Before revision:  Thus, we systematically analyze the LIF neuron. We start by deriving simple integration equations to which even a gradient can be assigned. Additionally, we prove that a Long-Short-Term-Memory unit can be tuned to show similar spiking properties. Additionally, LIF units are applied to an image classification task, trained with backpropagation .
After revision:  Thus, we derived simple update-rules for the LIF units from the differential equations, which are easy to numerically integrate. We apply a novel approach to train the LIF units supervisedly via backpropagation, by assigning a constant value to the derivative of the neuron activation function exclusively for the backpropagation step. This simple mathematical trick helps to distribute the error between the neurons of the pre-connected layer. We apply our method to the IRIS blossoms image data set and show that the training technique can be used to train LIF neurons on image classification tasks. Furthermore, we show how to integrate our method in the KERAS (tensorflow) framework and efficiently run it on GPUs. To generate a deeper understanding of the mechanisms during training we developed interactive illustrations, which we provide online .