by layer through the random feedback connections, the networks in [@Nokland_etal16; @Neftci_etal17a] directly use a fixed random projection of the top layer error as the error signal in deep layers. Although this permits a single global error signal communicated in common to all layers, is still incurs substantial wait times and memory requirements for the weight updates as a forward pass through the entire network has to be completed before the error signal is available, which requires deep layers to hold their states for the duration of the full forward pass.

We propose a learning approach where weights in any given layer are trained based on local errors that are generated solely based on neural state variables in that layer. These errors are generated directly from the training labels using a classifier with fixed random weights and no hidden layers, and whose input is the neural activations in the layer being trained. Instead of minimizing a global objective function, training thus minimizes many local objective functions. As such this approach compromises one of the core tenets of standard backpropagation: the adjustment of all parameters in concert to minimize a unified objective. Nevertheless, training with local errors still allows a deep 