  Recent breakthroughs in neuromorphic computing show that local forms of
gradient descent learning are compatible with Spiking Neural Networks (SNNs)
and synaptic plasticity. Although SNNs can be scalably implemented using
neuromorphic VLSI, an architecture that can learn using gradient-descent in
situ is still missing. In this paper, we propose a local, gradient-based,
error-triggered learning algorithm with online ternary weight updates. The
proposed algorithm enables online training of multi-layer SNNs with memristive
neuromorphic hardware showing a small loss in the performance compared with the
state of the art. We also propose a hardware architecture based on memristive
crossbar arrays to perform the required vector-matrix multiplications. The
necessary peripheral circuitry including pre-synaptic, post-synaptic and write
circuits required for online training, have been designed in the sub-threshold
regime for power saving with a standard 180 nm CMOS process.
