  The recent discovered spatial-temporal information processing capability of
bio-inspired Spiking neural networks (SNN) has enabled some interesting models
and applications. However designing large-scale and high-performance model is
yet a challenge due to the lack of robust training algorithms. A bio-plausible
SNN model with spatial-temporal property is a complex dynamic system. Each
synapse and neuron behave as filters capable of preserving temporal
information. As such neuron dynamics and filter effects are ignored in existing
training algorithms, the SNN downgrades into a memoryless system and loses the
ability of temporal signal processing. Furthermore, spike timing plays an
important role in information representation, but conventional rate-based spike
coding models only consider spike trains statistically, and discard information
carried by its temporal structures. To address the above issues, and exploit
the temporal dynamics of SNNs, we formulate SNN as a network of infinite
impulse response (IIR) filters with neuron nonlinearity. We proposed a training
algorithm that is capable to learn spatial-temporal patterns by searching for
the optimal synapse filter kernels and weights. The proposed model and training
algorithm are applied to construct associative memories and classifiers for
synthetic and public datasets including MNIST, NMNIST, DVS 128 etc.; and their
accuracy outperforms state-of-art approaches.
