolutional layer to yield the errors at the outputs of the previous/lower convolutional layer. We also use batch normalization when training using feedback alignment. The extra scaling parameters introduced by batch normalization are trained using the randomly backpropagated errors arriving at the batch-normalized layer’s output.

All experiments in this paper were carried out using Theano [@Bastien_etal12; @Bergstra_etal10], and all parameters were optimized using ADAM [@Kingma_Ba14].

Hardware Implications of Learning Using Local Errors {#sec:hw}
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[0.62]{} ![Memory traffic and number 