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Here, we show that a deep learning algorithm that utilizes multi-compartment neurons might help us to understand how the brain optimizes cost functions. Like neocortical pyramidal neurons, neurons in our model receive sensory information and higher-order feedback in electrotonically segregated compartments. Thanks to this segregation, the neurons in different layers of the network can coordinate synaptic weight updates. As a result, the network can learn to categorize images better than a single layer network. Furthermore, we show that our algorithm takes advantage of multilayer architectures to identify useful representations---the hallmark of deep learning. 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