That said, I have come across them before. Architecturally they are similar to any other neural network except that each individual neuron's complexity is higher like with product unit neural networks - which, by the way, I quite like. This added complexity makes spiking neural networks "more similar" to biological neural networks in the sense that neuron activation is not a continuous process, it is discontinuous. Which is actually how I came across them originally :-): I was researching applications for jump diffusion stochastic processes one of which is modelling the firing rate of neurons in spiking neural networks. But like I said, I haven't worked with them or studied them explicitly and I am not one hundred perfect sure of their use cases.
Training the weights in a neural network can be modeled as a non-linear global optimization problem. A target function can be formed to evaluate the fitness or error of a particular weight vector as follows: First, the weights in the network are set according to the weight vector. Next, the network is evaluated against the training sequence. Typically, the sum-squared-difference between the predictions and the target values specified in the training sequence is used to represent the error of the current weight vector. Arbitrary global optimization techniques may then be used to minimize this target function.
Time delayed connections are connections between neurons (often from the same layer, and even connected with themselves) that don’t get information from the previous layer, but from a layer from the past (previous iteration, mostly). This allows temporal (time, sequence or order) related information to be stored. These types of connections are often manually reset from time to time, to clear the “state” of the network. The key difference with regular connections is that these connections are continuously changing, even when the network isn’t being trained.