network to compose the features learned by lower layers into more complex features in higher layers. This is evidenced below by the improvement in accuracy of the random local classifiers in deeper layers. Training with local errors thus retains the hierarchical composition of features, one of the key strengths of deep networks.

To implement weight updates based on backpropagation in a biologically inspired network, the pre- or post-synaptic neurons need to buffer the past activity of the pre-synaptic neurons and reproduce this past activity in sync with the corresponding errors arriving from top layers in order to update the weights. This is incompatible with biologically motivated synaptic weight update rules that are typically triggered by pre-synaptic events and depend on the relative timing of pre- and post-synaptic spikes and/or state variables in the post-synaptic neuron. Our learning mechanism bypasses biological implausibility arguments against standard backpropagation by generating errors locally in each layer using fixed random projections. Weight updates could thus be carried out while the synaptic currents in post-synaptic neurons (the neurons receiving the local error signal) still retain a memory of recent pre-synaptic activity. Weight symmetry in the forward and backward passes in standard backpropagation learning is another biologically 