unrealistic aspect. In our case, the weight symmetry requirement arises in the one-step error backpropagation from the output of the local random classifier to the neurons in the layer being trained. Similar to ref. [@Lillicrap_etal16], we experimented with relaxing this symmetry requirement by using a different set of random, fixed weights to map the classifier error to the error at the layer being trained. We analyze the implications of the proposed learning approach for the design of custom hardware devices for learning the parameters of deep networks. In the proposed learning approach, there is no explicit backward pass as errors are locally generated and can be used to directly update the weights. We show that our approach drastically reduces memory traffic compared to standard backpropagation in the typical situation when the network weights and activations can not all fit into the compute device memory. We achieve this reduction even despite an increased number of parameters in the network due to the addition of the random local classifier weights in each layer. These weights, however, are fixed allowing them to be generated on the fly using pseudo-random number generators (PRNGs). Only the negligibly small random seeds of the PRNGs for each 