  We present a fully memristive spiking neural network (MSNN) consisting of
novel memristive neurons trained using the backpropagation through time (BPTT)
learning rule. Gradient descent is applied directly to the memristive
integrated-and-fire (MIF) neuron designed using analog SPICE circuit models,
which generates distinct depolarization, hyperpolarization, and repolarization
voltage waveforms. Synaptic weights are trained by BPTT using the membrane
potential of the MIF neuron model and can be processed on memristive crossbars.
The natural spiking dynamics of the MIF neuron model are fully differentiable,
eliminating the need for gradient approximations that are prevalent in the
spiking neural network literature. Despite the added complexity of training
directly on SPICE circuit models, we achieve 97.58% accuracy on the MNIST
testing dataset and 75.26% on the Fashion-MNIST testing dataset, the highest
accuracies among all fully MSNNs.
