A Note on Some Numerical Approaches to Solve aθ˙Neuron Networks Model

Space time integration plays an important role in analyzing scientific and engineering models. In this paper, we consider an integrodifferential equation that comes from modelingθ˙neuron networks. Here, we investigate various schemes for time discretization of a theta-neuron model. We use collocation and midpoint quadrature formula for space integration and then apply various time integration schemes to get a full discrete system. We present some computational results to demonstrate the schemes.

Spike-Timing Error Backpropagation in Theta Neuron Networks

The main contribution of this letter is the derivation of a steepest gradient descent learning rule for a multilayer network of theta neurons, a one-dimensional nonlinear neuron model. Central to our model is the assumption that the intrinsic neuron dynamics are sufficient to achieve consistent time coding, with no need to involve the precise shape of postsynaptic currents; this assumption departs from other related models such as SpikeProp and Tempotron learning. Our results clearly show that it is possible to perform complex computations by applying supervised learning techniques to the spike times and time response properties of nonlinear integrate and fire neurons. Networks trained with our multilayer training rule are shown to have similar generalization abilities for spike latency pattern classification as Tempotron learning. The rule is also able to train networks to perform complex regression tasks that neither SpikeProp or Tempotron learning appears to be capable of.