  Spintronic devices are considered as promising candidates in implementing
neuromorphic systems or hardware neural networks, which are expected to perform
better than other existing computing systems for certain data classification
and regression tasks. In this paper, we have designed a feedforward Fully
Connected Neural Network (FCNN) with no hidden layer using spin orbit torque
driven domain wall devices as synapses and transistor based analog circuits as
neurons. A feedback circuit is also designed using transistors, which at every
iteration computes the change in weights of the synapses needed to train the
network using Stochastic Gradient Descent (SGD) method. Subsequently it sends
write current pulses to the domain wall based synaptic devices which move the
domain walls and updates the weights of the synapses. Through a combination of
micromagnetic simulations, analog circuit simulations and numerically solving
FCNN training equations, we demonstrate "on-chip" training of the designed FCNN
on the MNIST database of handwritten digits in this paper. We report the
training and test accuracies, energy consumed in the synaptic devices for the
training and possible issues with hardware implementation of FCNN that can
limit its test accuracy.
