SVHN datasets, approaching the performance of standard backpropagation. Our approach highlights a potential biological mechanism for the supervised, or task-dependent, learning of feature hierarchies. In addition, we show that it is well suited for learning deep networks in custom hardware where it can drastically reduce memory traffic and data communication overheads.

Introduction
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Gradient descent training techniques [@Bottou91] have been remarkably successful in training a broad range of network architectures. This success is often attributed to the use of deep architectures with many non-linearity stages [@Ba_Caruna14] where backpropagation is used to calculate the direction of weight updates in deep layers. In convolutional networks in particular, multiple cascaded convolutional layers allow simple, lower-level, features to be successively composed into more complex features, allowing networks to obtain highly complex and relevant features from the top convolutional layers [@Razavian_etal14]. Deep convolutional neural networks trained using backpropagation are thus achieving record performance in a variety of large-scale machine vision tasks [@Krizhevsky_etal12; @Simonyan_Zisserman14; @LeCun_etal15; @He_etal16; @Zagoruyko_Komodakis16; @Huang_etal16]. For deep convolutional networks trained in a supervised setting, the training objective is typically the minimization of classification error at the top network layer. This objective is sometimes augmented by auxiliary objectives defined using the outputs of intermediate 