  Motivated by the celebrated discrete-time model of nervous activity outlined
by McCulloch and Pitts in 1943, we propose a novel continuous-time model, the
McCulloch-Pitts network (MPN), for sequence learning in spiking neural
networks. Our model has a local learning rule, such that the synaptic weight
updates depend only on the information directly accessible by the synapse. By
exploiting asymmetry in the connections between binary neurons, we show that
MPN can be trained to robustly memorize multiple spatiotemporal patterns of
binary vectors, generalizing the ability of the symmetric Hopfield network to
memorize static spatial patterns. In addition, we demonstrate that the model
can efficiently learn sequences of binary pictures as well as generative models
for experimental neural spike-train data. Our learning rule is consistent with
spike-timing-dependent plasticity (STDP), thus providing a theoretical ground
for the systematic design of biologically inspired networks with large and
robust long-range sequence storage capacity.
